Theories of Neutrino Masses and Mixings

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Spontaneous R-Parity violation bounds

with gauginos which have the feature that they are sfermion-mass independent. Precision measurements of rare processes put rather strong constraints on such spontaneous R-breaking terms. These interactions appear in explicit bilinear breaking as soft dimensionful Higgslepton superﬁeld mixing parameter. In this work we study the phenomenological implications of spontaneous R-parity breaking in the supersymmetric Lagrangian. We analyse the general form of the gaugino-higgsinolepton mixing and set the most general bounds on the mixing elements based on rare treelevel and one-loop level processes. The advantage of setting bounds on the mixing elements lies in their generality: they apply to any supersymmetric model with spontaneous R-parity breaking, or even to a SUSYGUT scenario with an enriched gauge sector. Our paper is organized as follows: we describe and parametrize spontaneous R-parity breaking in section 2, then discuss tree-level constraints in section 3, one-loop level constraints in section 4, before reaching our conclusion in section 5.

The Neutrino World：中微子的世界

In such models, there are N > 3 i, and U is N x N, but still unitary.
11
Just as each neutrino of definite flavor is a superposition of mass eigenstates i, so each mass eigenstate is a superposition of flavors .
The mixing matrix U is 3 x 3 and unitary: UU† = U†U = 1.
Some models include “sterile” neutrinos — neutrinos that experience none of the known forces of nature except gravity.
2
These discoveries come from the observation of
neutrino oscillation.
3
The Physics of Neutrino Oscillation
4
Neutrinos Come in at Least Three Flavors
The known neutrino flavors:
8
Leptonic mixing —
le e, l , l
When W+ l+ + ,
e, , or
the produced neutrino state |> is
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TASI 2002 lectures on neutrinos

1
I.
INTRODUCTION
The success of the Standard Model (SM) can be seen as a proof that it is an eﬀective low energy description of Nature. We are therefore interested in probing the more fundamental theory. One way to go is to search for new particles that can be produced in yet unreached energies. Another way to look for new physics is to search for indirect eﬀects of heavy unknown particles. In this set of lectures we explain how neutrino physics is used to probe such indirect signals of physics beyond the SM. In the SM the neutrinos are exactly massless. This prediction, however, is rather speciﬁc to the SM. In almost all of the SM extensions the neutrinos are massive and they mix. The search for neutrino ﬂavor oscillation, a phenomenon which is possible only for massive neutrinos, is a search for new physics beyond the SM. The recent experimental indications for neutrino oscillations are indirect evidences for new physics, most likely, at distances much shorter than the weak scale. In the ﬁrst lecture the basic mechanisms for generating neutrino masses are described and the ingredients of the SM that ensure massless neutrinos are explained. Then, the neutrino oscillation formalism is developed. In the second lecture the current experimental situation is summarized. In particular, we describe the oscillation signals observed by solar neutrino experiments, atmospheric neutrino experiments and long baseline terrestrial neutrino experiments. Each of these results separately can be accounted for by a rather simple modiﬁcation to the SM. Trying to accommodate all of them simultaneously, however, is not trivial. In the third lecture we explain what are the theoretical challenges in trying to combine all the experimental indications for neutrino masses, and give several examples of models that cope with some of these challenges. These lecture notes are aimed to provide an introduction to the topic of neutrino physics. They are not meant to be a review. Therefore, many details are not given and many references are omitted. There are many textbooks [1] and reviews [2–4] about neutrinos. There is also a lot of information about neutrinos on the web [5, 6]. All these sources provide more detailed discussions with complete set of references on the topics covered in these lectures. Moreover, they also cover many subjects that are not mentioned here. In preparing the lectures I used mainly the recent review by Gonzalez-Garcia and Nir [4]. This review is a very good starting point to anyone who wants to learn more about neutrino physics.

Neutrino masses and mixings

a rXiv:h ep-ph/976301v19J un1997MITH-97/06Neutrino masses and mixings She-Sheng Xue ⋆INFN,Section of Milan,Via Celoria 16,Milan,Italy Physics Department,University of Milan,Italy Abstract We propose a novel theoretical understanding of neutrino masses and mix-ings,which is attributed to the intrinsic vector-like feature of the regularized Standard Model at short distances.We try to explain the smallness of Dirac neutrino masses and the decoupling of the right-handed neutrino as a free particle.Neutrino masses and mixing angles are completely related to each other in the Schwinger-Dyson equations for their self-energy functions.The solutions to these equations and a possible pattern of masses and mixings are discussed.May,1997PACS 11.15Ha,11.30.Rd,11.30.Qc1.Since their appearance,neutrinos have always been extremely peculiar. Their charge neutrality,near masslessness,ﬂavour mixing,and parity-violating coupling have been at the centre of a conceptual elaboration[1,2]and an in-tensive experimental analysis[3]that have played a major role in donating to mankind the beauty of the Standard Model(SM).In the present letter, we propose a novel theoretical understanding of neutrino masses and mix-ings in a left-right symmetric extension of the SM,inspired by the intrinsic vector-like feature of chiral gauge theories at high-energies.The notion of the vector-like feature stands for:given any conserved quantum numbers of chiral gauge symmetries of a regularized quantumﬁeld theory,there must be the exactly equal numbers of left-handed and right-handed fermions,and parity-conserving gauge couplings at short distances1. The feature is clearly phenomenologically unacceptable.However,it really implies right-handed neutrinos and parity-conserving gauge theories in short distances2.This calls for the left-right symmetric model(SU L(2)⊗SU R(2)⊗U B−L(1))[5],where parity is unbroken at high energies and its nonconser-vation at low-energies occurs through a spontaneous symmetry breakdown mechanism.The left-right symmetric extension that we suggest still possesses SU L(2)⊗U Y(1)gauge symmetries.The right-handed doublets are assigned to bound three-fermion states(i=e,µ,τ):ν3i i3 R;ν3iR∼(¯νR·νi L)νR,i3R∼(¯i R·i L)i R,(1) whereνR is a gauge singlet and a unique right-handed neutrino for three fam-ilies.These three-fermion states(1)carry the appropriate quantum numbers of the SU L(2)⊗U Y(1)gauge symmetries so that the SM gauge symmetries are preserved.We do not need new elementary gauge and fermionﬁelds for the SU R(2)sector.The neutrinoﬁelds(both elementary and composite(1)) considered in this letter are purely Weyl neutrinos.These three-fermion states can be formed[6]by eﬀective high-dimension operators of fermionicﬁelds,L h.d.o.,which are due to the underlying physicsat the cutoﬀΛ,L eﬀective=L SM+L h.d.o..(2) Before knowing what the dynamics of underlying physics is,a priori,we conceive that the possibilities for L h.d.o.are those allowed by the gauge sym-metries of the SM or other uniﬁcation models,e.g.,SO(10)[7,8].In order to consistently achieve parity-violation at low-energies,we pos-tulate that at an intermediate energy-thresholdǫ:250GeV≪ǫ<Λ,(3) the three-fermion states(1)dissolve into their constituents,i.e.turn into the virtual states of their constituents(three-fermion cuts).This is due to the vanishing of the binding energy of three-fermion states(1)at the thresholdǫ(3)[6].This phenomenon could be realized on the basis that the eﬀective high-dimension operators for binding the three-fermion states are momentum-dependent.However,it is diﬃcult to demonstrate this dynamics, since it relates to a non-perturbative issue ofﬁnding the inferredﬁx point and determining the spectrum and relevant high-dimension operators that realize the symmetries.It should be pointed out that this phenomenon is not spontaneous symmetry breaking and no Goldstone bosons occur.In this letter,we consider the above extension of the SM as a model instead of a demonstrated theory.For the purpose of studying neutrino masses and mixings,we only discuss the three-fermion state(1)and disregard the U B−L(1)symmetry.Presumably,the spectrum of right-handed three-fermion states should be much richer than(1),so as to preserve chiral gauge symmetries of a uniﬁed theory.2.νR couples to other fermions via L h.d.o.in(2).The1PI(one-particle irreducible)vertices betweenνR andνi L give Dirac neutrino masses.Rather than the Sea-Saw mechanism[8],we discuss another possible dynamics for decouplingνR and small Dirac neutrino masses.We assume,the couplings ofνR low-frequency modes(p≪Λ)to other fermions are suppressed by pΛ 2. Thus,at low-energies,νR decouples from other fermions,as a result,Dirac neutrino masses are very small andνR is a free particle.On the other hand,2νR high-frequency modes(250GeV≪ǫ<p<Λ)couple strongly enough to other fermions to form three-fermion states(1).This is equivalent to assuming that L h.d.o.(2)possess the followingνR shift-symmetry[9],νR(x)→νR(x)+δ,(4) whereδis a constant.The decoupling ofνR can be shown by the Ward identities of this shift-symmetry[6],γµ∂µν′R(x)+ ∂µδ¯ν′R(x)=0,(5)where“Γ”is the eﬀective potential with non-vanishing external sources(J,η); the externalﬁeldν′R≡ νR ,and ˆO(x) is the expectation value of the operatorˆO w.r.t.the generating functional Z[J,η].Based on this Ward identity,we can get all1PI vertices containing at least one externalν′R.Theﬁrst are the self-energy functionsΣνi (p)(i=e,µ,τ)of neutrinos.Performing a functional derivative of eq.(5)w.r.t.the primedﬁeldν′i L(0)and then putting external sourcesη=J=0,we obtain,∂µδν′iL (0)δ¯ν′R(x)=0,(6)where ˆO i(x) ◦≡ ˆO i(x) |J=η=0,and as a result,x e−ipxδ2Γ2Σi(p)= p2µδν′αR(0)δ¯ν′βR(x)=0.(8) The two-point function is then given by,x e−ipxδ(2)Γindicating thatνR does not receive wave-function renormalization Z3.The third are the n-point(n>2)1PI interacting vertices.Analogously, we can obtain,δ(n)ΓΛ2 ,n>2.(10) whereδ(n−1)indicates(n−1)derivatives w.r.t.other externalﬁelds.These three identities,eqs.(7,9)and(10),show us two conclusions owing to theνR shift-symmetry(or onlyνR high-frequence modes coupling to other fermions):(i)the Dirac neutrino masses due to high-dimension operators (L h.d.o.)are extremely small;(ii)the right-handed neutrinoνR at low-energies is a free particle and decouples from other physical particles.3.Once the soft spontaneous symmetry breaking occurs at the weak scale, the right-handed fermion states are the mixed states comprising the elemen-tary stateνR(i R)and the composite stateν3iR(i3R)(i=e,µ,τ):Ψνi R=(νR,ν3iR);Ψi R=(i R,i3R).(11)The self-energy functionsΣνi (p)(Σi(p))of neutrinos(charged leptons)arecouplings betweenνi L(i L)and mixing right-handed fermion statesΨνi R(Ψi R), rather than the couplings between only elementary statesνi L(i L)andνR(i R)in the SM.This will become very clear in the Schwinger-Dyson(SD)equations for the self-energy functions.For the reason that the three-fermion states(1)carry the SU L(2)quantum number,there must be an interacting1PI vertex between W±,Z◦bosons and composite right-handed fermions(1)in the high-energy region.We may write this eﬀective1PI coupling for W±as,Γijµ(q)=i g22V ijγµ(P L+f(q))(12)f(q)=0,q≥ǫ,(13) where g2is the SU L(2)coupling and V ij is the CKM matrix[10],and that for the Z◦is similar.At the energy threshold(3),where the three-fermion states dissolve into their constituents,the eﬀective1PI vertex function f(q) must vanish,f(q)|q→ǫ+0+→0,(14)4which results in the parity-violating gauge-couplings in low-energies.In L h.o.d.of the eﬀective lagrangian(2),we may have following gauge-invariant operators interacting between up quarks(q u i=u,c,t)and neutri-nos,and between down quarks(q d i=d,s,b)and charged leptons(i=e,µ,τ),G¯ψβiL(x)· ∂2µΛ2 Σq u i(Λ),(17)Σ◦i(Λ)=Σq di(Λ),(18) where we are henceforth in the basis of mass eigenstates.Eq.(17)shows thatthe neutrinoΣ◦νi (p)decouples from the quarkΣq ui(Λ)for p≪Λ,which agreeswith(7).Eq.(18)is reminiscent of the predictions in the SU(5)uniﬁcation model[12].It should be pointed out that there are other possible gauge-invariant four-fermion interactions and their corresponding tadpole diagrams contribute to eqs.(17,18)as well.We consider all such contributions to eqs.(17,18)as lep-ton’s bare masses at the cutoﬀ,which are actually explicit symmetry breaking terms in the full SD equations(19,20).4.Turning on all gauge interactions,we study the full SD equations for the lepton self-energy functions.In the rainbow approximation and the Landau gauge,these equations can be written as,Σνi (p)=Σ◦νi(p)+Zνi(p)+Wνi(p),(19)Σi(p)=Σ◦i(Λ)+Z1i(p)+Z3i(p)+W i(p)+γi(p),(20)whereγi(p)=3e2 Λp′1p′2+Σ2i(p′2)(21)Z1i(p)=3λ2 Λp′1p′2+Σ2i(p′2),(22)λ=g2tgθw(sin2θw−12√(p−p′)2+M2wΣj(p′2)2cosθw 2 Λ|p′|≥ǫf(p′−p)p′2+Σ2νi(p′2);(24)W i(p)= g22 2|V ij|2 Λ|p′|≥ǫf(p′−p)p′2+Σ2νj(p′2),(25) Z3i(p)= g2cos2θw(p−p′)2+M2zΣi(p′2)where αw (p )≃ g 22 2 Λ|p ′|≥ǫf (p ′−p )p ′2.(28)In the high-energy region (x =p 2>ǫ≫1),where M2w ,M2z and nonlin-earity are negligible,the SD integral equations (19,20)can be converted to the following boundary value problems 4,d 4Σνi (x )=0,(29)Λ2Σ′νi (Λ2)+Σνi (Λ2)=Σ◦νi (Λ)+αw (Λ)|V ij |2Σj (Λ);(30)d 4Σi (x )=0,(31)Λ2Σ′i (Λ2)+Σi (Λ2)=Σ◦i (Λ)+αw (Λ)|V ij |2Σνj (Λ),(32)where f n ,f c are perturbative functions of electroweak couplings.These are diﬀerential equations with the inhomogeneous boundary conditions at the cutoﬀ.The generic solutions to eqs.(29,31)for (x ≫1)are given by,Σνi (x )≃A νi µ2x sinh 11−f n ℓn (x√2 µ2) ,(34)where A νi ,A i are arbitrary constants and µis an inferred scale.Substituting(33)into (30)and (34)into (32)in the low-energy limit (µ≪Λ),we obtain the gap-equations:αw (Λ)|V ij |2Σj (Λ)=122Σi (Λ)+11−f c Σi (Λ)−Σ◦i (Λ).(36)Since the lepton bare masses (17,18)are deﬁned when all gauge interactions are turned oﬀ,we can rewrite the RHS of the gap-equations (35,36),αw (Λ)|V ij |2Σj (Λ)=−f n4Σi (Λ).(38)As a consequence of the gap-equations(35,36),the lepton self-energy functions must be non-trivial(Λ)=0;andΣj(Λ)=0,(39)Σνiif quarks are massive.The gap-equations(18)strongly imply that the hier-archical pattern of charged lepton masses is mainly due to the hierarchical pattern of down quark masses.Eqs.(37,38)show that the pattern of neutrino masses is determined by the CKM-mixing angles and charged lepton masses.6.The six gap-equations(37,38)relate neutrino and charged lepton masses at the cutoﬀ.Noticing the fact thatΣ(p)must be continuous functions of “p”from p=Λto p≪ǫfor the locality of quantumﬁeld theories,and the ratios ofΣ(p)’s in the same charge sector(but diﬀerent generations)should be scale invariant(renormalization group invariant),we take ratios between the two equations of eqs.(37),the two equations of eqs.(38)respectively and scale them down to the low-energy scale.We end up with four independent equations:mνe|Vνµe|2m e−|Vνµµ|2mµ+|Vνµτ|2mτ,(40)mνµ|Vντe|2m e−|Vντµ|2mµ+|Vνττ|2mτ,(41) andm e|Vµνe|2mνe−|Vµνµ|2mνµ+|Vµντ|2mντ,(42) mµ|Vτνe|2mνe−|Vτνµ|2mνµ+|Vτντ|2mντ.(43) In these equations,all fermion masses are deﬁned at the same low-energy scale.We make an appropriate chiral rotation in the second family and all fermion masses are positive.Given charged lepton masses,four relation-ships satisﬁed by four mixing angles and three neutrino masses,which are no longer seven free parameters.These equations give a class of solutions for the possible patterns of neutrino masses and mixing angles.8Setting θ13=0so that θ13and δ13decouple from eqs.(40-43),and assum-ing m νe ≪m νµ≪m ντ,we get a possible pattern:tg 2θ12=m e m ντ ,m νe ∼sin 2θ13=0,(44)sin 2θ23=m µ+m em ντ ,m νµongoing and future neutrino experiments.References[1]A.Yu.Smirnov,Review talk presented at the Neutrino’96,Helsinki;hep-ph/(in the proceedings),references therein.[2]R.N.Mohapatra,invited talk presented at the Neutrino’96,Helsinki;hep-ph/(in the proceedings),references therein.[3]J.Ellis,invited talk presented at the conclusion of the Neutrino’96conference,Helsinki;hep-ph/9612209(in the proceedings),references therein.[4]H.B.Nielsen and M.Ninomiya,Nucl.Phys.B185(1981)20,ibid.B193(1981)173,Phys.Lett.B105(1981)219.[5]J.C.Pati and A.Salam,Phys.Rev.D10(1975)275;R.N.Mohapatra and P.C.Pati,ibid D11(1975)566;D11(1975)2558;G.Senjanovi´c and R.N.Mohopatra,Phys.Rev.D12(1975)1502;R.N.Mohopatra and G.Senjanovi´c,Phys.Rev.D23(1981)165and Phys.Rev.Lett.44(1980)912.[6]S.-S.Xue,Phys.Lett.B381(1996)277,Nucl.Phys.B486(1997)282.[7]H.Georgi and D.V.Nanopoulos,Nucl.Phys.B155(1979)52.[8]RM.Gell-Mann,P.Ramond,and R.Slansky in Supergravity,edited byD.Freedman st al.(1979);R.N.Mohapatra and G.Senjanovi´c,Phys.Rev.Lett.44(1980)912, Phys.Rev.D23(1981)165.[9]M.F.L.Golterman and D.N.Petcher,Phys.Lett.B225(1989)159.[10]Review of Particle Physics,Phys.Rev.D54(1996)1.[11]W.A.Bardeen,C.T.Hill and M.Linder,Phys.Rev.D41(1990)1647.[12]H.Georgi and S.L.Glashow,Phys.Rev.Lett.32(1974)438.10[13]A.Koci´c,S.Hands,B.Kogut and E.Dagotto,Nucl.Phys.B347(1990)217,references therein.[14]S.-S.Xue,Phys.Lett.B398(1997)177.11。

ASTROPHYSICAL IMPLICATIONS OF NEUTRINO MASS AND MIXINGS

dubbed the Mikheyev-Smirnov-Wolfenstein (MSW) e ect, does not require ne-tuning of mass di erences and mixing angles and could possibly provide an elegant solution to the solar neutrino problem within current theoretical prejudices 13, 14]. The non-adiabatic MSW solution with m2 10?5 eV2 and sin 0:1 is consistent with the data from those four experiments. This MSW solution is still plausible after incorporating the uncertainties in the solar model 15]. An astrophysical solution for the solar neutrino problem is unlikely, but still not ruled out 15, 16]. Solar neutrinos are not the only experimental probes of the sun. Information from helioseismological p-wave observations complement information obtained by solar neutrino experiments. The p-waves cause the solar surface to vibrate with a characteristic period of about ve minutes. By observing red- and blue-shifts of patches of the solar surface, projecting them on spherical harmonics, and nally Fourier transforming with respect to the observation time one can obtain eigenfrequencies of the solar p-modes. (One should exercise a little bit of caution with regard to using spherical harmonics, since we only observe half the sun). For very high overtones (for a spherically-symmetric three-dimensional object such as the sun these are characterized by two large integers), the equations describing p-modes simplify 17] and one can reliably obtain a sound velocity pro le for the outer half of the sun. The sound density pro le obtained this way agrees with the predictions of the standard solar model. By studying discontinuities in the sound velocity pro le, it is also possible to reliably extract the location of the bottom of the convective zone 18].

Neutrino Mass Spectrum and Future Beta Decay Experiments

. Yu. Smirnov
c,d ‡
Scuola Internazionale superiore di Studi Avanzati via Beirut 4, I,34014 Trieste, Italy
b
Instituto de F´ ısica Gleb Wataghin, Universidade Estadual de Campinas, UNICAMP 13083-970 Campinas SP, Brazil The Abdus Salam International Centre for Theoretical Physics, I-34100 Trieste,Italy
hep-ph/0105105 February 1, 2008
Neutrino Mass Spectrum and Future Beta Decay Experiments
arXiv:hep-ph/0105105v3 26 May 2001
Y. Farzan
a
a ∗
, O. L. G. Peres
spectrum, one can put an upper bound on the neutrino mass assuming, however, that there is no conspiracy which leads to cancellation of diﬀerent eﬀects [4]. Therefore independent measurements of the neutrino mass are needed and their results will be used in the analysis of the cosmological data as an input deduced from particle physics. Several methods have been proposed to determine neutrino masses by using the supernova neutrino data. One method is based on searches for the energy ordering of events which has, however, rather low sensitivity [5]. The limits on the mass can be also obtained from observations of sharp time structures in the signals. It was suggested to study the time distribution of detected neutrino events emitted from supernova which entails to black hole formation [6]. By this method Super-Kamiokande can measure values of the νe mass down to 1.8 eV and SNO can put an upper bound 20 eV on the νµ and ντ masses [6] . (Clearly this bound on the νµ and ντ masses is much weaker than bounds implied by combined analysis of the solar and atmospheric neutrino data and direct measurements of the νe mass.) In this case one can check the still non-excluded possibility in which the solar neutrino problem is solved by the oscillations to sterile neutrino and the masses of νµ and ντ are in 20 eV range. (Such neutrinos should be unstable in cosmological time.) The absolute values of the neutrino masses can be determined in the assumption that the cosmic rays with energies above the GZK cutoﬀ are produced in annihilation of the ultra-high energy neutrinos with the cosmological relic neutrinos [7, 8, 9]. The analysis of the observed energy spectrum of cosmic rays above 1020 eV gives the mass mν = (1.5 − 3.6) eV, if the power-like part of the ultra-high energy cosmic rays spectrum is produced in Galactic halo, and mν = (0.12 − 0.46) eV, if this part has the extragalactic origin [10]. Neutrinoless double beta decay (2β 0ν ) searches are sensitive to the Majorana mass of the electron neutrino. However, in the presence of mixing the situation can be rather complicated: The eﬀective Majorana mass of νe relevant for the 2β 0ν -decay, mee , is a combination of mass eigenvalues and mixing parameters given by mee =

An origin for small neutrino masses in the NMSSM

s: abada@th.u-psud.fr E-mail address: greg@cftp.ist.utl.pt
1
I
Introduction
The most severe theoretical drawback of the Standard Model (SM) is probably the gauge hierarchy problem (see for example [1]). In well deﬁned supersymmetric extensions of the SM, the property of cancellation of quadratic divergences allows to address this problem. With regard to the ﬁeld content, the most economical candidate for such a realistic extension is the Minimal Supersymmetric Standard Model (MSSM). Nevertheless, within the MSSM, there are two unexplained hierarchies. The ﬁrst one is intrinsic to supersymmetric models: it is named as the µ problem [2]. It arises from the presence of a mass (µ) term for the Higgs ﬁelds in the superpotential. The only two natural values for this µ parameter are either zero or the Planck energy scale. While the former value is excluded by experiments as it gives rise to the unacceptable existence of an axion, the latter one reintroduces the gauge hierarchy problem. The other hierarchy with an unknown origin is the one existing between the small neutrino masses and the electroweak symmetry breaking scale (∼ 100GeV). Indeed, during last years, neutrino oscillation experiments have conﬁrmed that neutrinos are massive. Furthermore, the additional results, extracted from tritium beta decay experiments and cosmological data, indicate that the values of absolute neutrino masses are typically smaller than the eV scale. In this paper, we propose a supersymmetric scenario which has the virtue of addressing simultaneously both of these hierarchy questions: the µ value naturalness and the neutrino mass smallness. A nice feature of our scenario is that the mechanisms explaining the two hierarchy origins are connected, since they involve the same additional gauge-singlet superﬁeld, providing thus a common source to the solutions of these two independent problems. Our framework is the Next to Minimal Supersymmetric Standard Model (NMSSM) [3] 1 . The NMSSM provides an elegant solution to the µ problem through the introduction of a new gauge-singlet superﬁeld S entering the scale invariant superpotential. The scalar component of S acquires naturally a Vacuum Expectation Value (VEV) of the order of the supersymmetry breaking scale, generating an eﬀective µ parameter of order of the electroweak scale. Another appealing feature of the NMSSM is to soften the “little ﬁne tuning problem” of the MSSM [5]. The introduction of suitable non-renormalizable operators [6] can avoid the possibility of a cosmological domain wall problem [7]. There exist diﬀerent explanations for a µ value of order of the electroweak scale, but those arise in extended frameworks. In supersymmetric extensions of the SM, there exist coupling terms violating the so-called R-parity symmetry [8, 9] which acts on ﬁelds like (−1)3B +L+2S , B , L and S being respectively the Baryon number, Lepton number and Spin. From a purely theoretical point of view, these terms must be considered, even if some phenomenological limits apply on the R-parity violating (Rp ) coupling constants [10, 11, 12, 13, 14]. As a matter of fact, these terms are supersymmetric, gauge invariant and some of them are renormalizable. Moreover, from the points of view of scenarios with discrete gauge symmetries [16], Grand Uniﬁed Theories (GUT) [17]-[18] as well as string theories [23], there exists no fundamental argument against the violation of the R-parity symmetry [10]. In the present work, we consider the ‘bilinear’ R-parity violating term Hu L appearing in the superpotential, Hu and L being respectively the up Higgs and lepton doublet superﬁelds. The existence/inﬂuence of the other Rp terms will also be discussed. This bilinear interaction has been recently considered within the NMSSM context [15]. In particular, this type of interaction, which breaks the lepton number, mixes the higgsino and neutrinos together so that the neutrino ﬁeld picks up a Majorana mass [24] (the generation of such a neutrino mass requires two units of L violation). Hence, no additional right

Can neutrinos be unified with quarks

邓建儒 2012141441300 电气信息学院
Can neutrinos be unified with quarks ?
邓建儒 2012141441300 电气信息学院 In my opinion, neutrinos cannot be unified with quarks.
Neutrino
1. Theories about neutrino: Pauli's proposal The neutrino was postulated first by Wolfgang Pauli in 1930 to explain how beta decay could conserve energy, momentum, and angular momentum (spin). Pauli hypothesized an undetected particle that he called a "neutron" in keeping with convention employed for naming both the proton and the electron, which in 1930 were known to be respective products for alpha and beta decay. He considered that the new particle was emitted from the nucleus together with the electron or beta particle in the process of beta decay. Fermi’s theory Enrico Fermi, who developed the theory of beta decay, coin

Zee Neutrino Mass Model in SUSY Framework

The above two neutrino-mass diﬀerences can be accommodated by the three species of neutrinos that we know from the SM. There is also another indication for neutrino oscillation from the accelerator experiment at the Liquid Scintillation Neutrino Detector (LSND) [3], which requires an oscillation of νµ into another neutrino with

0 meµ meτ , m 0 ǫ eµ meτ ǫ 0

(2)
where ǫ is small compared with meµ and meτ , is able to provide a compatible mass pattern that explains the atmospheric and solar neutrino data. The generic Zee model guarantees the vanishing of the diagonal elements, while the suppression of the mµτ entry, here denoted by the small parameter ǫ, has to be otherwise enforced. Moreover, meµ ∼ meτ is required to give the maximal mixing solution for the atmospheric neutrinos. We shall describe the features in more detail in the next section. So far the Zee model is not embedded into any grand uniﬁed theories or supersymmetric models. Here we analyze the embedding of the Zee model into the minimal supersymmetric standard model (MSSM) with minimal extensions, namely, the R-parity violation. The righthanded sleptons in SUSY have the right quantum number to play the role of the charged Zee scalar. The R-parity-violating λ-type couplings (λLLE ) could provide the terms in Eq.(1). It is also easy to see that the R-parity-violating bilinear µ-type couplings (µi LH2 ) would allow the second Higgs doublet H2 in SUSY to be the second ingredient of the Zee model. So far so good. However, the SUSY framework dictates extra contributions to neutrino masses, which deviate from the texture of the Zee mass matrix of Eq. (2). The major objective of this paper is to address the feasibility of the embedding and to determine under what conditions could one make a supersymmetric Zee model within the R-parity-violating SUSY framework while retaining the successful ﬂavor of the former. We will also discuss brieﬂy more generic versions of supersymmetric Zee model. There is also a study of Zee mass matrix within the framework of gauge-mediated SUSY breaking with the messenger ﬁeld as the Zee singlet [7]. In R-parity-violating SUSY, there are three other sources for neutrino masses, in addition to the Zee model contribution. They are (i) the tree-level mixing with the higgsinos and gauginos, (ii) the one-loop diagram that involves the usual mass mixing between the lefthanded and right-handed sleptons proportional to mℓ (AE − µ tan β ), and (iii) the one-loop ℓ 3

Supersymmetric Neutrino Masses and Mixing with R-parity Violation

[9] [5, 10] [7]
(1) (2) (3)
With ordinary three neutrinos, any two of the mass-squared diﬀerences in the above equations can be obtained: that is, those corresponding to (i) solar and atmospheric (S+A), (ii) solar and LSND (S+L), or (iii) atmospheric and LSND (A+L) neutrino data. For (S+A), the LSND result has to be disregarded. In the case of (S+L) or (A+L), the presence of a sterile neutrino is necessary for the explanation of the atmospheric or solar neutrino experiment, respectively. One of the desirable features of the supersymmetric extension of the standard model would be the generation of small neutrino masses within its context, as the supersymmetric standard model with the minimal particle content (MSSM) allows for the lepton (L) and baryon number (B) violating operators. In order to ensure the longevity of a proton, one usually assumes the conservation of R-parity, forbidding both (renormalizable) B and L violating operators. As a consequence, the lightest supersymmetric particle (LSP) is stable and thus cold dark matter of the universe may consist of neutral LSP’s. However, there is no obvious theoretical reason why R-parity needs to be conserved, or why both B and L conservation have to be imposed. L-violation would be present in the MSSM and it may be the origin of nonzero neutrino masses and mixing that explain current experimental data, while proton stability is ensured by B conservation alone. The L-violating operators in the MSSM are µi Li H2 ,

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UMD-PP-00-014
Theories of Neutrino Masses and Mixings
R. N. Mohapatra∗
Departmentof P hysics, U niversityof M aryland, CollegeP ark, M D20742, U SA (October, 1999)
I. INTRODUCTION
History of weak interaction physics has to a large extent been a history of our understanding of the properties of the elusive spin half particles ed the neutrinos. Evidence for only lefthanded neutrinos being emitted in beta decay was the cornerstone of the successful V-A theory of weak interactions suggested by Sudarshan, Marshak, Feynman and Gell-Mann; evidence for the neutral current interactions in early seventies provided brilliant conﬁrmation of the successful gauge uniﬁcation of weak and electromagnetic interactions proposed by Glashow, Salam and Weinberg. Today as we enter a new millenium, we again have evidence for a very important new property of the neutrinos i.e. they have mass and as a result like the quarks, they mix with each other and lead to the phenomenon of neutrino oscillation. This is contrary to the expectations based on the standard model as well as the old V-A theory (in fact one may recall that one way to make the V-A theory plausible was to use invariance of the weak Lagrangian under the so called γ5 invariance of all fermions, a principle which was motivated by the assumption that neutrinos have zero mass). The simple fact that neutrino masses vanish in the standard model is proof that its nonzero mass is an indication of new physics at some higher scale (or shorter distances). Study of details of neutrino masses and mixings is therefore going to open up new vistas in our journey towards a deeper understanding of the properties of the weak interactions at very short distances. This no doubt will have profound implications for the nature of the ﬁnal theory of the particles, forces and the universe. We are of course far from a complete picture of the masses and mixings of the various neutrinos and cannot therefore have a full outline of the theory that explains them. However there exist enough information and indirect indications that constrain the masses and mixings among the neutrinos that we can see a narrowing of the possibilities for the theories.
arXiv:hep-ph/9910365v2 27 Oct 1999
Abstract
Recent developments in our understanding of neutrino masses and their implications for physics beyond the standard model are reviewed.
II. NEUTRINO MASS IS DIFFERENT FROM ELECTRON MASS
The electron and the neutrino are in many ways very similar particles: they are both spin half objects; they both participate in weak interactions with same strength; in fact they are so similar that in the limit of exact gauge symmetries they are two states of the same object and therefore in principle indistinguishable. Yet there are profound diﬀerences between them in the standard model: after gauge symmetry breaking, only electron has electric charge. Another diﬀerence is that only the lefthanded neutrino is included in the standard model and not its righthanded counterpart; this is unlike the electron both whose helicity states are included. In fact it is this property of the standard model coupled with B − L being an exact symmetry which leads to neutrino remaining massless to all orders in perturbation theory as well as after the inclusion of nonperturbative eﬀects. The fact that the neutrino has no electric charge endows it with certain properties not shared by other fermions of the standard model such as the quarks and the electron (all of whom are electrically charged). The point is that for neutral fermions one can write two kinds of Lorentz invariant mass terms, the Dirac and Majorana masses, whereas for the charged fermions, conservation of electric charge allows only the Dirac type mass terms. In ¯ , whereas the the four component notation for the fermions, the Dirac mass has the form ψψ T −1 Majorana mass is of the form ψ C ψ , where ψ is the four component spinor and C is the charge conjugation matrix. One can also discuss the two diﬀerent kinds of mass terms using the two component notation for the spinors. If we denote by χ and φ the two two-component spinors which make up the four component object ψ , then a Dirac mass is χT σ2 φ whereas a Majorana mass is given by χT σ2 χ, where σa are the Pauli matrices. To make correspondence with the four component notation, we point out that χ and iσ2 φ∗ are nothing but the ψL and ψR respectively. It is then clear that χ and φ have opposite electric charges; therefore the Dirac mass χT σ2 φ maintains electric charge conservation (as well as any other kind of charge like lepton number etc.). This richness in the possibility for neutrino masses also has a down side in the sense that in general, there are more parameters describing the masses of the neutrinos than those for the quarks and leptons. For instance for the electron and quarks, dynamics (electric charge 2