SLAC-PUB-8173 June 1999 Neutrino masses and sneutrino mixing in R-parity violating supersymmetry Yuval Grossmana and Howard E.. Haberb aStanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 bSanta Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064 Invited talk presented at American Physical Society (APS) Meeting of the Division of Particles and Fields (DPOF 99), 1/5/99—1/9/99, Los Angeles, CA, USA Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 Work supported by Department of Energy contract DE–AC03–76SF00515. SLAC-PUB-8173 SCIPP-99/24 hep-ph/yymmnnn June, 1999 Neutrino masses and sneutrino mixing in R-parity violating y sup ersymmetry a b Yuval Grossman and Howard E. Hab er a Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 b Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064 Abstract R-parity-violating sup ersymmetry with a conserved baryon number B pro- vides a framework for particle physics with lepton number L violating in- teractions. Two imp ortant prob es of the L-violating physics are neutrino masses and sneutrino-antisneutrino mass-splittings. Weevaluate these quan- tities in the context of the most general CP-conserving, R-parity-violating B -conserving extension of the minimal sup ersymmetric standard mo del. In generic three-generation mo dels, three sneutrino-antisneutrino mass splittings are generated at tree-level. In contrast, only one neutrino mass is generated at tree-level; the other two neutrinos acquire masses at one-lo op. In many mo dels, the dominant contribution to the radiative neutrino masses is induced by the non-zero sneutrino-antisneutrino mass splitting. Invited talk presented by Yuval Grossman at the American Physical So ciety APS meeting of the division of particles and elds DPF99. y YG is supp orted by the U.S. Department of Energy under contract DE-AC03-76SF00515, and HEH is supp orted in part by the U.S. Department of Energy under contract DE-FG03-92ER40689. 1 I. INTRODUCTION The solar and atmospheric neutrino anomalies provide strong indications that the neutri- nos are massive. In particular, the data suggest that there is near-maximal mixing b etween and but that their masses are hierarchically separated [1]. To accommo date this data, the Standard Mo del must be extended, either by intro ducing right-handed neutrinos or by adding Ma jorana neutrino mass terms that violate lepton number by two units. In low-energy sup ersymmetric extensions of the Standard Mo del, lepton number and baryon numb er conservation is not automatically resp ected by the most general set of renor- malizable interactions. However, the constraints on baryon number violation are extremely severe in order to avoid fast proton decay. If one wants to enforce lepton numb er and baryon number conservation in the tree-level sup ersymmetric theory, it is sucient to imp ose one extra discrete symmetry. In the minimal sup ersymmetric standard mo del MSSM, a mul- tiplicative symmetry called R-parity is intro duced, where the R quantum number of an [3B L+2S ] MSSM eld of spin S , baryon number B and lepton number L is given by 1 . By intro ducing this symmetry, one eliminates all dimension-four lepton numb er and baryon numb er-violating interactions. Ma jorana neutrino masses can be generated in an R-parity- conserving extension of the MSSM involving new L = 2 interactions through the sup er- symmetric see-saw mechanism [2,3]. Such L = 2 interaction have an imp ortant impact on sneutrino phenomena [3{5]. The sneutrino ~ and antisneutrino ~, which are eigenstates of lepton numb er, are no longer mass eigenstates. The mass eigenstates are therefore sup erp ositions of ~ and ~, and sneutrino mixing e ects can lead to a phenomenology analogous to that of K { K and B { B mixing. The mass splitting between the two sneutrino mass eigenstates is related to the magnitude of lepton number violation, which is typically characterized by the size of neutrino masses. In some cases the sneutrino mass splitting may b e enhanced by a factor as 3 large as 10 compared to the corresp onding neutrino mass [3,6]. As a result, the sneutrino mass splitting is exp ected generally to b e very small. Yet, it can b e detected in many cases, if one is able to observe the lepton number oscillation [3]. The primary motivation for intro ducing a conserved R-parity ab ove was to imp ose a conserved baryon number to avoid fast proton decay. However, this can also be achieved in low-energy sup ersymmetric mo dels where B is conserved but L is violated so that R- parity is also violated. In this pap er, we fo cus on the B -conserving R-parity-violating RPV extension of the MSSM. In such a mo del, neutrinos are massive [7{11] and sneutrino{ antisneutrino pairs are no longer mass-degenerate [3{5]. In Section I I, weintro duce the most general RPV extension of the MSSM with a conserved baryon number and establish our notation. In Section I I I, we showhow a tree-level mass for one neutrino is generated due to neutrino{neutralino mixing. In Section IV, we exhibit how tree-level mass splittings for the three sneutrino{antisneutrino pairs are generated due to sneutrino{Higgs b osons mixing. In Section V, we calculate the neutrino masses generated at one lo op. In Section VI, we argue that in many mo dels, the dominant contribution to the one-lo op neutrino masses is induced by the non-zero sneutrino{antisneutrino mass splittings. A brief summary and conclusions are given in Section VI I. 2 II. R-PARITY VIOLATION FORMALISM In RPV low-energy sup ersymmetry, there is no conserved quantum number that distin- ^ ^ guishes the lepton sup ermultiplets L and the down-typ e Higgs sup ermultiplet H . Here, m D m is a generation lab el that runs from 1 to 3. Each sup ermultiplet transforms as a Y = 1 weak doublet under the electroweak gauge group. It is therefore convenient to denote the ^ four sup ermultiplets by one symbol L =0;1;2;3. The Lagrangian of the theory is xed by the sup erp otential and the soft-sup ersymmetry-breaking terms. The most general renormalizable sup erp otential resp ecting baryon number is given by: h i j j i i 0 i j i j 1 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ L H + W = ; 1 L L E + L Q D h H Q U ij m m m nm m U nm n U n 2 ^ ^ where H is the up-typ e Higgs sup ermultiplet, the Q are doublet quark sup ermultiplets, U n ^ ^ ^ U [D ] are singlet up-typ e [down-typ e] quark sup ermultiplets and the E are the sin- m m m glet charged lepton sup ermultiplets. Our notational conventions follow those of ref. [4]. Without loss of generality, the co ecients are taken to be antisymmetric under the m interchange of the indices and . Note that the -term of the MSSM is now extended to an 4-comp onentvector, . Then, the trilinear terms in the sup erp otential prop ortional 0 to and contain lepton numb er violating generalizations of the down quark and charged lepton Yukawa matrices. Next, we consider the most general set of renormalizable soft-sup ersymmetry-breaking terms. In addition to the usual soft-sup ersymmetry-breaking terms of the R-parity- conserving MSSM, one must also add new A and B terms corresp onding to the RPV terms of the sup erp otential. In addition, new RPV scalar squared-mass terms also exist. As ab ove, we can streamline the notation by extending the de nitions of the co ecients of the R-parity-conserving soft-sup ersymmetry-breaking terms to allow for an index of typ e which can run from 0 to 3 while Latin indices m and n run from 1 to 3. Explicitly, 2 i i 2 2 f f e e e e D D U U +M Q Q +M V =M mn n mn n mn soft m m m n e e e D U Q j 2 2 i i i 2 2 e e e e ~ E E + m jH j b L H +h:c: L L +M +M mn n U ij m U U e e E L j j i j i 0 i 1 e e f e e e e e U +h:c:] + [ Q D a H Q L L E + a a L m ij m U nm m m n U n nm 2 i h a a 1 f e e f ee + W +M BB +h:c: : 2 M gg +M W 1 3 2 2 Note that the single B term of the MSSM is extended to a 4-comp onentvector b , and the squared-mass term for the down-typ e Higgs b oson and the 3 3 lepton scalar squared-mass matrix are combined intoa44 matrix. In addition, the matrix A-parameters of the MSSM are extended in the obvious manner [analogous to the Yukawa coupling matrices in eq. 1]; in particular, a is antisymmetric under the interchange of and . It is sometimes m convenient to follow the more conventional notation in the literature and de ne the A and B parameters as follows: a A ; a h A ; m m E m U nm nm U nm 0 0 a A ; b B ; 3 D nm nm nm where rep eated indices are not summed over in the ab ove equations.