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Muon-To-Electron Conversion in Mirror Fermion Model with Electroweak

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Muon-To-Electron Conversion in Mirror Fermion Model with Electroweak JID:NUPHB AID:14362 /FLA [m1+; v1.283; Prn:30/05/2018; 11:22] P.1(1-34) Available online at www.sciencedirect.com ScienceDirect 1 1 2 2 Nuclear Physics B ••• (••••) •••–••• 3 3 www.elsevier.com/locate/nuclphysb 4 4 5 5 6 6 7 7 8 Muon-to-electron conversion in mirror fermion model 8 9 9 10 with electroweak scale non-sterile right-handed 10 11 neutrinos 11 12 12 13 13 a,b a c d,e 14 P.Q. Hung , Trinh Le , Van Que Tran , Tzu-Chiang Yuan 14 15 15 a 16 Department of Physics, University of Virginia, Charlottesville, VA 22904-4714, USA 16 b 17 Center for Theoretical and Computational Physics, Hue University College of Education, Hue, Viet Nam 17 c Department of Physics, National Taiwan Normal University, Taipei 116, Taiwan 18 d 18 Institute of Physics, Academia Sinica, Nangang, Taipei 11529, Taiwan 19 e 19 Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan 20 20 Received 7 February 2018; received in revised form 19 April 2018; accepted 25 May 2018 21 21 22 Editor: Hong-Jian He 22 23 23 24 24 25 25 Abstract 26 26 27 The muon-to-electron conversion in aluminum, titanium and gold nuclei is studied in the context of a 27 28 class of mirror fermion model with non-sterile right-handed neutrinos having masses at the electroweak 28 29 scale. We show that the electric and magnetic dipole operators from the photon exchange diagrams provide 29 the dominant contributions, which enables us to derive a simple formula to relate the conversion rate with the 30 30 on-shell radiative decay rate of muon into electron at the limit of zero momentum transfer and large mirror 31 31 lepton masses. Current experimental limits (SINDRUM II) and projected sensitivities (Mu2e, COMET and 32 32 PRISM) for the muon-to-electron conversion rates in various nuclei and latest limit from MEG for the 33 33 radiative decay rate of muon into electron are used to put constraints on the parameter space of the model. 34 Sensitivities to the new Yukawa couplings can reach the range of one tenth to one hundred-thousandth, 34 35 depending on the mixing scenarios and mirror fermion masses in the model as well as the nuclei targets 35 36 used in future experiments. 36 37 © 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license 37 3 38 (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP . 38 39 39 40 40 41 41 42 42 43 E-mail addresses: [email protected] (P.Q. Hung), [email protected] (T. Le), [email protected] (V.Q. Tran), 43 44 [email protected] (T.-C. Yuan). 44 45 https://doi.org/10.1016/j.nuclphysb.2018.05.020 45 46 0550-3213/© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license 46 47 (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 47 JID:NUPHB AID:14362 /FLA [m1+; v1.283; Prn:30/05/2018; 11:22] P.2(1-34) 2 P.Q. Hung et al. / Nuclear Physics B ••• (••••) •••–••• 1 1. Introduction 1 2 2 3 As is well known, lepton flavor is an accidental conserved quantity in Standard Model (SM) 3 4 with strictly massless neutrinos. For example, a muon never decays radiatively into an elec- 4 5 tron plus a photon and neutrinos do not oscillate in the SM. However various experiments have 5 6 now established firmly that neutrinos do oscillate from one flavor to another. The common wis- 6 7 dom, motivated by the physics of K − K oscillation in the kaon system, is to give tiny masses 7 8 with small mass differences to the various light neutrino species. Radiative decay of the muon 8 9 into electron is then possible but with an unobservable rate highly suppressed by the minus- 9 10 cule neutrino masses [1,2]. Searches for lepton flavor violating rare processes in high intensity 10 11 experiments are thus important for new physics beyond the SM. 11 12 The most recent limit on the branching ratio B(μ → eγ ) is from the MEG experiment [3] 12 13 13 → ≤ × −13 14 B(μ eγ ) 4.2 10 (90% C.L.) (MEG 2016), (1) 14 15 and its projected improvement [4]is 15 16 16 → ∼ × −14 17 B(μ eγ ) 4 10 . (2) 17 18 Recent data from the T2K experiment [5] agrees well with the global analysis of neutrino oscil- 18 19 lation data [6–9], suggesting that the normal neutrino mass hierarchy (NH) with a CP violating 19 20 Dirac phase δCP ∼ 3π/2is slightly preferred. The best fit result for the central values of the 20 21 PMNS matrix elements in the normal neutrino mass hierarchy can be extracted from [6] 21 22 ⎛ ⎞ 22 − + 23 0.8240 0.5471 0.02302 0.14536i 23 NH = ⎝ − + + ⎠ 24 UPMNS 0.40085 0.08042i 0.63131 0.053399i 0.65685 . 24 + − + 25 0.38169 0.09054i 0.5437 0.06012i 0.73952 25 26 (3) 26 27 For the μ − e conversion in nuclei, the present experimental upper limits on the branching 27 28 ratios were obtained by SINDRUM II experiment [10,11]for the targets titanium and gold, 28 29 29 − − −12 30 B(μ + Ti → e + Ti)<4.3 × 10 (90% C.L.) , (4) 30 − − − 31 B(μ + Au → e + Au)<7 × 10 13 (90% C.L.) . (5) 31 32 32 − 33 Significant improvements are expected for μ e conversion at future experiments like the Mu2e 33 − 34 at Fermilab in US and the COMET at J-PARC in Japan. Projected sensitivities of μ e conver- 34 35 sion are [12,14,13,15,16] 35 − − − 36 B(μ + Al → e + Al)<3 × 10 17 (Mu2e, COMET), (6) 36 37 37 − + → − + −18 38 B(μ Ti e Ti)<10 (Mu2e II, PRISM). (7) 38 39 A positive signal of any of the above processes (or any process with charged lepton flavor vi- 39 40 olation (CLFV)) at the current or projected sensitivities of various high intensity experiments 40 41 would be a clear indication of new physics as well, just like neutrino oscillations. Given the fact 41 42 that no new physics has showed up yet at the high energy frontier of the Large Hadron Collider 42 43 (LHC), it is not a surprise that many recent works have been focused on new physics implication 43 44 of CLFV in the high intensity frontier. For a review on this topics and its possible connection 44 45 with the muon anomaly, see [17] and references therein. 45 46 In a recent work [18], we updated a previous calculation [19]for the radiative process μ → eγ 46 47 in the mirror fermion model with electroweak scale non-sterile right-handed neutrinos [20]to an 47 JID:NUPHB AID:14362 /FLA [m1+; v1.283; Prn:30/05/2018; 11:22] P.3(1-34) P.Q. Hung et al. / Nuclear Physics B ••• (••••) •••–••• 3 1 extended version [21] where a horizontal A4 symmetry was imposed in the lepton and scalar 1 2 sectors. In this work we extend this previous analysis [18]to the μ − e conversion in nuclei, in 2 3 particular for aluminum, gold and titanium. 3 4 The μ − e conversion had been studied extensively in many low-scale seesaw models beyond 4 5 the SM [22–27]. One crucial difference is that the right-handed neutrinos are sterile in these 5 6 models while in the mirror fermion model that we are studying they are non-sterile. This may 6 7 lead to distinctive signatures like two jets or same sign dilepton in association with missing 7 8 transverse energies and displaced vertices at the collider searches for the mirror quarks [28]or 8 9 leptons [29]. 9 10 This paper is organized as follows. In Sec. 2, we provide some highlights of the crucial 10 11 features of the extended mirror fermion model. In Sec. 3, we briefly review the effective La- 11 12 grangian [30,31]for describing μ − e coherent conversion processes. In Sec. 4, we present the 12 13 detailed calculation of μ − e conversion in the model. In Sec. 5, we derive a simple relation 13 14 between the μ − e conversion rate and the radiative decay rate of μ → eγ in the limit of zero 14 15 momentum transfer and large mirror lepton masses. Numerical results are shown in Sec. 6. We 15 16 summarize our results in Sec. 7. In Appendix A, we collect some useful formulas used in Secs. 4 16 17 and 5. 17 18 18 19 2. Mirror fermion model 19 20 20 21 In this section, we will provide some highlights for the original mirror fermion model [20] 21 22 and its A4 extension [21]. 22 23 23 24 2.1. Motivation 24 25 25 26 The motivation of introducing mirror fermions in [20]was manifold. First of all, it is aes- 26 27 thetically satisfactory to have parity restoration at a higher energy scale while the maximal 27 28 parity violating interaction (V−A interaction) in the SM emerges from spontaneous symmetry 28 29 breaking. This is one of the main reasons for various left-right symmetric models in the litera- 29 30 ture [32–35]. Secondly, it is important to study non-perturbative effects in the SM by discretizing 30 31 it on the lattice.
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