Koji TSUMURA NTU B 3 SM 23 25102011

Koji TSUMURA (NTU) B 3 SM 23 -25/10/2011 mu-e Conversion with Four generations N. Deshpande, T. Enkhbat, T. Fukuyama, X. -G. He, L. -H. Tsai and K. Tsumura Phys. Lett. B 703 (2011) 26

Outline p Lepton flavor violation (LFV) p LFV in SM 3 and in SM 4 p p m eg p m 3 e p m e conversion in nuclei p Numerical results Summary 3 rd b 3 sm Koji Tsumura (ntu) 2

Motivations p Quark and neutrino flavor violations has been observed !! p Neutrinos are members of lepton doublet charged LFV can be induced. p Clear evidence of Beyond SM p In SM 3 + massive v Extremely small SM effect Petcov, Sov. J. Nucl. Phys. 25: 340(1977) 3 rd b 3 sm Koji Tsumura (ntu) 3

Current experimental limit p Muon LFV decays are highly constrained !! p Order of 10 improvement on muon LFV in 60 years Less constrained t LFV ~10 -8 New m eg limit < 2. 4 x 10 -12 since EPS 2011 by MEG It will be improved to 10 -13 Current upper limit of B(m eg) and BR(m 3 e) in ~10 -12 3 rd b 3 sm Koji Tsumura (ntu) 4

Current experimental limit p Muon LFV decays are highly constrained !! p m-e conversion in nuclei Less constrained t LFV ~10 -8 New m eg limit Slightly better than m eg and m 3 e It will be improved to 10 -18 for Ti !! 3 rd b 3 sm Koji Tsumura (ntu) (much better future prospects) 5

Beyond the SM p Possible new physics contributions Hisano et. al. , PRD 53: 2442(1996) Nakagawa, Takasu, PTP 59, 548(1977) Fourth generation neutrino !! Shanker, NPB 206, 253 (1982) X. -G. He et. al. (1990) Chang, Ng, PRD 50, 4589(1994) 3 rd b 3 sm Koji Tsumura (ntu) 6

m eg in SM 4 p Chang, Ng, PRD 50, 4589(1994), Lacker, Menzel, JHEP 07, 006(2010) Buras et. al. JHEP 09, 104(2010), Deshpande et. al. PLB 703, 26(2011) Here after, we assume Dirac neutrino for definiteness. (But, it is true for Majorana neutrino from Type-I seesaw if MR is large. ) More precise loop function Small v mass limit Large contrib. from heavy neutrinos Heavy neutrino 3 rd b 3 sm Koji Tsumura (ntu) 7

4 th generation neutrino p Mass bound for 4 th generation neutrinos p Lower bound from Direct search p Upper bound from unitarity 1. 2 Te. V for heavy leptons Chanowtz, PLB 78, 285(1978) v 4 can induce observable m eg Heavy neutrino 3 rd b 3 sm Koji Tsumura (ntu) 8

m eg in SM 4 p Large BR possible if neutrino mixing is large current experimental bound can be converted to bound on lme 3 rd b 3 sm Koji Tsumura (ntu) 9

Chang, Ng, PRD 50, 4589(1994), Buras et. al. JHEP 09, 104(2010) Deshpande et. al. PLB 703, 26(2011) m 3 e in SM 4 p Effective Lagrangian On-shell photon penguin Off-shell photon p Z photon Box diagrams On-shell photon penguin dominant case (in general) Hisano, Nomura, PRD 59, 116005(1999) 2 -3 orders magnitude smaller Additional QED suppression 3 rd b 3 sm Koji Tsumura (ntu) 10

m 3 e in SM 4 p Effective Lagrangian On-shell photon penguin Off-shell photon p Z photon Box diagrams Z penguin becomes important in SM 4 FZ FW*, FB, FW Increase for large v 4 mass 3 rd b 3 sm Koji Tsumura (ntu) 11

m 3 e and m eg in SM 4 p Compare two results: On-shell photon penguin m 3 e will be better for heavy v 4 (due to Z penguin) 3 rd b 3 sm Koji Tsumura (ntu) 12

Buras et. al. JHEP 09, 104(2010) Deshpande et. al. PLB 703, 26(2011) m e conversions in SM 4 p Effective Lagrangian On-shell photon penguin Off-shell photon p Z photon Box diagrams m e conversion rate for nucleus A: Nucleus dependent parts were calculated several methods. Kitano, Koike, Okada, PRD 66, 096002(2002) Weinberg, Feinberg, PRL 3, 111(1959) Shanker, PRD 20, 1608(1979) 3 rd b 3 sm Koji Tsumura (ntu) 13

LFV in SM 4 p Loop induced LFV always proportional to p Compare LFV processes by taking ratio (cancel lme) m e conv. would be better if exp. limit are the same level 3 rd b 3 sm Koji Tsumura (ntu) 14

LFV in SM 4 p Large BR possible if neutrino mixing is large current experimental bound can be converted to bound on lme The best bound from m e conv. in Au. 3 rd b 3 sm Koji Tsumura (ntu) 15

LFV in SM 4 (Prospects) p Large BR possible if neutrino mixing is large current experimental bound can be converted to bound on lme Current bound from m e in Au is comparable level with projected m e g and m 3 e exp in SM 4. m e conv. can improve lme by 3 orders of magnitude in future. Several projects are proposed. 3 rd b 3 sm Koji Tsumura (ntu) 16

Summary p LFV in SM 4 p GIM suppression in SM 3 p v 4 enhance LFV rate significantly p m 3 e is better than m eg for heavy v 4 (due to Z penguin) p m e conversion in Au gives the best bound on lme m e conv. can improve lme by 3 orders of magnitude in future. 3 rd b 3 sm Koji Tsumura (ntu) 17