We discuss Lepton-Flavour-Violating phenomena such as $\mu \to e \gamma$,
$\mu \to eee$, and $\mu \to e$ conversion in nuclei in SUSY models with and
without R-parity. We stress that experimental searches for all the LFV
processes are important to distinguish between the different models.Comment: 4 pages, talk given at 8th International Workshop on Deep Inelastic
  Scattering and QCD (DIS 2000), Liverpool, England, 25-30 Apr 200

Tobe, Kazuhiro

English

arXiv

We discuss Lepton-Flavour-Violating phenomena such as $\mu \to e \gamma$, $\mu \to eee$, and $\mu \to e$ conversion in nuclei in SUSY models with and without R-parity. We stress that experimental searches for all the LFV processes are important to distinguish between the different models

Tobe, K

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CERN-TH/2000-169LEPTON-FLAVOUR-VIOLATION IN SUSY MODELSWITH AND WITHOUT R-PARITY aKAZUHIRO TOBECERN, Theory Division, CH-1211, Geneva 23, SwitzerlandE-mail: kazuhiro.tobe@cern.chWe discuss Lepton-Flavour-Violating phenomena such as  → eγ,  → eee, and→ e conversion in nuclei in SUSY models with and without R-parity. We stressthat experimental searches for all the LFV processes are important to distinguishbetween the different models.Recently, the atmospheric neutrino experiment SuperKamiokande has an-nounced evidence for non-zero neutrino mass, which indicates the existenceof physics beyond the Standard Model (SM). Generally in models that ac-commodate neutrino oscillations, lepton-flavour-violating phenomena (LFV)can occur not only in the neutrino, but also in the charged-lepton sector. Inthis paper, we will discuss LFV in processes such as  ! eγ,  ! eee, and ! e conversion in nuclei in two models, which are extensions of the minimalSUSY SM (MSSM): one is the MSSM with right-handed neutrinos (without R-parity violation),1 the other is the MSSM with R-parity violation.2 Especiallythe latter model can also be tested by the HERA experiments;3 however, thelow energy muon-decay experiments provide very stringent bounds on some ofthe couplings, which are not constrained by HERA. We will also discuss thedierent features of LFV in these two models.1 LFV in the MSSM with right-handed neutrinosIn this section, we consider the MSSM with right-handed neutrinos. The su-perpotential in the lepton sector is given byW = f ieH1Eci Li + fiνVijH2Nci Lj +MR2N ci Nci ; (1)where for simplicity we assumed that the right-handed neutrino mass matrix isproportional to the unit matrix. In this framework, the small neutrino massesarise through the seesaw mechanism; if the right-handed neutrino mass scaleMR is much larger than the electroweak scale, we can obtain very tiny neutrinomasses: mνi = (mDνi)2=MR; imass = Vijjflavor, where mDν is a Dirac neutrinomass (mDνi =fiνv sin β2 ), and the mass eigenstates (mass) of neutrinos are relatedto the flavour eigenstates (flavor) via the mixing matrix V . An importantaTalk given at the 8th International Workshop on Deep Inelastic Scattering and QCD(DIS 2000), Liverpool, England, 25-30 April 20001point is that,because of the LFV mixing V , LFV is induced in the sleptonmass terms even if we assume universal scalar mass (m0) at the gravitationalscale M = 2  1018GeV. We can calculate the LFV in slepton masses bysolving the renormalization group equations numerically. The approximatesolution is given by (m2~L)ij ’ −jfkν j2VkiVkj16pi2 (6 + 2a20)m20 log(M=MR). Notethat large neutrino Yukawa couplings and large mixing V induce large flavour-violating masses. The LFV masses (m2~L)ij generate LFV processes, e.g.(m2~L)23 induces  ! γ, and (m2~L)12 generates  ! e flavour violation.The atmospheric neutrino experiments indicate large mixing V32. This largemixing can induce large branching ratio for  ! γ 1,4. Moreover, some ofthe solar neutrino solutions suggest large V21, which can induce large  ! eflavour violation.4 In Fig. 1, we present the branching ratios of  ! eγ and ! e conversion in Ti assuming thatV =1p21212−1p212120 −1p21p2 ; mνi = (0; 0:006; 0:055)i eV; (2)which provides a solution to the atmospheric neutrino problem, as well as alarge-angle MSW solution to the solar neutrino problem.b We also checkedthat Br( ! eee)=Br( ! eγ) ’ 6  10−3. Therefore the present and futureexperiments with a sensitivity of 10−14 for the  ! eγ rate 5 and 10−16 forthe  ! e conversion rate in Al 6ccan probe the LFV in a large region of theparameter space of this model.2 LFV in SUSY models with R-parity violationSubsequently, we consider the MSSM with R-parity violation in which thesmall R-parity violation can potentially explain small neutrino masses. Thesuperpotential isW = f ieH1Eci Li +fijk2LiLjEck + f0ijkLiQjDck: (3)Here we assume that the baryon-number-violating terms U cDcDc are forbiddenby baryon parity in order to avoid rapid proton decay.dThe Yukawa couplingsf and f 0 violate lepton flavour number as well as lepton number. The LFVbIn the case with other solar neutrino solutions, see Ref.4cWe numerically checked that the R( → e in Al) ' 0:6R( → e in Ti).dWe neglect R-parity violation in soft SUSY-breaking terms. This could be importantfor neutrino masses. Here we do not consider any particular models for neutrino masses.2Br()eµγ1010101010-10-11-12-13-14200 400 600 800 1000m (GeV)eL~Experimental boundtan =30tan =10tan =3βββM =200GeVa =0 20R()eµ1010101010-12-13-14-15-16200 400 600 800 1000m (GeV)Le~a =0 M =200GeV0 2Experimental boundtan =30tan =10tan =3βββ(a) (b)Figure 1: Event rates for (a)  → eγ (b)  → e conversion in Ti as a function of theleft-handed selectron mass. We fixed the right-handed neutrino mass to MR = 1013 GeV.experiments put the most stringent bounds on certain combinations of theYukawa couplings f and f 0.7,8 We list the bounds in Table 1. To understandan interesting feature of the LFV in this model, let us consider some simpleexamples. If only f131 and f231 are non-zero, the ratios of the event ratesbetween the LFV processes are given byBr( ! eγ)Br( ! eee) = 1 10−4;R( ! e in Ti (Al))Br( ! eee) = 2 10−3 (1 10−3); (4)where we took all m~l to be 100 GeV. The rate of  ! eee is much larger thanthose of the other LFV processes. This is because  ! eee is generated at treelevel, while the rest of the LFV processes are induced at the one-loop level. Ifonly f132 and f232 are non-zero, the event rates are given byBr( ! eγ)Br( ! eee) = 1:2;R( ! e in Ti (Al))Br( ! eee) = 18 (11); (5)where we took m~l = 100 GeV. Even though all processes are induced at the one-loop level in this case, the branching ratio of  ! eee is still comparable to thatof  ! eγ, and the rate of  ! e conversion is even much larger because of alog-enhancement in the o-shell photon penguin contributions.8 Therefore  !eee and  ! e conversion are important in this model. The interesting pointis that the relations in Eqs.(4), (5) are quite dierent from those of the MSSMwith right-handed neutrinos discussed in the previous section. Therefore, inorder to distinguish between the dierent models, the study of all the LFVprocesses can be important. Note that at present the future proposal for3 ! eγ  ! 3e  ! e in nucleijf131f231j 2 10−4 (7 10−6) 7 10−7 1 10−5 (2 10−7)jf132f232j 2 10−4 (7 10−6) 7 10−5 1 10−5 (2 10−7)jf133f233j 2 10−4 (7 10−6) 1 10−4 2 10−5 (4 10−7)jf121f122j 8 10−5 (2 10−6) 7 10−7 6 10−6 (1 10−7)jf131f132j 8 10−5 (2 10−6) 7 10−7 7 10−6 (1 10−7)jf231f232j 8 10−4 (2 10−6) 4 10−5 8 10−6 (1 10−7)jf 0111f 0211j 7 10−4 (2 10−5) 1 10−4 5 10−6 (2 10−7)jf 0112f 0212j 7 10−4 (2 10−5) 1 10−4 4 10−7 (7 10−9)jf 0113f 0213j 7 10−4 (2 10−5) 2 10−4 4 10−7 (7 10−9)jf 0121f 0221j 7 10−4 (2 10−5) 2 10−4 4 10−7 (6 10−9)jf 0122f 0222j 7 10−4 (2 10−5) 2 10−4 4 10−5 (7 10−7)jf 0123f 0223j 7 10−4 (2 10−5) 3 10−4 5 10−5 (9 10−7)jf 0131f 0231j 2 10−3 (6 10−5) 4 10−4 4 10−7 (6 10−9)jf 0132f 0232j 2 10−3 (6 10−5) 5 10−4 9 10−5 (2 10−6)jf 0133f 0233j 2 10−3 (6 10−5) 9 10−4 2 10−4 (3 10−6)Table 1: Present (Future) constraints on R-parity-violating couplings from LFV processes.The present limits (future expectations) on the event rates are given by Br( → eγ) < 1:2×10−11 (10−14), Br(→ 3e) < 1:0× 10−12, and R(→ e in Ti (Al)) < 6:1× 10−13 (10−16).We took mν˜ = ml˜R= 100 GeV and mq˜ = 300 GeV. ! eee is missing. Furthermore, we should stress here that not only low-energy muon probes but also other experiments3 should be encouraged in orderto investigate the R-parity-violating SUSY since this theory is well-motivatedfrom the recent neutrino data.AcknowledgementsThe author would like to thank A. de Gouve^a, G.F. Giudice, and S. Lola foruseful discussions.References1. J. Hisano et al., Phys. Lett. B 357, 579 (1995); J. Hisano et al., Phys.Rev. D 53, 2442 (1996); K. Tobe, Nucl. Phys. Proc. Suppl. B59 (1997)223.2. A. de Gouve^a, G.F. Giudice, S. Lola, and K. Tobe, work in progress.3. R. Kerger, in these proceedings.4. J. Hisano and D. Nomura, Phys. Rev. D 59, 116005 (1999).5. L.M. Barkov et al., Research Proposal to PSI, 1999.46. M. Bachman et al. (MECO Collaboration), Proposal to BNL, 1997.7. D. Choudhury and P. Roy, Phys. Lett. B 378, 153 (1996):8. K. Huitu et al.,Phys. Lett. B 430, 355 (1998).5

Lepton-Flavour-Violation in SUSY Models with and without R-parity

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