On Neutrino Masses and Mixings from Extra Dimensions

First District Association, based in Litchfield, Minnesota, U.S., produces a wide variety of cheeses. Quality is of the utmost importance for First District and, when the time came to renovate and remodel their testing labs, they chose the leader in quality instrumentation – METTLER TOLEDO.Upholding High StandardsFirst District Association is an independent dairy cooperative that maximizes returns for its pro-ducers and employees through innovation and providing progressive quality products to a glob-al market. They play a prominent role in the dairy industry and have a very distinct and proud history which has influenced the birth and formation of modern dairy cooperatives.First District produces a wide variety of cheese for use in all types of applications. They pro-duce 500 lb barrels and 40 lb blocks as well as whey protein concentrate (WPC) and lactose. Cheese produced by First District is used in processed cheese products, shredded cheese, and First District AssociationMoisture testing Ash testingQuality Cheese Guaranteed by Top-Quality Instruments Laboratory Case StudyFood & BeverageXP BalanceMettler-Toledo AGLaboratory DivisionIm LangacherCH-8606 Greifensee, Switzerland Subject to technical changes.© Mettler-Toledo AG 07/11Printed in SwitzerlandGlobal MarCom Switzerland cheese sauces and powders. The new testing labs required updated equipment to help speed up produc-tion. First District was also interested in a way to move from manual result transcription to an electronic format. Reliable Moisture & Ash Control First District prides itself on product quality. Each batch of WPC and lactose is lab-tested and must fall into a specific range of moisture and ash in order to meet the es-tablished standard. The moisture testing process begins by taking a small sample from each batch and weighing it. The sample is then dried out in an oven and weighed again. Determining the weight dif-ference in the sample before and after the drying process provides a simple calculation for the amount of moisture present. The ash testingprocess measures the amount of ash remaining in the sample after heating it in a muffle furnace. The remaining ash is weighed to ensure it falls within a standard range. First District chose the Excellence Plus (XP) series of analytical balances for both of these tests. They chose the XP for its speed and for the flex-ibility of the grid-style weighing pan for easy cleaning.Correct pH Level Ensures Quality First District also tests the pH levels of each batch of cheese. They grind the cheese samples and pack them into sample cups. During pH testing, a combination electrode is inserted into the cheese. The S40 pH meter then automatically reads the data and prepares it for output. Determin-ing the correct pH level ensures the quality of flavor, body and texture of each batch of cheese. To complete the package, First Dis-trict purchased METTLER TOLEDO’s LabX Direct pH and Balance soft-ware. This software suite will be connected through a LIMS system as the remaining lab renovations are completed. LabX software eliminates the need to manually note each quality test and the connection to the LIMS system will send the results directly into a host computer which reduces the likelihood of transcrip-tion errors. First District now has an up-to-date solution for their quality assurance testing. Production is moving faster and the new equipment ensures the quality and taste of each batch of cheese produced. The addition of the LIMS system and software will further enhance and streamline the lab completing the entire testing package. /xp-analytical /pHlab/LabX Office building of First District Association.S40 pH Meter.。

a r X i v :0803.2889v 2 [h e p -p h ] 14 J u l 2008Mapping Out SU (5)GUTs with Non-Abelian Discrete Flavor SymmetriesFlorian Plentinger ∗and Gerhart Seidl †Institut f¨u r Physik und Astrophysik,Universit¨a t W¨u rzburg,Am Hubland,D 97074W¨u rzburg,Germany(Dated:December 25,2013)We construct a class of supersymmetric SU (5)GUT models that produce nearly tribimaximal lepton mixing,the observed quark mixing matrix,and the quark and lepton masses,from discrete non-Abelian flavor symmetries.The SU (5)GUTs are formulated on five-dimensional throats in the flat limit and the neutrino masses become small due to the type-I seesaw mechanism.The discrete non-Abelian flavor symmetries are given by semi-direct products of cyclic groups that are broken at the infrared branes at the tip of the throats.As a result,we obtain SU (5)GUTs that provide a combined description of non-Abelian flavor symmetries and quark-lepton complementarity.PACS numbers:12.15.Ff,11.30.Hv,12.10.Dm,One possibility to explore the physics of grand unified theories (GUTs)[1,2]at low energies is to analyze the neutrino sector.This is due to the explanation of small neutrino masses via the seesaw mechanism [3,4],which is naturally incorporated in GUTs.In fact,from the perspective of quark-lepton unification,it is interesting to study in GUTs the drastic differences between the masses and mixings of quarks and leptons as revealed by current neutrino oscillation data.In recent years,there have been many attempts to re-produce a tribimaximal mixing form [5]for the leptonic Pontecorvo-Maki-Nakagawa-Sakata (PMNS)[6]mixing matrix U PMNS using non-Abelian discrete flavor symme-tries such as the tetrahedral [7]and double (or binary)tetrahedral [8]groupA 4≃Z 3⋉(Z 2×Z 2)and T ′≃Z 2⋉Q,(1)where Q is the quaternion group of order eight,or [9]∆(27)≃Z 3⋉(Z 3×Z 3),(2)which is a subgroup of SU (3)(for reviews see, e.g.,Ref.[10]).Existing models,however,have generally dif-ficulties to predict also the observed fermion mass hierar-chies as well as the Cabibbo-Kobayashi-Maskawa (CKM)quark mixing matrix V CKM [11],which applies especially to GUTs (for very recent examples,see Ref.[12]).An-other approach,on the other hand,is offered by the idea of quark-lepton complementarity (QLC),where the so-lar neutrino angle is a combination of maximal mixing and the Cabibbo angle θC [13].Subsequently,this has,in an interpretation of QLC [14,15],led to a machine-aided survey of several thousand lepton flavor models for nearly tribimaximal lepton mixing [16].Here,we investigate the embedding of the models found in Ref.[16]into five-dimensional (5D)supersym-metric (SUSY)SU (5)GUTs.The hierarchical pattern of quark and lepton masses,V CKM ,and nearly tribi-maximal lepton mixing,arise from the local breaking of non-Abelian discrete flavor symmetries in the extra-dimensional geometry.This has the advantage that theFIG.1:SUSY SU (5)GUT on two 5D intervals or throats.The zero modes of the matter fields 10i ,5H,24H ,and the gauge supermul-tiplet,propagate freely in the two throats.scalar sector of these models is extremely simple without the need for a vacuum alignment mechanism,while of-fering an intuitive geometrical interpretation of the non-Abelian flavor symmetries.As a consequence,we obtain,for the first time,a realization of non-Abelian flavor sym-metries and QLC in SU (5)GUTs.We will describe our models by considering a specific minimal realization as an example.The main features of this example model,however,should be viewed as generic and representative for a large class of possible realiza-tions.Our model is given by a SUSY SU (5)GUT in 5D flat space,which is defined on two 5D intervals that have been glued together at a common endpoint.The geom-etry and the location of the 5D hypermultiplets in the model is depicted in FIG.1.The two intervals consti-tute a simple example for a two-throat setup in the flat limit (see,e.g.,Refs.[17,18]),where the two 5D inter-vals,or throats,have the lengths πR 1and πR 2,and the coordinates y 1∈[0,πR 1]and y 2∈[0,πR 2].The point at y 1=y 2=0is called ultraviolet (UV)brane,whereas the two endpoints at y 1=πR 1and y 2=πR 2will be referred to as infrared (IR)branes.The throats are supposed to be GUT-scale sized,i.e.1/R 1,2 M GUT ≃1016GeV,and the SU (5)gauge supermultiplet and the Higgs hy-permultiplets 5H and2neously broken to G SM by a 24H bulk Higgs hypermulti-plet propagating in the two throats that acquires a vac-uum expectation value pointing in the hypercharge direc-tion 24H ∝diag(−12,13,15i ,where i =1,2,3is the generation index.Toobtainsmall neutrino masses via the type-I seesaw mechanism [3],we introduce three right-handed SU (5)singlet neutrino superfields 1i .The 5D Lagrangian for the Yukawa couplings of the zero mode fermions then readsL 5D =d 2θ δ(y 1−πR 1) ˜Y uij,R 110i 10j 5H +˜Y d ij,R 110i 5H +˜Y νij,R 15j5i 1j 5H +M R ˜Y R ij,R 21i 1j+h.c. ,(3)where ˜Y x ij,R 1and ˜Y x ij,R 2(x =u,d,ν,R )are Yukawa cou-pling matrices (with mass dimension −1/2)and M R ≃1014GeV is the B −L breaking scale.In the four-dimensional (4D)low energy effective theory,L 5D gives rise to the 4D Yukawa couplingsL 4D =d 2θ Y u ij 10i 10j 5H +Y dij10i 5H +Y νij5i ∼(q i 1,q i 2,...,q i m ),(5)1i ∼(r i 1,r i 2,...,r im ),where the j th entry in each row vector denotes the Z n jcharge of the representation.In the 5D theory,we sup-pose that the group G A is spontaneously broken by singly charged flavon fields located at the IR branes.The Yukawa coupling matrices of quarks and leptons are then generated by the Froggatt-Nielsen mechanism [21].Applying a straightforward generalization of the flavor group space scan in Ref.[16]to the SU (5)×G A represen-tations in Eq.(5),we find a large number of about 4×102flavor models that produce the hierarchies of quark and lepton masses and yield the CKM and PMNS mixing angles in perfect agreement with current data.A distri-bution of these models as a function of the group G A for increasing group order is shown in FIG.2.The selection criteria for the flavor models are as follows:First,all models have to be consistent with the quark and charged3 lepton mass ratiosm u:m c:m t=ǫ6:ǫ4:1,m d:m s:m b=ǫ4:ǫ2:1,(6)m e:mµ:mτ=ǫ4:ǫ2:1,and a normal hierarchical neutrino mass spectrumm1:m2:m3=ǫ2:ǫ:1,(7)whereǫ≃θC≃0.2is of the order of the Cabibbo angle.Second,each model has to reproduce the CKM anglesV us∼ǫ,V cb∼ǫ2,V ub∼ǫ3,(8)as well as nearly tribimaximal lepton mixing at3σCLwith an extremely small reactor angle 1◦.In perform-ing the group space scan,we have restricted ourselves togroups G A with orders roughly up to 102and FIG.2shows only groups admitting more than three valid mod-els.In FIG.2,we can observe the general trend thatwith increasing group order the number of valid modelsper group generally increases too.This rough observa-tion,however,is modified by a large“periodic”fluctu-ation of the number of models,which possibly singlesout certain groups G A as particularly interesting.Thehighly populated groups would deserve further system-atic investigation,which is,however,beyond the scopeof this paper.From this large set of models,let us choose the groupG A=Z3×Z8×Z9and,in the notation of Eq.(5),thecharge assignment101∼(1,1,6),102∼(0,3,1),103∼(0,0,0),52∼(0,7,0),52↔4FIG.3:Effect of the non-Abelian flavor symmetry on θ23for a 10%variation of all Yukawa couplings.Shown is θ23as a function of ǫfor the flavor group G A (left)and G A ⋉G B (right).The right plot illustrates the exact prediction of the zeroth order term π/4in the expansion θ23=π/4+ǫ/√2and the relation θ13≃ǫ2.The important point is that in the expression for θ23,the leading order term π/4is exactly predicted by thenon-Abelian flavor symmetry G F =G A ⋉G B (see FIG.3),while θ13≃θ2C is extremely small due to a suppression by the square of the Cabibbo angle.We thus predict a devi-ation ∼ǫ/√2,which is the well-known QLC relation for the solar angle.There have been attempts in the literature to reproduce QLC in quark-lepton unified models [26],however,the model presented here is the first realization of QLC in an SU (5)GUT.Although our analysis has been carried out for the CP conserving case,a simple numerical study shows that CP violating phases (cf.Ref.[27])relevant for neutri-noless double beta decay and leptogenesis can be easily included as well.Concerning proton decay,note that since SU (5)is bro-ken by a bulk Higgs field,the broken gauge boson masses are ≃M GUT .Therefore,all fermion zero modes can be localized at the IR branes of the throats without intro-ducing rapid proton decay through d =6operators.To achieve doublet-triplet splitting and suppress d =5pro-ton decay,we may then,e.g.,resort to suitable extensions of the Higgs sector [28].Moreover,although the flavor symmetry G F is global,quantum gravity effects might require G F to be gauged [29].Anomalies can then be canceled by Chern-Simons terms in the 5D bulk.We emphasize that the above discussion is focussed on a specific minimal example realization of the model.Many SU (5)GUTs with non-Abelian flavor symmetries,however,can be constructed along the same lines by varying the flavor charge assignment,choosing different groups G F ,or by modifying the throat geometry.A de-tailed analysis of these models and variations thereof will be presented in a future publication [30].To summarize,we have discussed the construction of 5D SUSY SU (5)GUTs that yield nearly tribimaximal lepton mixing,as well as the observed CKM mixing matrix,together with the hierarchy of quark and lepton masses.Small neutrino masses are generated only by the type-I seesaw mechanism.The fermion masses and mixings arise from the local breaking of non-Abelian flavor symmetries at the IR branes of a flat multi-throat geometry.For an example realization,we have shown that the non-Abelian flavor symmetries can exactly predict the leading order term π/4in the sum rule for the atmospheric mixing angle,while strongly suppress-ing the reactor angle.This makes this class of models testable in future neutrino oscillation experiments.In addition,we arrive,for the first time,at a combined description of QLC and non-Abelian flavor symmetries in SU (5)GUTs.One main advantage of our setup with throats is that the necessary symmetry breaking can be realized with a very simple Higgs sector and that it can be applied to and generalized for a large class of unified models.We would like to thank T.Ohl for useful comments.The research of F.P.is supported by Research Train-ing Group 1147“Theoretical Astrophysics and Particle Physics ”of Deutsche Forschungsgemeinschaft.G.S.is supported by the Federal Ministry of Education and Re-search (BMBF)under contract number 05HT6WWA.∗********************************.de †**************************.de[1]H.Georgi and S.L.Glashow,Phys.Rev.Lett.32,438(1974);H.Georgi,in Proceedings of Coral Gables 1975,Theories and Experiments in High Energy Physics ,New York,1975.[2]J.C.Pati and A.Salam,Phys.Rev.D 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贵阳市2024年高三年级适应性考试（二）英语2024年5月本试卷共10页。

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1. What are the speakers doing?A. Putting out a fire.B. Trying to create smoke.C. Conducting an experiment.2. What does the woman complain about?A. The poor movie set.B. The interruption to the movie.C. The delay of a football match.3. What caused the man's mouth to burn?A. Hot peppers.B. Alcohol.C. Fruit and nuts.4. Why does the man put thin plastic with his regular rubbish?A. It's harmless.B. It's wrongly classified.C. It's unable to be recycled.5. What will the score be if two balloons are hit?A. 5 points.B. 6 points.C. 16 points.第二节（共15小题；每小题1. 5分，满分22. 5分）听下面5段对话或独白。

a r X i v :a s t r o -p h /0208563v 1 30 A u g 2002Proceedings of the 270.WE-Heraeus Seminar on:“Neutron Stars,Pulsars and Supernova Remnants”Physikzentrum Bad Honnef,Germany,Jan.21-25,2002,eds.W.Becker,H.Lesch &J.Tr¨u mper,MPE Report 278,pp.300-302Neutron Stars,Pulsars and Supernova Remnants:concluding remarksF.Pacini 1,21Arcetri Astrophysical Observatory,L.go E.Fermi,5,I-50125Firenze,Italy2Dept.of Astronomy and Space Science,University of Florence,L.go E.Fermi,2,I-50125Firenze,Italy1.IntroductionMore than 30years have elapsed since the discovery of pul-sars (Hewish et al.1968)and the realization that they are connected with rotating magnetized neutron stars (Gold 1968;Pacini 1967,1968).It became soon clear that these objects are responsible for the production of the relativis-tic wind observed in some Supernovae remnants such as the Crab Nebula.For many years,the study of pulsars has been car-ried out mostly in the radio band.However,many recent results have come from observations at much higher fre-quencies (optical,X-rays,gamma rays).These observa-tions have been decisive in order to establish a realistic demography and have brought a better understanding of the relationship between neutron stars and SN remnants.The Proceedings of this Conference cover many aspects of this relationship (see also previous Conference Proceed-ings such as Bandiera et al.1998;Slane and Gaensler,2002).Because of this reason,my summary will not re-view all the very interesting results which have been pre-sented here and I shall address briefly just a few issues.The choice of these issues is largely personal:other col-leagues may have made a different selection.2.Demography of Neutron Stars:the role of the magnetic field For a long time it has been believed that only Crab-like remnants (plerions)contain a neutron star and that the typical field strength of neutron stars is 1012Gauss.The basis of this belief was the lack of pulsars associated with shell-type remnants or other manifestations of a relativis-tic wind.The justification given is that some SN explo-sions may blow apart the entire star.Alternatively,the central object may become a black hole.However,the number of shell remnants greatly exceeds that of pleri-ons:it becomes then difficult to invoke the formation of black holes,an event much more rare than the formation of neutron stars.The suggestion that shell remnants such as Cas A could be associated with neutron stars which have rapidly lost their initial rotational energy because of an ultra-strong magnetic field B ∼1014−1015Gauss (Cavaliere &Pacini,1970)did receive little attention.The observa-tional situation has now changed:a compact thermal X-ray source has been discovered close to the center of Cas A (Tananbaum,1999)and it could be the predicted ob-ject.Similar sources have been found in association with other remnants and are likely to be neutron stars.We have also heard during this Conference that some shell-type remnants (including Cas A)show evidence for a weak non-thermal X-ray emission superimposed on the thermal one:this may indicate the presence of a residual relativis-tic wind produced in the center.Another important result has been the discovery of neutron stars with ultra-strong magnetic fields,up to 1014−1015G.In this case the total magnetic energy could be larger than the rotational en-ergy (”magnetars”).This possibility had been suggested long time ago (Woltjer,1968).It should be noticed,how-ever,that the slowing down rate determines the strength of the field at the speed of light cylinder and that the usually quoted surface fields assume a dipolar geometry corresponding to a braking index n =3.Unfortunately the value of n has been measured only in a few cases and it ranges between 1.4−2.8(Lyne et al.,1996).The present evidence indicates that neutron stars man-ifest themselves in different ways:–Classical radio pulsars (with or without emission at higher frequencies)where the rotation is the energy source.–Compact X-ray sources where the energy is supplied by accretion (products of the evolution in binary sys-tems).–Compact X-ray sources due to the residual thermal emission from a hot surface.–Anomalous X-ray pulsars (AXP)with long periods and ultra strong fields (up to 1015Gauss).The power emit-ted by AXPs exceeds the energy loss inferred from the slowing down rate.It is possible that AXPs are asso-ciated with magnetized white dwarfs,rotating close to the shortest possible period (5−10s)or,alternatively,they could be neutron stars whose magnetic energy is dissipated by flares.–Soft gamma-ray repeaters.2 F.Pacini:Neutron Stars,Pulsars and Supernova Remnants:concluding remarks In addition it is possible that some of the unidentifiedgamma ray sources are related to neutron stars.Thepresent picture solves some previous inconsistencies.Forinstance,the estimate for the rate of core-collapse Super-novae(roughly one every30-50years)was about a factorof two larger than the birth-rate of radio pulsars,suggest-ing already that a large fraction of neutron stars does not appear as radio pulsars.The observational evidence supports the notion of a large spread in the magnetic strength of neutron stars and the hypothesis that this spread is an important factor in determining the morphology of Supernova remnants.A very strongfield would lead to the release of the bulk of the rotational energy during a short initial period(say, days up to a few years):at later times the remnant would appear as a shell-type.A more moderatefield(say1012 Gauss or so)would entail a long lasting energy loss and produce a plerion.3.Where are the pulses emitted?Despite the great wealth of data available,there is no gen-eral consensus about the radiation mechanism for pulsars. The location of the region where the pulses are emitted is also controversial:it could be located close to the stellar surface or,alternatively,in the proximity of the speed of light cylinder.The radio emission is certainly due to a coherent pro-cess because of the very high brightness temperatures(T b up to and above1030K have been observed).A possible model invokes the motion of bunches of charges sliding along the curvedfield lines with a relativistic Lorentz fac-torγsuch that the critical frequencyνc∼c2π:Ψ∼10−2;B⊥∼104G;γ∼102−103.The model leads to the expectation of a very fast de-crease of the synchrotron intensity with period because of the combination of two factors:a)the reduced particles flux when the period increases;b)the reduced efficiency of synchrotron losses(which scale∝B2∝R−6L∝P−6)at the speed of light cylinder(Pacini,1971;Pacini&Salvati 1983,1987).The predictionfits the observed secular de-crease of the optical emission from the Crab Nebula and the magnitude of the Vela pulsar.A recent re-examination of all available optical data confirms that this model can account for the luminosity of the known optical pulsars (Shearer and Golden,2001).If so,the optical radiation supports strongly the notion that the emitting region is located close to the speed of light cylinder.4.A speculation:can the thermal radiation fromyoung neutron stars quench the relativisticwind?Myfinal remarks concern the possible effect of the ther-mal radiation coming from the neutron star surface upon the acceleration of particles.This problem has been inves-tigated for the near magnetosphere(Supper&Truemper, 2000)and it has been found that the Inverse Compton Scattering(ICS)against the thermal photons is impor-tant only in marginal cases.However,if we assume that the acceleration of the relativistic wind and the radiation of pulses occur close to the speed of light cylinder,the sit-uation becomes different and the ICS can dominate over synchrotron losses for a variety of parameters.The basic reason is that the importance of ICS at the speed of light distance R L scales like the energy density of the thermal photons uγ∝R−2L∝P−2;on the other hand, the synchrotron losses are proportional to the magnetic energy density in the same region u B∝R−6L∝P−6.Numerically,onefinds that ICS losses dominate over synchrotron losses ifT6>0.4B1/2121012G; P s is the pulsar period in seconds).The corresponding upper limit for the energy of the electrons,assuming that the acceleration takes place for a length of order of the speed of light distance and that the gains are equal to the losses is given by:E max≃1.2×103T6−4P s GeV.F.Pacini:Neutron Stars,Pulsars and Supernova Remnants:concluding remarks3Provided that the particles are accelerated and radi-ate in proximity of the speed of light cylinder distance,weconclude that the thermal photons can limit the acceler-ation of particles,especially in the case of young and hotneutron stars.It becomes tempting to speculate that thismay postpone the beginning of the pulsar activity untilthe temperature of the star is sufficiently low.The mainmanifestation of neutron stars in this phase would be aflux of high energy photons in the gamma-ray band,dueto the interaction of the quenched wind with the thermalphotons from the stellar surface.This model and its ob-servational consequences are currently under investigation(Amato,Blasi,Pacini,work in progress).ReferencesAloisio,R.,&Blasi,P.2002,Astrop.Phys.,Bandiera,R.,et al.1998,Proc.Workshop”The Relationshipbetween Neutron Stars and Supernova Remnants”,Mem.Societ Astronomica Italiana,vol.69,n.4Cavaliere,A.,&Pacini,F.1970,ApJ,159,170Gold,T.1968,Nature,217,731Hewish A.,et al.1968,Nature217,709Lyne,G.,et al.1996,Nature,381,497Pacini,F.1967,Nature,216,567Pacini,F.1968,Nature,219,145Pacini,F.1971,ApJ,163,L17Pacini,F.,&Salvati,M.1983,ApJ,274,369Pacini F.,&Salvati,M.1987,ApJ.,321,447Shearer,A.,and Golden,A.2001,ApJ,547,967Slane,P.,Gaensler,B.2002,Proc.Workshop”Neutron Starsin Supernova Remnants”ASP Conference Proceedings(inpress)Supper,R.,&Trumper,J.2000,A&A,357,301Tananbaum,B,et al.1999,IAU Circular7246Thompson,C.,Duncan,R.C.1996,ApJ,473,322Woltjer,L.1968,ApJ,152,179。

a rXiv:h ep-ph/9291v33Jan21An Explanation on Negative Mass-Square of Neutrinos Tsao Chang Center for Space Plasma and Aeronomy Research University of Alabama in Huntsville Huntsville,AL 35899Email:changt@ Guangjiong Ni Department of Physics,Fudan University Shanghai,200433,China Abstract:It has been known for many years that the measured mass-square of neutrino is probably negative.For solving this puzzle,we have further investigated the hypothesis that neutrinos are superlumi-nal fermions.A new Dirac-type equation is proposed and a tachyonic quantum theory is briefly discussed.This equation is equivalent to two Weyl equations coupled together via nonzero mass while respecting the maximum parity violation,and it reduces to one Weyl equation when the neutrino mass becomes zero.PACS number:14.60.Lm,14.60.Pq,14.60.St11.IntroductionThe square of the neutrino mass is measured in tritium beta decay experiments byfitting the shape of the beta spectrum near endpoint. In many experiments,it has been found to be negative.Most recent data are listed in”Review of Particle Physics,2000”[1]and references therein.The weighted average from two experiments reported in1999 [2-3]ism2(νe)=−2.5±3.3eV2(1) However,other nine measurements from different experiments in1991-1995are not used for averages.For instance,a value of m2(νe)=-130±20eV2with95%confidence level was measured in LLNL in1995[4].Furthermore,the pion decay experiment also obtained a negative value forµ-neutrinos[5].m2(νµ)=−0.016±0.023MeV2(2) The negative value of the neutrino mass-square simply means:E2/c2−p2=m2(νe)c2<0(3) The right-hand side in Eq.(3)can be rewritten as(-m2s c2),then m s has a positive value.Eq.(1)and(2)suggests that neutrinos might be particles faster than light,no matter how small the m s is.This possibility is further investigated in this paper.Based on special relativity and known as re-interpretation rule,su-perluminal particles were proposed by Bilaniuk et al in the Sixties[6-8]. The sign of4-D world line element,ds2,is associated with three classes of particles.For simplicity,let dy=dz=0,then>0ClassI(subluminal particles)ds2=c2dt2−dx2=0ClassII(photon)(4)<0ClassIII(superluminal particles) For Class III particles,i.e.superluminal particle,the relation of mo-mentum and energy is shown in Eq.(3).The negative value on the right-hand side of Eq.(3)for superluminal particles means that p2 is greater than(E/c)2.The velocity of a superluminal particle,u s,is2greater than the speed of light.The momentum and energy in terms of u s are as follows:p=m s u su2s/c2−1,E=m s c2u2s/c2−1(5)where the subscript s means superluminal particle,i.e.tachyon.From Eq.(5),it is easily seen that when u s is increased,both of p and E would be decreased.This property is opposite to Class I particle.Any physical reference system is built by Class I particles(atoms, molecules etc.),which requires that any reference frame must move slower than light.On the other hand,once a superluminal particle is created in an interaction,its speed is always greater than the speed of light.Neutrino is the most possible candidate for a superluminal particle because it has left-handed spin in any reference frame.On the other hand,anti-neutrino always has right-handed spin.Thefirst step in this direction is usually to introduce an imagi-nary mass,but these efforts could not reach a point for constructing a consistent quantum theory.Some early investigations of a Dirac-type equation for tachyonic fermions can be found in Ref.[9].An alterna-tive approach was investigated by Chodos et al.[10].They examined the possibility that neutrinos might be tachyonic fermions.A form of the lagrangian density for tachyonic neutrinos was proposed.Al-though they did not obtain a satisfatory quantum theory for tachyonic fermions,they suggested that more theoretical work would be needed to determine physically acceptable tachyonic theory.2.A new Dirac-type equationIn this paper,we will start with a different approach to derive a new Dirac-type equation for tachyonic neutrinos.In order to avoid introducing imaginary mass,Eq.(3)can be rewritten asE=(c2p2−m2s c4)1/2(6) where m s is called proper mass,for instance,m s(νe)=1.6eV from Eq.(1).We follow Dirac’s search[11],Hamiltonian must befirst order in momentum operatorˆp:ˆE=−c( α·ˆp)+βsm s c2(7)3with(ˆE=i¯h∂/∂t,ˆp=−i¯h∇),where α=(α1,α2,α3)andβs are4×4 matrix,which are defined asαi= 0σiσi0 ,βs= 0I−I0 (8)whereσi is2×2Pauli matrix,I is2×2unit matrix.Notice thatβs is a new matrix,which is different from the one in the traditional Dirac equation.the relation between the matrixβs and the traditional matrix βis as follows:βs=βγ5(9) whereβ= I00−I ,γ5= 0110 (9a) When we take square for both sides in Eq.(7),and consider the following relations:αiαj+αjαi=2δijαiβs+βsαi=0β2s=−1(10) the relation in Eq.(3)or Eq.(6)is reproduced.Since Eq.(6)is related to Eq.(5),this meansβs is a right choice to describe neutrinos as superluminal particles.Denote the wave function asΨ= ϕ( x,t)χ( x,t) withϕ= ϕ1ϕ2,χ= χ1χ2(11)From Eq.(7),the complete form of the new Dirac-type equation be-comesˆEΨ=−c( α·ˆp)Ψ+βsm s c2Ψ(7a) Sinceβ2s=−1in the Eq.(7a),the new Dirac-type equation is different from the traditional Dirac equation in any covariant representation in terms of theγmatrices.We now study the spin-1/2property of neutrino as a tachyonic Fermion.Eq.(7a),can be rewritten as a pair of two-component equa-tions:i¯h∂ϕ∂χi¯h+∇· j=0(14)∂tand we haveρ=ϕ†χ+χ†ϕ, j=−c(ϕ† σϕ+χ† σχ)(15) whereρand j are the probability density and current;ϕ†andχ†are the Hermitian adjoint ofϕandχrespectively.Eq.(15)can be rewritten asρ=Ψ†γ5Ψ, j=c(Ψ†γ5 αΨ)(15a) It is easy to see that the probability densityρis positive definite when the components inϕandχare positive.Considering a plane wave along the z axis for a left-handed particle ( σ· p)/p=−1,the equations(12)yields the following solution:cp−m s c2χ=√√In terms of Eq.(17),the equation(12)can be rewritten in the Weyl representation:∂ξi¯h=−ic¯h σ·∇η+m s c2ξ(19)∂tIn the above equations,bothξandηare coupled via nonzero m s.In order to compare Eq.(19)with the well known two-component Weyl equation,we take a limit m s=0,then thefirst equation in Eq.(19)reduces to∂ξνmass-square is negative.Therefore,more accurate tritium beta decay experiments are needed to further determine the neutrino mass-square.According to special relativity[16],if there is a superluminal par-ticle,it might travel backward in time.However,a re-interpretation rule has been introduced since the Sixties[6-8].Another approach is to introduce a kinematic time under a non-standard form of the Lorentz transformation[17-20].Therefore,special relativity can be extended to space-like region,and superluminal particles are allowed without causality violation.We wish to thank S.Y.Zhu and Y.Takahashi for helpful discussions References[1]”Review of Particle Physics”,Euro.Phys.Journ.C15(2000)350.[2]Ch.Weinhermer et al.,Phys.Lett.B460(1999)219.[3]V.M.Lobashev et al.,Phys.Lett.B460(1999)227.[4]W.Stoefflet al.,Phys.Rev.Lett.,75(1995)3237.[5]K.Assamagan et al.,Phys.Rev.D53(1996)6065.[6]O.M.P.Bilaniuk et al,Am.J.Phys.,30(1962)718.[7]E.Recami et al,Tachyons,Monopoles and Related Topics,North-Holland,(1978),and references therein.[8]G.Feinberg,Phys.Rev.159(1967)1089.[9]See e.g.E.C.G.Sudarshan:in Proceedings of the VIII Nobel Sym-posium,ed.by N.Swartholm(J.Wiley,New York,1970),P.335;J.Bandukwala and D.Shay,Phys.Rev.D9(1974)889;D.Shay, Lett.Nuovo Cim.19(1977)333[10]A.Chodos et al.,Phys.Lett.B150(1985)431.[11]P.A.M.Dirac,Proc.R.Soc.Ser,A117;610,118(1928)351.7[12]G-j Ni and Chen,On the essence of special relativity,Fudan Uni-versity,(Natural Science),35(1996)325.[13]G-j.Ni et al,Chin.Phys.Lett.,17(2000)393.[14]T.D.Lee and C.N.Yang,Phys.Rev.104(1956)254;Phys.Rev.105(1957)1671.[15]C.S.Wu et al.,Phys.Rev.105(1957)1413.[16]A.Einstein,H.A.Lorentz,H.Minkowski,and H.Weyl,The Prin-ciple of Relativity(collected papers),Dover,New York(1952).[17]R.Tangherlini,Nuov.Cim Suppl.,20(1961)1.[18]T.Chang,J.Phys.A12(1979)L203;”Does a free tachyon exist?”,Proceedings of the Sir A.Eddington Centenary Symposium, Vol.3,Gravitational Radiation and Relativity”,p.431(1986). [19]J.Rembielinski,Phys.Lett.,A78(1980)33;Int.J.Mod.Phys.,A12(1997)1677.[20]T.Chang and D.G.Torr,Found.Phys.Lett.,1(1988)343.8。

a rXiv:h ep-ph/9912427v12Dec1999DFTT 71/99hep-ph/9912427Neutrino oscillations and neutrinoless double-βdecay C.Giunti INFN,Sezione di Torino,and Dipartimento di Fisica Teorica,Universit`a di Torino,Via P.Giuria 1,I–10125Torino,Italy Abstract We consider the scheme with mixing of three neutrinos and a mass hierarchy.We shown that,under the natural assumptions that massive neutrinos are Majorana particles and there are no unlikely fine-tuned cancellations among the contributions of the different neutrino masses,the results of solar neutrino experiments imply a lower bound for the effective Majorana mass in neutri-noless double-βdecay.We also discuss briefly neutrinoless double-βdecay in schemes with mixing of four neutrinos.We show that one of them is favored by the data.Presented at TAUP’99,6–10September 1999,College de France,Paris,France.Typeset using REVT E XNeutrino oscillations[1]have been observed in solar and atmospheric neutrino experi-ments.The corresponding neutrino mass-squared differences are∆m2sun∼10−6−10−4eV2(MSW),(0.1)in the case of MSW transitions,or∆m2sun∼10−11−10−10eV2(VO),(0.2)in the case of vacuum oscillations,and∆m2atm∼10−3−10−2eV2.(0.3)These values of the neutrino mass-squared differences and the mixing required for the ob-served solar and atmospheric oscillations are compatible with the simplest and most natural scheme with three-neutrino mixing and a mass hierarchy:∆m2sunm1≪m2≪m3∆m2atm.(0.4)This scheme is predicted by the see-saw mechanism[1],which predicts also that the three light massive neutrinos are Majorana particles.In this case neutrinoless double-βdecay (ββ0ν)is possible and its matrix element is proportional to the effective Majorana mass| m |=k U2ek m k,(0.5)where U is the neutrino mixing matrix and the sum is over the contributions of all the mass eigenstate neutrinosνk(k=1,2,3).In principle the effective Majorana mass(0.5)can be vanishingly small because of can-cellations among the contributions of the different mass eigenstates.However,since the neutrino masses and the elements of the neutrino mixing matrix are independent quanti-ties,if there is a hierarchy of neutrino masses such a cancellation would be the result of an unlikelyfine-tuning,unless some unknown symmetry is at work.Here we consider the possibility that no such symmetry exist and no unlikelyfine-tuning operates to suppress the effective Majorana mass(0.5)[2].In this case we have| m |≃maxk| m |k,(0.6) where| m |k is the absolute value of the contribution of the massive neutrinoνk to| m |:| m |k≡|U ek|2m k.(0.7) In the following we will estimate the value of| m |using the largest| m |k obtained from the results of neutrino oscillation experiments.Let us consider first | m |3,which,taking into account that in the three-neutrino scheme under consideration m 3≃ ∆m 2atm ,is given by| m |3≃|U e 3|2 21− ∆m 2atm .One can seefrom Fig.1that theresults ofthe CHOOZ experiment imply that | m |3 2.7×10−2eV,the results of the Super-Kamiokande experiment imply that | m |3 3.8×10−2eV,and the combination of the results of the two experiments drastically lowers the upper bound to| m |3 2.5×10−3eV .(0.9)Since there is no lower bound for |U e 3|2from experimental data,| m |3could be much smaller than the upper bound in Eq.(0.9).Hence,the largest contribution to | m |could come from | m |2≡|U e 2|2m 2.In the scheme (0.4)m 2≃ ∆m 2sun and,since |U e 3|2is very small,|U e 2|2≃11−sin 22ϑsun [8],where ϑsun is the two-neutrino mixing angle used in the analysis of solar neutrino data.Therefore,| m |2is given by| m |2≃11−sin 22ϑsun ∆m 2sun .From Fig.2one can see that the LMA solution of thesolar neutrino problem implies that7.4×10−4eV | m |2 6.0×10−3eV .(0.13)Assuming the absence offine-tuned cancellations among the contributions of the three neu-trino masses to the effective Majorana mass,if|U e3|2is very small and| m |3≪| m |2, from Eqs.(0.6)and(0.13)we obtain7×10−4eV | m | 6×10−3eV.(0.14) Hence,assuming the absence of an unlikelyfine-tuned suppression of| m |,in the case of the LMA solution of the solar neutrino problem we have obtained a lower bound of about 7×10−4eV for the effective Majorana mass inββ0νdecay.Also the small mixing angle MSW(SMA)and the vacuum oscillation(VO)solutions of the solar neutrino problem imply allowed ranges for| m |2,but their values are much smaller than in the case of the LMA ing the99%CL allowed regions obtained in[10]from the analysis of the total rates measured in solar neutrino experiments we have 5×10−7eV | m |2 10−5eV(SMA),(0.15)10−6eV | m |2 2×10−5eV(VO).(0.16) If futureββ0νexperiments willfind| m |in the range shown in Fig.2and future long-baseline experiments will obtain a stronger upper bound for|U e3|2,it would mean that| m |2gives the largest contribution to the effective Majorana mass,favoring the LMA solution of the solar neutrino problem.On the other hand,if futureββ0νexperiments willfind| m |in the range shown in Fig.2and the SMA or VO solutions of the solar neutrino problem will be proved to be correct by future solar neutrino experiments,it would mean that| m |3gives the largest contribution to the effective Majorana mass and there is a lower bound for the value of|U e3|2.Finally,let us consider briefly the two four-neutrino mixing schemes compatible with all neutrino oscillation data[1],including the indications in favor ofνµ→νe oscillations found in the short-baseline(SBL)LSND experiment[11]:(A)∆m2atmm1<m2<∆m2sunm3<m4∆m2SBL,(0.17)(B)∆m2sunm1<m2<∆m2atmm3<m4∆m2SBL.(0.18)Since the mixing ofνe with the two massive neutrinos whose mass-squared difference gener-ates atmospheric neutrino oscillations is very small[1],the contribution of the two“heavy”mass eigenstatesν3andν4to the effective Majorana mass(0.5)is large in scheme A and very small in scheme B.Hence,the effective Majorana mass is expected to be relatively large in scheme A and strongly suppressed in scheme B.In particular,in the scheme A the SMA solution of the solar neutrino problem implies a value of| m |larger than the the present upper bound obtained inββ0νdecay experiments[12]and is,therefore,disfavored. Furthermore,since the measured abundances of primordial elements produced in Big-Bang Nucleosynthesis is compatible only with the SMA solution of the solar neutrino problem[13], we conclude that the scheme A is disfavored by the present experimental data and there is only one four-neutrino mixing scheme supported by all data:scheme B[2].REFERENCES[1]See:S.M.Bilenky,C.Giunti,and W.Grimus,Prog.Part.Nucl.Phys.43,1(1999).[2]C.Giunti,hep-ph/9906275(Phys.Rev.D).[3]M.Apollonio et al.(CHOOZ Coll.),Phys.Lett.B466,415(1999).[4]M.Nakahata,these proceedings.[5]G.L.Fogli,these proceedings.[6]S.M.Bilenky,C.Giunti,C.W.Kim and M.Monteno,Phys.Rev.D57,6981(1998).[7]S.M.Bilenky et al.,Phys.Lett.B465,193(1999).[8]S.M.Bilenky and C.Giunti,Phys.Lett.B444,379(1998).[9]Y.Fukuda et al.,Phys.Rev.Lett.82,1810(1999).[10]J.N.Bahcall,P.I.Krastev and A.Yu.Smirnov,Phys.Rev.D58,096016(1998).[11]D.H.White(LSND Coll.),Nucl.Phys.B(Proc.Suppl.)77,207(1999).[12]L.Baudis et al.,Phys.Rev.Lett.83,41(1999).[13]S.M.Bilenky,C.Giunti,W.Grimus and T.Schwetz,Astropart.Phys.11,413(1999).Figure2。

a r X i v :a s t r o -p h /0512374v 3 5 J u n 2006Cosmology with High-redshift Galaxy Survey:Neutrino Mass and InflationMasahiro Takada 1,Eiichiro Komatsu 2and Toshifumi Futamase 11Astronomical Institute,Tohoku University,Sendai 980-8578,Japan and 2Department of Astronomy,The University of Texas at Austin,Austin,TX 78712High-z galaxy redshift surveys open up exciting possibilities for precision determinations of neu-trino masses and inflationary models.The high-z surveys are more useful for cosmology than low-z ones owing to much weaker non-linearities in matter clustering,redshift-space distortion and galaxy bias,which allows us to use the galaxy power spectrum down to the smaller spatial scales that are inaccessible by low-z surveys.We can then utilize the two-dimensional information of the linear power spectrum in angular and redshift space to measure the scale-dependent suppression of matter clustering due to neutrino free-streaming as well as the shape of the primordial power spectrum.To illustrate capabilities of high-z surveys for constraining neutrino masses and the primordial power spectrum,we compare three future redshift surveys covering 300square degrees at 0.5<z <2,2<z <4,and 3.5<z <6.5.We find that,combined with the cosmic microwave background data expected from the Planck satellite,these surveys allow precision determination of the total neutrino mass with the projected errors of σ(m ν,tot )=0.059,0.043,and 0.025eV,respectively,thus yielding a positive detection of the neutrino mass rather than an upper limit,as σ(m ν,tot )is smaller than the lower limits to the neutrino masses implied from the neutrino oscillation experiments,by up to a factor of 4for the highest redshift survey.The accuracies of constraining the tilt and running index of the primordial power spectrum,σ(n s )=(3.8,3.7,3.0)×10−3and σ(αs )=(5.9,5.7,2.4)×10−3at k 0=0.05Mpc −1,respectively,are smaller than the current uncertainties by more than an or-der of magnitude,which will allow us to discriminate between candidate inflationary models.In particular,the error on αs from the future highest redshift survey is not very far away from the prediction of a class of simple inflationary models driven by a massive scalar field with self-coupling,αs =−(0.8−1.2)×10−3.PACS numbers:95.55.Vj,98.65.Dx,98.80.Cq,98.70.Vc,98.80.EsI.INTRODUCTIONWe are living in the golden age of cosmology.Vari-ous data sets from precision measurements of tempera-ture and polarization anisotropy in the cosmic microwave background (CMB)radiation as well as those of matter density fluctuations in the large-scale structure of the universe mapped by galaxy redshift surveys,Lyman-αforests and weak gravitational lensing observations are in a spectacular agreement with the concordance ΛCDM model [1,2,3,4].These results assure that theory of cos-mological linear perturbations is basically correct,and can accurately describe the evolution of photons,neu-trinos,baryons,and collisionless dark matter particles [5,6,7],for given initial perturbations generated during inflation [8,9].The predictions from linear perturbation theory can be compared with the precision cosmological measurements,in order to derive stringent constraints on the various basic cosmological parameters.Future obser-vations with better sensitivity and higher precision will continue to further improve our understanding of the uni-verse.Fluctuations in different cosmic fluids (dark matter,photons,baryons,and neutrinos)imprint characteristic features in their power spectra,owing to their interac-tion properties,thermal history,equation of state,and speed of sound.A remarkable example is the acoustic oscillation in the photon-baryon fluid that was generated before the decoupling epoch of photons,z ≃1088,which has been observed in the power spectrum of CMB tem-perature anisotropy [10],temperature–polarization cross correlation [11],and distribution of galaxies [12,13].Yet,the latest observations have shown convincingly that we still do not understand much of the universe.The standard model of cosmology tells us that the universe has been dominated by four components.In chronolog-ical order the four components are:early dark energy (also known as “inflaton”fields),radiation,dark mat-ter,and late-time dark energy.The striking fact is that we do not understand the precise nature of three (dark matter,and early and late-time dark energy)out of the four components;thus,understanding the nature of these three dark components has been and will continue to be one of the most important topics in cosmology in next decades.Of which,one might be hopeful that the next generation particle accelerators such as the Large Hadron Collider (coming on-line in 2007)would find some hints for the nature of dark matter particles.On the other hand,the nature of late-time dark energy,which was dis-covered by measurements of luminosity distance out to distant Type Ia supernovae [14,15],is a complete mys-tery,and many people have been trying to find a way to constrain properties of dark energy (see,e.g.,[16]for a review).How about the early dark energy,inflaton fields,which caused the expansion of the universe to accelerate in the very early universe?We know little about the nature of inflaton,just like we know little about the nature of late-time dark energy.The required property of infla-ton fields is basically the same as that of the late-time2dark energy component:both must have a large negativepressure which is less than−1/3of their energy density. To proceed further,however,one needs more informationfrom observations.Different inflation models make spe-cific predictions for the shape of the power spectrum[8](see also Appendix B)as well as for other statistical prop-erties[17]of primordial perturbations.Therefore,one ofthe most promising ways to constrain the physics of in-flation,hence the nature of early dark energy in the uni-verse,is to determine the shape of the primordial power spectrum accurately from observations.For example,theCMB data from the Wilkinson Microwave Anisotropy Probe[1],combined with the large-scale structure datafrom the Two-Degree Field Galaxy Redshift Survey[18], have already ruled out one of the popular inflationarymodels driven by a self-interacting massless scalarfield [19].Understanding the physics of inflation better willlikely provide an important implication for late-time dark energy.“Radiation”in the universe at around the matter-radiation equality mainly consists of photons and neu-trinos;however,neutrinos actually stop being radiationwhen their mean energy per particle roughly equals the temperature of the universe.The physics of neutrinoshas been revolutionized over the last decade by solar, atmospheric,reactor,and accelerator neutrino experi-ments having provided strong evidence forfinite neutrino masses via mixing between different neutrinoflavors,theso-called neutrino oscillations[20,21,22,23,24].These experiments are,however,only sensitive to mass squaredifferences between neutrino mass eigenstates,implying ∆m221≃7×10−5eV2and∆m232≃3×10−3eV2;thus, the most fundamental quantity of neutrinos,the abso-lute mass,has not been determined yet.Cosmologicalneutrinos that are the relic of the cosmic thermal his-tory have distinct influences on the structure formation.Their large energy density,comparable to the energy den-sity of photons before the matter-radiation equality,de-termines the expansion history of the universe.Even after the matter-radiation equality,neutrinos having be-come non-relativistic affect the structure formation by suppressing the growth of matter densityfluctuations at small spatial scales owing to their large velocity disper-sion[25,26,27,28,29,30](see Sec.II and Appendix A for more details).Therefore,the galaxy redshift surveys, combined with the CMB data,provide a powerful,albeit indirect,means to constraining the neutrino properties [31,32,33,34,35].This approach also complements the theoretical and direct experimental efforts for under-standing the neutrino physics.In fact,the cosmological constraints have placed the most stringent upper bound on the total neutrino mass,mν,tot<∼0.6eV(2σ)[36], stronger than the direct experiment limit<∼2eV[37].In addition,the result obtained from the Liquid Scintillator Neutrino Detector(LSND)experiment,which implies¯νµto¯νe oscillations with∆m2>∼0.2eV2[38]in an apparent contradiction with the other neutrino oscillation experi-ments mentioned above,potentially suggests the need for new physics:the cosmological observations will provide independent tests of this hypothesis.In this paper we shall study the capability of future galaxy surveys at high redshifts,combined with the CMB data,for constraining(1)the neutrino properties,more specifically the total neutrino mass,mν,tot,and the num-ber of non-relativistic neutrino species,N nrν,and(2)the shape of the primordial power spectrum that is parame-terized in terms of the spectral tilt,n s,and the running index,αs,motivated by inflationary predictions(see Ap-pendix B).For the former,we shall pay particular at-tention to our ability to simultaneously constrain mν,tot and N nrν,as they will provide important clues to resolv-ing the absolute mass scale as well as the neutrino mass hierarchy.The accuracy of determining the neutrino pa-rameters and the power spectrum shape parameters will be derived using the Fisher information matrix formal-ism,including marginalization over the other cosmologi-cal parameters as well as the galaxy bias.Our analysis differs from the previous work on the neutrino parameters in that we fully take into account the two-dimensional nature of the galaxy power spec-trum in the line-of-sight and transverse directions,while the previous work used only spherically averaged,one-dimensional power spectra.The geometrical distortion due to cosmology and the redshift space distortion due to the peculiar velocityfield will cause anisotropic features in the galaxy power spectrum.These features help to lift degeneracies between cosmological parameters,sub-stantially reducing the uncertainties in the parameter de-terminations.This is especially true when variations in parameters of interest cause modifications in the power spectrum shape,which is indeed the case for the neutrino parameters,tilt and running index.The usefulness of the two-dimensional power spectrum,especially for high-redshift galaxy surveys,has been carefully investigated in the context of the prospected constraints on late-time dark energy properties[39,40,41,42,43,44,45].We shall show the parameter forecasts for future wide-field galaxy surveys that are already being planned or seriously under consideration:the Fiber Multiple Object Spectrograph(FMOS)on Subaru telescope[46],its sig-nificantly expanded version,WFMOS[47],the Hobby–Ebery Telescope Dark Energy eXperiment(HETDEX) [48],and the Cosmic Inflation Probe(CIP)mission[49]. To model these surveys,we consider three hypothetical galaxy surveys which probe the universe over different ranges of redshift,(1)0.5≤z≤2,(2)2≤z≤4and (3)3.5≤z≤6.5.Wefix the sky coverage of each sur-vey atΩs=300deg2in order to make a fair compari-son between different survey designs.As we shall show below,high-redshift surveys are extremely powerful for precision cosmology because they allow us to probe the linear power spectrum down to smaller length scales than surveys at low redshifts,protecting the cosmological in-formation against systematics due to non-linear pertur-bations.We shall also study how the parameter uncertainties3 are affected by changes in the number density of sam-pled galaxies and the survey volume.The results wouldgive us a good guidance to defining the optimal surveydesign to achieve the desired accuracies in parameter de-terminations.The structure of this paper is as follows.In Sec.II,wereview the physical pictures as to how the non-relativistic(massive)neutrinos lead to scale-dependent modifica-tions in the growth of mass clustering relative to thepure CDM model.Sec.III defines the parameterization of the primordial power spectrum motivated by inflation-ary predictions.In Sec.IV we describe a methodology to model the galaxy power spectrum observable from aredshift survey that includes the two-dimensional nature in the line-of-sight and transverse directions.We thenpresent the Fisher information matrix formalism that is used to estimate the projected uncertainties in the cos-mological parameter determination from statistical errors on the galaxy power spectrum measurement for a givensurvey.After survey parameters are defined in Sec.V, we show the parameter forecasts in Sec.VI.Finally,wepresent conclusions and some discussions in Sec.VII.We review the basic properties of cosmological neutrinos inAppendix A,the basic predictions from inflationary mod-els for the shape of the primordial power spectrum in Ap-pendix B,and the relation between the primordial powerspectrum and the observed power spectrum of matter densityfluctuations in Appendix C.In the following,we assume an adiabatic,cold dark matter(CDM)dominated cosmological model withflatgeometry,which is supported by the WMAP results [1,36],and employ the the notation used in[51,52]:the present-day density of CDM,baryons,and non-relativistic neutrinos,in units of the critical density,aredenoted asΩc,Ωb,andΩν,respectively.The total mat-ter density is thenΩm=Ωc+Ωb+Ων,and fνis theratio of the massive neutrino density contribution toΩm: fν=Ων/Ωm.II.NEUTRINO EFFECT ON STRUCTUREFORMATIONThroughout this paper we assume the standard ther-mal history in the early universe:there are three neutrinospecies with temperature equal to(4/11)1/3of the photon temperature.We then assume that0≤N nrν≤3species are massive and could become non-relativistic by thepresent epoch,and those non-relativistic neutrinos have equal masses,mν.As we show in Appendix A,the den-sity parameter of the non-relativistic neutrinos is given byΩνh2=N nrνmν/(94.1eV),where we have assumed 2.725K for the CMB temperature today[50],and h is the Hubble parameter defined as H0=100h km s−1Mpc−1. The neutrino mass fraction is thus given byfν≡Ων0.658eV 0.141eVΩm h21+z 1/2.(2)Therefore,non-relativistic neutrinos with lighter masses suppress the growth of structure formation on larger spa-tial scales at a given redshift,and the free-streaming length becomes shorter at a lower redshift as neutrino velocity decreases with redshift.The most important property of the free-streaming scale is that it depends on the mass of each species,mν,rather than the total mass,N nrνmν;thus,measurements of k fs allow us to dis-tinguish different neutrino mass hierarchy models.For-tunately,k fs appears on the scales that are accessible by galaxy surveys:k fs=0.096−0.179Mpc−1at z=6−1 for mν=1eV.On the spatial scales larger than the free-streaming length,k<k fs,neutrinos can cluster and fall into gravi-tational potential well together with CDM and baryonic matter.In this case,perturbations in all matter com-ponents(CDM,baryon and neutrinos,denoted as‘cbν’hereafter)grow at the same rate given byD cbν(k,z)∝D(z)k≪k fs(z),(3) where D(z)is the usual linear growth factor(see,e.g., Eq.(4)in[53]).On the other hand,on the scales smaller than the free-streaming length,k>k fs,perturbations in non-relativistic neutrinos are absent due to the large ve-locity dispersion.In this case,the gravitational potential well is supported only by CDM and baryonic matter,and the growth of matter perturbations is slowed down rela-tive to that on the larger scales.As a result,the matter power spectrum for k>k fs is suppressed relative to that for k<k fs.In this limit the total matter perturbations grow at the slower rate given byD cbν(k,z)∝(1−fν)[D(z)]1−p k≫k fs(z),(4) where p≡(5−√4FIG.1:Suppression in the growth rate of total matter per-turbations(CDM,baryons and non-relativistic neutrinos), D cbν(a),due to neutrino free-streaming.(a=(1+z)−1is the scale factor.)Upper panel:D cbν(a)/Dν=0(a)for the neutrino mass fraction of fν=Ων/Ωm=0.05.The number of non-relativistic neutrino species is varied from N nrν=1,2,and3 (from thick to thin lines),respectively.The solid,dashed,and dotted lines represent k=0.01,0.1,and1h Mpc−1,respec-tively.Lower panel:D cbν(a)/Dν=0(a)for a smaller neutrino mass fraction,fν=0.01.Note that the total mass of non-relativistic neutrinos isfixed to mν,tot=N nrνmν=0.66eV and0.13eV in the upper and lower panels,respectively. Eq.(2).It is thus expected that a galaxy survey with different redshift slices can be used to efficiently extract the neutrino parameters,N nrνand mν.The upper and middle panels of Figure2illustrate how free-streaming of non-relativistic neutrinos suppresses the amplitude of linear matter power spectrum,P(k), at z=4.Note that we have normalized the primordial power spectrum such that all the power spectra match at k→0(see§III).To illuminate the dependence of P(k) on mν,wefix the total mass of non-relativistic neutri-nos,N nrνmν,by fν=0.05and0.01in the upper and middle panels,respectively,and vary the number of non-relativistic neutrino species as N nrν=1,2and3.The suppression of power is clearly seen as one goes from k<k fs(z)to k>k fs(z)(see Eq.[2]for the value of k fs).The way the power is suppressed may be easily un-derstood by the dependence of k fs(z)on mν;for example,linear power spectrum at z=4due to free-streaming of non-relativistic neutrinos.Wefix the total mass of non-relativistic neutrinos by fν=Ων/Ωm=0.05,and vary the number of non-relativistic neutrino species(which have equal masses, mν)as N nrν=1(solid),2(dashed),and3(dot-dashed). The mass of individual neutrino species therefore varies as mν=0.66,0.33,and0.22eV,respectively(see Eq.[1]).The shaded regions represent the1-σmeasurement errors on P(k) in each k-bin,expected from a galaxy redshift survey observ-ing galaxies at3.5≤z≤4.5(see Table I for definition of the survey).Note that the errors are for the spherically averaged power spectrum over the shell of k in each bin.Different N nrνcould be discriminated in this case.Middle panel:Same as in the upper panel,but for a smaller neutrino mass fraction, fν=0.01.While it is not possible to discriminate between different N nrν,the overall suppression on small scales is clearly seen.Lower panel:Dependences of the shape of P(k)on the other cosmological parameters.P(k)at smaller k is more suppressed for a smaller mν,as lighter neutrinos have longer free-streaming lengths.Onvery small scales,k≫k fs(z)(k>∼1and0.1Mpc−1for fν=0.05and0.01,respectively),however,the amountof suppression becomes nearly independent of k,and de-pends only on fν(or the total neutrino mass,N nrνmν) as∆P5 ≈8fν.(5)We therefore conclude that one can extract fνand N nrνseparately from the shape of P(k),if the suppression “pattern”in different regimes of k is accurately measured from observations.5Are observations good enough?The shaded boxes in the upper and middle panels in Figure2represent the1-σmeasurement errors on P(k)expected from one of the fiducial galaxy surveys outlined in Sec.V.Wefind thatP(k)will be measured with∼1%accuracy in each k bin. If other cosmological parameters were perfectly known,the total mass of non-relativistic neutrinos as small as mν,tot=N nrνmν>∼0.001eV would be detected at more than2-σ.This limit is much smaller than the lower mass limit implied from the neutrino oscillation exper-iments,0.06eV.This estimate is,of course,unrealistic because a combination of other cosmological parameters could mimic the N nrνor fνdependence of P(k).The lower panel in Figure2illustrates how other cosmolog-ical parameters change the shape of P(k).In the fol-lowing,we shall extensively study how well future high-redshift galaxy surveys,combined with the cosmic mi-crowave background data,can determine the mass of non-relativistic neutrinos and discriminate between different N nrν,fully taking into account degeneracies between cos-mological parameters.III.SHAPE OF PRIMORDIAL POWER SPECTRUM AND INFLATIONARY MODELSInflation generally predicts that the primordial power spectrum of curvature perturbations is nearly scale-invariant.Different inflationary models make specific predictions for deviations of the primordial spectrum from a scale-invariant spectrum,and the deviation is of-ten parameterized by the“tilt”,n s,and the“running index”,αs,of the primordial power spectrum.As the pri-mordial power spectrum is nearly scale-invariant,|n s−1| and|αs|are predicted to be much less than unity. This,however,does not mean that the observed mat-ter power spectrum is also nearly scale-invariant.In Ap-pendix C,we derive the power spectrum of total matter perturbations that is normalized by the primordial cur-vature perturbation(see Eq.[C6])k3P(k,z)5H20Ωm 2×D2cbν(k,z)T2(k) k2αs ln(k/k0),(6)where k0=0.05Mpc−1,δ2R=2.95×10−9A,and A is the normalization parameter given by the WMAP collaboration[1].We adopt A=0.871,which gives δR=5.07×10−5.(In the notation of[63,64]δR=δζ.) The linear transfer function,T(k),describes the evolu-tion of the matter power spectrum during radiation era and the interaction between photons and baryons be-fore the decoupling of photons.Note that T(k)depends only on non-inflationary parameters such asΩm h2and Ωb/Ωm,and is independent of n s andαs.Also,the effects of non-relativistic neutrinos are captured in D cbν(k,z); thus,T(k)is independent of time after the decoupling epoch.We use thefitting function found in[51,52]for T(k).Note that the transfer function and the growth rate are normalized such that T(k)→1and D cbν/a→1 as k→0during the matter era.In Appendix B we describe generic predictions on n s andαs from inflationary models.For example,inflation driven by a massive,self-interacting scalarfield predicts n s=0.94−0.96andαs=(0.8−1.2)×10−3for the num-ber of e-foldings of expansion factor before the end of inflation of50.This example shows that precision deter-mination of n s andαs allows us to discriminate between candidate inflationary models(see[8]for more details). IV.MODELING GALAXY POWER SPECTRUMA.Geometrical and Redshift-Space DistortionSuppose now that we have a redshift survey of galax-ies at some redshift.Galaxies are biased tracers of the underlying gravitationalfield,and the galaxy power spec-trum measures how clustering strength of galaxies varies as a function of3-dimensional wavenumbers,k(or the inverse of3-dimensional length scales).We do not measure the length scale directly in real space;rather,we measure(1)angular positions of galax-ies on the sky,and(2)radial positions of galaxies in redshift space.To convert(1)and(2)to positions in 3-dimensional space,however,one needs to assume a ref-erence cosmological model,which might be different from the true cosmology.An incorrect mapping of observed angular and redshift positions to3-dimensional positions produces a distortion in the measured power spectrum, known as the“geometrical distortion”[54,55,56].The geometrical distortion can be described as follows.The comoving size of an object at redshift z in radial,r ,and transverse,r⊥,directions are computed from the exten-sion in redshift,∆z,and the angular size,∆θ,respec-tively,asr =∆zH(z′),(8) where H(z)is the Hubble parameter given byH2(z)=H20 Ωm(1+z)3+ΩΛ .(9)6 HereΩm+ΩΛ=1,andΩΛ≡Λ/(3H20)is the present-daydensity parameter of a cosmological constant,Λ.A trickypart is that H(z)and D A(z)in Eq.(7)depend on cosmo-logical models.It is therefore necessary to assume somefiducial cosmological model to compute the conversionfactors.In the following,quantities in thefiducial cos-mological model are distinguished by the subscript‘fid’.Then,the length scales in Fourier space in radial,kfid ,and transverse,kfid⊥,directions are estimated from theinverse of rfid and rfid⊥.Thesefiducial wavenumbers arerelated to the true wavenumbers byk⊥=D A(z)fidH(z)fidkfid .(10)Therefore,any difference between thefiducial cosmolog-ical model and the true model would cause anisotropicdistortions in the estimated power spectrum in(kfid⊥,kfid )space.In addition,shifts in z due to peculiar velocities ofgalaxies distort the shape of the power spectrum alongthe line-of-sight direction,which is known as the“redshiftspace distortion”[57].From azimuthal symmetry aroundthe line-of-sight direction,which is valid when a distant-observer approximation holds,the linear power spectrumestimated in redshift space,P s(kfid⊥,kfid ),is modeled in[39]asP s(kfid⊥,kfid )=D A(z)2fid H(z)k2⊥+k22×b21P(k,z),(11)where k=(k2⊥+k2)1/2andβ(k,z)≡−1d ln(1+z),(12)is a function characterizing the linear redshift space distortion,and b1is a scale-independent,linear biasparameter.Note thatβ(k,z)depends on both red-shift and wavenumber via the linear growth rate.Inthe infall regime,k≪k fs(z),we have b1β(k,z)≈−d ln D(z)/d ln(1+z),while in the free-streaming regime, k≫k fs(z),we have b1β(k,z)≈−(1−p)d ln D(z)/d ln(1+ z),where p is defined below Eq.(4).One might think that the geometrical and redshift-space distortion effects are somewhat degenerate in the measured power spectrum.This would be true only if the power spectrum was a simple power law.For-tunately,characteristic,non-power-law features in P(k) such as the broad peak from the matter-radiation equal-ity,scale-dependent suppression of power due to baryons and non-relativistic neutrinos,the tilt and running of the primordial power spectrum,the baryonic acoustic os-cillations,etc.,help break degeneracies quite efficiently [39,40,41,42,43,44,47,55,56].ments on Baryonic OscillationsIn this paper,we employ the linear transfer function with baryonic oscillations smoothed out(but includes non-relativistic neutrinos)[51,52].As extensively in-vestigated in[39,44,47],the baryonic oscillations can be used as a standard ruler,thereby allowing one to precisely constrain H(z)and D A(z)separately through the geo-metrical distortion effects(especially for a high-redshift survey).Therefore,our ignoring the baryonic oscillations might underestimate the true capability of redshift sur-veys for constraining cosmological parameters.We have found that the constraints on n s andαs from galaxy surveys improve by a factor of2–3when baryonic oscillations are included.This is because the baryonic os-cillations basicallyfix the values ofΩm,Ωm h2andΩb h2, lifting parameter degeneracies betweenΩm h2,Ωb h2,n s, andαs.However,we suspect that this is a rather opti-mistic forecast,as we are assuming aflat universe dom-inated by a cosmological constant.This might be a too strong prior,and relaxing our assumptions about geom-etry of the universe or the properties of dark energy will likely result in different forecasts for n s andαs.In this paper we try to separate the issues of non-flat universe and/or equation of state of dark energy from the physics of neutrinos and inflation.We do not include the bary-onic oscillations in our analysis,in order to avoid too optimistic conclusions about the constraints on the neu-trino parameters,n s,andαs.Eventually,the full analysis including non-flat uni-verse,arbitrary dark energy equation of state and its time dependence,non-relativistic neutrinos,n s,andαs, using all the information we have at hand including the baryonic oscillations,will be necessary.We leave it for a future publication(Takada and Komatsu,in prepara-tion).C.Parameter Forecast:Fisher Matrix Analysis In order to investigate how well one can constrain the cosmological parameters for a given redshift survey de-sign,one needs to specify measurement uncertainties of the galaxy power spectrum.When non-linearity is weak, it is reasonable to assume that observed density perturba-tions obey Gaussian statistics.In this case,there are two sources of statistical errors on a power spectrum measure-ment:the sampling variance(due to the limited number of independent wavenumbers sampled from afinite sur-vey volume)and the shot noise(due to the imperfect sampling offluctuations by thefinite number of galax-ies).To be more specific,the statistical error is given in [58,59]by∆P s(k i)N k 1+1。

a r X i v :h e p -p h /0010077v 1 9 O c t 2000Mass Spectrum and the Nature of Neutrinos.M.Czakon,J.Gluza,J.Studnik and M.Zra l ek Department of Field Theory and Particle Physics,Institute of Physics,University of Silesia,Uniwersytecka 4,PL-40-007Katowice,Poland Taking as input the best fit solar neutrino anomaly description,MSW LMA,and the tritium beta decay results we estimate the allowed range of neutrino masses independently of their nature.Adding the present bound on the effective neutrino mass coming from neutrinoless double beta decay,we narrow this range for Majorana neutrinos.We complete the discussion by considering future perspectives on determining the neutrino masses,when the oscillation data will be improved and the next experiments on (ββ)0νand 3H decay give new bounds or obtain concrete life-times or distortions in the energy distribution.We know much more about neutrino masses than yet a few years ago.The observed anoma-lies in atmospheric,solar and possibly the LSND neutrino experiments,which we believe are explained by neutrino oscillations,supplied with the tritium beta decay data give hints on neutrino masses independently of whether they are Dirac or Majorana particles.Additional constraints on Majorana neutrino masses come from the fact that no neutrinoless double beta decay has been observed to this day.In this work we present an up to date analysis and future perspectives of finding the neutrino mass spectrum without any constraints from theoretical models.We consider only the three neutrino case (i.e.without considering the LSND anomaly),and the latest best fit solar neutrino problem solution,the MSW LMA 1.The oscillation param-eters inferred from atmospheric and solar data are given in Table 1.The four neutrino case and other currently acceptable solutions of the solar anomaly are considered elsewhere 3.As there are definitely two scales of δm 2,δm 2atm ≫δm 2sol ,two possible neutrino mass spectra must be con-sidered.The first,known as normal mass hierarchy (A 3)where δm 2sol =δm 221≪δm 232≈δm 2atm and the second,inverse mass hierarchy spectrum (A inv 3)with δm 2sol =δm 221≪δm 2atm ≈−δm 231.Both schemes are not distinguishable by present experiments.There is hope that future neutrino factories will do that 4.Two elements of the first row of the mixing matrix |U e 1|and |U e 2|can be expressed by theTable1:The allowed range(95%of CL)and the bestfit values of sin22θandδm2for the atmospheric neutrino oscillation and the bestfit MSW LMA solution of the solar neutrino problem.Allowed range Bestfitδm2[eV2]sin22θsolar(1.5−6)×10−30.84−1Solar neutrinos(MSW LMA)18×10−50.66third element|U e3|and the sin22θsolar|U e1|2=(1−|U e3|2)11−sin22θsolar),(1)and|U e2|2=(1−|U e3|2)11−sin22θsolar).(2)The value of the third element|U e3|is notfixed yet and only different bounds exist for it.We will take the bound directly inferred from the CHOOZ and SK experiments5|U e3|2<0.04(with95%of CL).(3) Since in both schemes there is(mν)2max=(mν)2min+δm2solar+δm2atm,(4) the oscillation experiments alone give(mν)max≥δm2solar+δm2atm.(6) Translating the above into numbers(again at95%CL)2we end up with(mν)max≥0.04eV,|m i−m j|<0.08eV.(7) The next important data comes from the tritium beta decay experiments.The following bound has been lately obtained63i=1|U ei|2m2i 1/2≡mβ<κ′=2.2eV(8) this obviously leads only to the double inequality(mν)min≤mβ≤(mν)max.(9) Therefore0≤(mν)min≤2.2eV.(10) (mν)max remains unfortunately unlimited from above.Supplying the tritium decay with oscil-lations wefind that7m2β=(mν)2min+Ωscheme,(11) and(mν)2max=m2β+Λscheme,(12)whereΩandΛare scheme dependent.For example,in the A3schemeΩ(A3)=(1−|U e1|2)δm2solar+|U e3|2δm2atm,(13) andΛ(A3)=|U e1|2δm2solar+(1−|U e3|2)δm2atm.(14) This provides limits for both(mν)min and(mν)max0≤(mν)min≤+δm2atm≤(mν)max≤δm2solarFigure2:of(mν)min in the case of the A3shaded and hashed regions represent the are taken into account.The present and band is an example of a0.05)eV.The observed10(19) There are future plans to go down to| mν |≃0.02eV or even to| mν |≃0.006eV11.Do we have a chance offinding the Majorana mass spectrum if a value of| mν |is found within such a small range12?This answer as we will see is not very promising.We shall neglect the difficulties connected with the determination of| mν |from the half life time of germanium13.As the phases of U ei remain unknown,we are not in position to predict the value of| mν |.However, the lower| mν |min and upper| mν |max ranges as function of(mν)min can be inferred14.They are shown in Fig.2for the A3scheme and for the MSW LMA solar neutrino problem solution. The shaded and hashed regions give the uncertainties connected with the allowed ranges of the input parameters(sin22θsolar,δm2atm(Table1)and|U e3|2(Eq.3).Future better knowledge of these parameters will reduce the uncertainty regions shown in Fig.2,but the min-max range caused by the unknown CP phases will remain.The present experimental bound on| mν |(Eq.19)gives the following limit on the possible (mν)min for Majorana neutrinos(mν)min<0.86eV.(20) This bound strongly depends on the unknown oscillation parameters,most notably on sin22θsolar. In Fig.3we plot this dependence for two different sets ofδm2atm and|U e3|2values.The limit given in Eq.20is valid for sin22θsolar=0.92,|U e3|2=0.04andδm2atm=6×10−3eV2.If in future,the(ββ)0νexperiments observe no decay,and a new bound is only found,the next better limit that can be derived from Fig.3(with the present oscillation results),is(mν)min<0.092eV GENIUS I,(21) and(mν)min<0.037eV GENIUS II.(22)Figure3:ofδm2atm and|U e3|2. In the we can try to predict the value of| mν | and on the of| mν |values is given of values allowed by oscillations(mν)min(ββ)0νmin ≤(mν)min≤(mν)max(ββ)0νmin.(23)With the present day uncertainties on the oscillation parameters,the range of possible values determined by Eq.23is not satisfactorily small.For example,with| mν |≃0.05eV(mν)min∈(0.03−0.6)eV.(24)For smaller values of| mν |we can only say that(mν)min<0.2eV.A better knowledge of the oscillation parameters changes the situation slightly.For example,if the oscillation parameters are known with negligible error bars for| mν |≃0.05eV,then the range Eq.24changes to(mν)min∈(0.04−0.1)eV.(25)The ignorance of the CP breaking phases in the mixing matrix is fully responsible for this smearing.The bounds on the effective neutrino mass| mν |in the inverse hierarchy mass scheme A inv3 and the MSW LMA solution of the solar neutrino problem are depicted in Fig.4.We see that the present bound on| mν |(Eq.19),gives a similar limit on the possible range of(mν)min of Majorana neutrino masses(mν)min<0.86eV.(26) Thefirst stage of GENIUS can yield(mν)min<0.077eV,(27)while the second would exclude the A inv3scheme.In conclusion,the present data allow for the following statementsFigure4:of(mν)min in the case ofthe A inv3and hashed regions represent the taken into account.The•we•the but the latter depends strongly on the oscillation parameters.•the oscillation and tritium beta decay experiments are able to determine the spectrum ofneutrino masses for values of mβwhich differ in the A3(mβ≥0.04eV)and the A inv3 (mβ≥0.2eV)schemes.•the oscillation and(ββ)0νexperiments are able tofind the range of possible(mν)min values.However,this range is not small even with oscillation parameters of negligible error bars. AcknowledgmentsOne of us(MZ)would like to thank all the organizers and especially Prof.Tran Tanh Van for invitation and a very good atmosphere at the perfectly prepared conference.This work was supported by the Polish Committee for Scientific Research under Grant No.2P03B05418and 2P03B04919.References1.N.Hata,ngacker,Phys.Rev.D56,6107(1997);J.N.Bahcall,P.Krastev,A.Yu.Smirnov,Phys.Rev.D58,096016(1998);V.Banger,K.Whisnant,Phys.Rev.D59,093007(1999);M.C.Gonzalez-Garcia,P.C.de Holanda, C.Pena-Garay,J.W.J.Valle,hep-ph/9906469;A.de Gouvea,A.Friedland,A.Murayama,hep-ph/0002064;M.G.Gonzalez-Garcia,C.Pena-Garay,hep-ph/0002186;G.L.Fogli,E.Lisi,D.Montanino andA.Palazzo,hep-ph/9912231;M.C.Gonzalez-Garcia,C.Pena-Garay,hep-ph/00099041.2.Y.Fukuda et al.,Phys.Lett.B433,9(1998);Phys.Lett.B436,33(1998);Phys.Rev.Lett.81,1562(1998);Phys.Rev.Lett.82,2644(1999);W.A.Mann,hep-ex/9912007;A.De Rujula,M.B.Gavela,P.Hernandez,hep-ph/0001124;N.Fornengo,M.C.Gonzalez-Garcia,J.W.F.Valle,hep-ph/0002147;S.Fukuda et al.(Superkamiokande Coll.),hep-ex/00090001;G.L.Fogli,E.Lisi,A.Marrone,D.Nontanino,hep-ph/0009269.3.M.Czakon,J.Studnik,M.Zra l ek,hep-ph/0006339;M.Czakon,J.Gluza,M.Zra l ek,hep-ph/0003161.4.SuperKamiokande homepage,http://www-sk.icrr.u-tokyo.ac.jp/doc/sk;SNO homepage,http://snodaq.phy.queensu.ca/SNO/sno.html;BOREX-INO homepage,http://almime.mi.infn.it;HERON homepage, /research/heron;HELLAZ homepage, /hellaz;K.Nishikawa,Nucl.Phys.(Proc.Supp.)77,198(1999);B.C.Barish,Nucl.Phys.(Proc.Supp.)70,227(1999);A.Cervera et al.,hep-ph/0002108;V.Barger,S.Geer,R.Raja,K.Whisnant,hep-ph/0007181;S.Geer,hep-ph/0008155;R.Burton,hep-ph/008222.5.G.L.Fogli,E.Lisi,A.Marrone,G.Scioscia,Phys.Rev.D59,033001(1999);CHOOZcoll.,Phys.Lett.B466,415.(1999)6.C.Weinheimer et al.,Phys.Lett.B460,219(1999);V.M.Lobashev et al.,Phys.Lett.B460,227(1999);Mainz Collaboration,Neutrino2000,Canada.pare V.Barger and K.Whisnant,Phys.Lett.B456,54.,(1999)S.Goswami,D.Ma-jumdar and A.Raychaudhuri,hep-ph/9909453.8.K.Zuber,hep-ph/9911362.9.see e.g.M.Doi,T.Kotani,E.Takasugi,Prog.Theor.Phys.(supplement)83,1.(1985)10.L.Baudis et al.,Phys.Rev.Lett.83,41.(1999)11.H.V.Klapdor-Kleigrothaus,hep-ex/9907040;L.Baudis et al.,GENIUS(Collaboration),hep-ph/9910205.12.S.T.Petcov,A.Y.Smirnov,Phys.Lett.B322,109(1994);S.M.Bilenky,A.Bottino,C.Giunti,C.Kim,Phys.Rev.D54,1881(1996);S.M.Bilenky,C.Giunti,C.Kim,S.Petcov,Phys.Rev.D54,4444(1996);J.Hellmig,H.V.Klapdor-Kleingrothaus,Z.Phys.A359,351(1997);H.V.Klapdor-Kleingrothaus,J.Hellmig,M.Hirsch,J.Phys.G24, 483(1998);H.Minataka,O.Yasuda,Phys.Rev.D56,1692,(1997)Nucl.Phys.B523, 597(1998);S.M.Bilenky,C.Giunti,C.W.Kim,M.Monteno,Phys.Rev.D54,6981, (1998)hep-ph/9904328;F.Vissani,hep-ph/9708482,hep-ph/9904349,hep-ph/9906525;T.Fukuyama,K.Matsuda,H.Nishiura,hep-ph/9708397;Mod.Phys.Lett.A13,2279 (1998);S.M.Bilenky,C.Giunti,W.Grimus,hep-ph/9809368;S.Bilenky,C.Giunti,hep-ph/9904328;S.Bilenky,C.Giunti,W.Grimus,B.Kayser,S.T.Petcov,hep-ph/9907234, Phys.Lett.B465,193(1999);H.Georgi,S.L.Glashow,hep-ph/9808293;V.Barger,K.Whisnant,Phys.Lett.B456,194(1999);J.Ellis,S.Lola,hep-ph/9904279,Phys.Lett.B458,310(1999);G.C.Branco,M.N.Rebelo,J.I.Silva-Marcos,Phys.Rev.Lett.82, 683(1999);C.Giunti,Phys.Rev.D61,036002(2000);R.Adhikari,G.Rajasekaran, hep-ph/9812361;Phys.Rev.D61,031301(2000);K.Matsuda,N.Takeda,T.Fukuyama,H.Nishiura,hep-ph/0003055;M.Czakon,M.Zralek and J.Gluza,Acta Phys.Polon.B30,3121(1999)M.Czakon,J.Gluza and M.Zralek,Phys.Lett.B465,211.(1999)13.H.V.Klapdor-Kleingrothaus,H.Paes,A.Yu.Smirnov,hep-ph/0003219;14.M.Czakon,J.Studnik,M.Zralek and J.Gluza,Acta Phys.Polon.B31,1365(2000);。

In the vast tapestry of human culture, food stands as a vibrant thread that weaves through the fabric of our daily lives. It is not merely sustenance but also a reflection of our heritage, traditions, and social interactions. The culinary practices of the East and West offer a fascinating contrast, each with its unique characteristics and philosophies. This essay aims to explore the differences between Chinese and Western diets, drawing from personal experiences and broader cultural insights.Growing up in a Chinese household, I was immersed in a culinary tradition that emphasized the harmony of flavors and the balance of nutrients. Chinese cuisine is renowned for its complexity and diversity, with each region boasting its signature dishes. For instance, the fiery kick of Sichuan peppercorns, the succulent Peking duck from Beijing, and the delicate dim sum from the Guangdong province are all testaments to the rich tapestry of Chinese gastronomy.In contrast, Western diets, particularly those from Europe and North America, tend to focus on simplicity and individual components of a meal.A typical Western meal might consist of a protein source such as meat or fish, accompanied by a starch like potatoes or rice, and vegetables. The Western approach to cooking often involves grilling, baking, or roasting, which highlights the natural flavors of the ingredients.One of the most striking differences between the two is the use of ingredients and the preparation methods. Chinese cooking relies heavily on a variety of spices and condiments, such as soy sauce, ginger, and garlic, to create depth and complexity in flavor. The art of stirfrying is aquintessential technique that allows for quick cooking while preserving the nutrients and flavors of the ingredients.On the other hand, Western cuisine often employs dairy products and butter, which impart a creamy texture and richness to dishes. The use of herbs like rosemary, thyme, and basil adds a distinct aroma and taste to Western dishes. Moreover, the practice of pairing food with wine in Western culture is a testament to the importance of enhancing the dining experience through complementary flavors.The dining experience itself is another area where East and West diverge. In Chinese culture, meals are often communal affairs, with multiple dishes shared among family and friends. This practice encourages social interaction and the enjoyment of a variety of flavors in one sitting. In contrast, Western meals tend to be more individualistic, with each person having their own plate and set of utensils.Furthermore, the concept of food as medicine is deeply ingrained in Chinese culture. Traditional Chinese medicine TCM often prescribes specific foods to balance ones bodys energy, or qi, and to prevent illnesses. This holistic approach to health and wellness is reflected in the Chinese diet, which emphasizes the consumption of whole, unprocessed foods and the avoidance of overly greasy or spicy dishes that may disrupt the bodys balance.In Western culture, while there is a growing awareness of the importance of a balanced diet, the focus is often more on individual nutritional needsrather than a collective approach to health. The rise of dietary trends and fads in the West, such as veganism and keto diets, reflects a more personalized approach to eating.In conclusion, the culinary traditions of the East and West offer a rich tapestry of flavors, techniques, and philosophies that enrich our global food culture. While Chinese cuisine emphasizes harmony, balance, and the use of spices, Western diets focus on simplicity, individual components, and the natural flavors of ingredients. The dining experience, use of ingredients, and approach to health and wellness all contribute to the unique characteristics of each culinary tradition. As we continue to share and learn from each others food practices, we can appreciate the diversity and depth of human culture through the universal language of food.。

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文档下载后可定制随意修改，请根据实际需要进行相应的调整和使用，谢谢!并且，本店铺为大家提供各种各样类型的实用资料，如教育随笔、日记赏析、句子摘抄、古诗大全、经典美文、话题作文、工作总结、词语解析、文案摘录、其他资料等等，如想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by theeditor. I hope that after you download them,they can help yousolve practical problems. The document can be customized andmodified after downloading,please adjust and use it according toactual needs, thank you!In addition, our shop provides you with various types ofpractical materials,such as educational essays, diaryappreciation,sentence excerpts,ancient poems,classic articles,topic composition,work summary,word parsing,copyexcerpts,other materials and so on,want to know different data formats andwriting methods,please pay attention!Jelly Making。

Jelly making is a fun and delicious activity that canbe enjoyed by people of all ages. It's a simple processthat involves turning fruit juice into a wobbly, gel-like substance that is a delight to eat. All you need is somefruit juice, gelatin, and a little bit of patience.First, you need to choose your fruit juice. You can use any kind of fruit juice you like apple, orange, grape, or even a combination of different juices. The choice is yours! Just make sure that the juice is pure and doesn't contain any added sugars or preservatives.Next, you need to heat the fruit juice in a saucepan until it's warm but not boiling. This will help to dissolve the gelatin and ensure that it sets properly. Once thejuice is warm, sprinkle the gelatin over the top and stirit in until it's completely dissolved.Now comes the fun part pouring the mixture into molds. You can use any kind of mold you like small cups, silicone molds, or even ice cube trays. Just make sure that the molds are clean and dry before you pour in the jelly mixture. Fill the molds almost to the top, leaving a little bit of space for the jelly to expand as it sets.Once you've filled the molds, you need to refrigerate them for at least a few hours, or until the jelly is set. This can take anywhere from two to four hours, depending on the size of your molds and the temperature of your refrigerator. It's best to leave the jelly in the fridge overnight to ensure that it's fully set.When the jelly is set, you can remove it from the molds and enjoy it! You can eat it as it is, or you can get creative and use it in other desserts. You can layer it with yogurt or whipped cream, or you can even chop it up and use it as a topping for ice cream or cake. The possibilities are endless!Jelly making is a great way to have fun in the kitchen and create a tasty treat at the same time. It's a versatile recipe that can be customized to suit your taste preferences, and it's a great way to use up any leftover fruit juice you may have. So why not give it a try? You won't be disappointed!。

The mysteries of the universe CosmicneutrinosCosmic neutrinos are one of the most intriguing mysteries of the universe. These elusive particles are produced in various cosmic events, such as supernovae, gamma-ray bursts, and even the Big Bang. They are incredibly small and nearly massless, making them difficult to detect. Despite their elusive nature, cosmic neutrinos play a crucial role in our understanding of the universe's most extreme phenomena. One of the most fascinating aspects of cosmic neutrinos is theirability to travel vast distances through space without being absorbed or deflected by matter. Unlike other particles, neutrinos interact very weakly with other matter, allowing them to travel through stars, planets, and even entire galaxies without being affected. This unique property makes them valuable messengers from the most distant and energetic events in the universe. The detection of cosmic neutrinos has opened up a new window into the universe, allowing scientists to study phenomena that were previously inaccessible. By observing cosmic neutrinos, scientists can learn more about the processes that occur in the most extreme environments, such as the cores of supernovae or the vicinity of black holes. This information can help us better understand the fundamental laws of physics that govern the universe. Despite their importance, cosmic neutrinos are incredibly challenging to detect. Because they interact so weakly with matter, they can pass through vast amounts of material without leaving a trace. This makes it difficult for scientists to capture and study cosmic neutrinos, requiring sophisticated detectors and observatories to catch these elusive particles in action. The study of cosmic neutrinos is a truly international effort, with scientists from around the world collaborating on experiments and observations. By working together, researchers can pool their resources and expertise to tackle the challenges of detecting and studying cosmic neutrinos. This collaborative approach has led to significant advancements in our understanding of these mysterious particles and the phenomena that produce them. In conclusion, cosmic neutrinos are afascinating and enigmatic aspect of the universe. Despite their elusive nature, these particles play a crucial role in helping us unravel the mysteries of thecosmos. By studying cosmic neutrinos, scientists can gain valuable insights into the most extreme events in the universe and deepen our understanding of the fundamental laws of physics. While the study of cosmic neutrinos presents many challenges, the collaborative efforts of researchers around the world continue to push the boundaries of our knowledge and bring us closer to unlocking the secrets of the universe.。

A watch is a timekeeping accessory that has been an integral part of our daily lives for centuries.It is not just a tool to tell time,but also a fashion statement and a symbol of status.Here is an introduction to watches in English:1.History of Watches:The concept of timekeeping devices dates back to ancient civilizations,but the modern wristwatch evolved in the19th century.Initially,watches were pocketsized,but as technology advanced,they became smaller and more portable, eventually leading to the wristwatch.2.Types of Watches:Watches come in various forms,including mechanical,quartz,and digital.Mechanical Watches operate through a complex system of gears and springs powered by a wound mainspring.Quartz Watches use a quartz crystal that vibrates at a constant frequency when an electric current is applied,making them highly accurate.Digital Watches display time in a digital format,often with additional features like alarms,timers,and even calculators.3.Functions of a Watch:Beyond telling time,watches can have additional functions such as:Date Display:Shows the day,date,or both.Chronograph:A stopwatch function,useful for measuring elapsed time.Moon Phase:Indicates the current phase of the moon.Tachymeter:A scale on the watchs bezel used to measure speed.4.Materials Used:Watches are made from a variety of materials,including stainless steel, gold,titanium,and even plastics.The choice of material can affect the watchs durability, weight,and appearance.5.Brands and Models:There are numerous watch brands,each with its own signature style and range of models.Some of the most renowned brands include Rolex,Omega, Patek Philippe,and TAG Heuer,each offering a wide array of models for different occasions and preferences.6.Cultural Significance:Watches are often associated with prestige and are given as gifts for milestones such as graduations,weddings,and anniversaries.They can also be a reflection of ones personality and taste.7.Maintenance:Proper care and maintenance are essential for a watch to function accurately and last long.This includes regular cleaning,avoiding exposure to extremetemperatures,and servicing by a professional every few years.8.Smartwatches:With the advent of technology,smartwatches have become popular. They combine the traditional timetelling function with features like fitness tracking, notifications,and even the ability to make phone calls.9.Customization:Many watch enthusiasts enjoy customizing their watches with different straps,bezels,or even engravings to make their timepiece unique.10.Collecting Watches:For some,watches are more than just accessories they are collectibles.Collectors often seek out rare or limitededition models,appreciating the craftsmanship and history behind each piece.In conclusion,watches are not only essential for keeping track of time but also serve as a form of selfexpression and a testament to the ingenuity of human engineering.Whether you prefer a classic analog watch or a cuttingedge smartwatch,there is a timepiece out there to suit every style and need.。