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Higgs Quadruplet for Type III Seesaw and Implications for → e and −e Conversion Ren Bo Coauther : Koji Tsumura, Xiao - Gang He arXiv:

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I. Introduction A Higgs Quadruplet for Type III Seesaw Model II. The electroweak constraints III. Loop induced neutrino mass with just one triplet lepton IV. Some phenomenological implications 1. Neutrino mass and mixing 2. →e and −e Conversion V. Conclusions Outline

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I. Introduction

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In the minimal SM : Gauge group : Quark and charged lepton masses are from the following Yukawa couplings Nothing to pair up with In minimal SM, neutrinos are massless ! Extensions needed : Give neutrino masses and small ones !

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For simplicity, we consider two flavor neutrino mixing and oscillation. Two flavor oscillation

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The oscillation probability for an appearance neutrino experiment: The conversion and survival probability in realistic units: Due to the smallness of (1,3) mixing, both solar & atmospheric neutrino oscillations are roughly the 2- flavor oscillation.

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Type - I : SM + 3 right - handed Majorana ’ s ( Minkowski 77; Yanagida 79; Glashow 79; Gell - Mann, Ramond, Slanski 79; Mohapatra, Senjanovic 79) Type - II : SM + 1 Higgs triplet ( Magg, Wetterich 80; Schechter, Valle 80; Lazarides et al 80; Mohapatra, Senjanovic 80; Gelmini, Roncadelli 80) Type - III : SM + 3 triplet fermions ( Foot, Lew, He, Joshi 89) A natural theoretical way to understand why 3 - masses are very small.

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Type - III ( Triplet ) Seesaw : add one fermions triplet into the SM. The Lagrangian of neutrino and charged lepton masses is where the ‘ c ’ denote the charge conjugation and In the component we have where

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Now introduce the quadruplet Higgs representation The neutrino and charged lepton mass matrices are given by the basis where Dirac mass term

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A non - zero will modify the neutrino and charged lepton mass matrices The tree level light neutrino mass matrix, defined by the neutrino mass is The light neutrino mass matrix can be diagonalized by the PMNS mixing matrix V where is the diagonalized light neutrino mass matrix.

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II. The electroweak constraints

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The electroweak precision data constrain the VEV of Higgs representation. The Higgs representation with isospin I and hypercharge Y will modify the parameter at tree level with, The experimental data is constrained to be less than 5.8GeV which is about 40 times smaller than that of the doublet Higgs VEV. For our case of one doublet and quintuplet, we have

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III. Loop induced neutrino mass with just one triplet lepton

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where alpha denotes and index for SU (2) contractions. The most general Higgs potential is given by The summations of SU (2) index are written as

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The above terms will generate a neutrino mass matrix proportional to for the first term and, for the second term. The masses of component fields in χ are given by neglecting the contribution from terms proportional to At one loop level Majorana masses will be generated for light neutrinos. Just keep proportional to terms

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The Mass matrix for singly charged scalars can also be approximately given by where One - loop generation of neutrino mass.

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Collecting the tree and loop contribution, the neutrino mass matrix as The explicit dependence on is given where and are masses of neutral and charged heavy leptons, and I ( x ) = x ln x /(1 − x ).

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IV. Some phenomenological implications

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1. Neutrino masses and mixing Mass squared differences of neutrino masses and neutrino mixing have been measured to good precision. The best-fit values and allowed 1, 2 and 3 ranges for the mass-mixing parameters. G. L. Fogli, E. Lisi, A. Marrone, A. Palazzo, A. M. Rotunno, [arXiv: [hep-ph]].

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In our model, for normal hierarchy, For inverted hierarchy,

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To the leading order, the mixing pattern can be approximated by the tribimaximal mixing matrix The light neutrino mass matrix can be made to fit data. In case the light neutrino mass can be written as For normal hierarchy case, the Yukawa couplings can be taken to the forms then, If the heavy neutrino mass is the order of 1TeV, we get

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For the inverted hierarchy, then, If the heavy neutrino mass is the order of 1TeV, we get The parameter is proportional to the Higgs potential. If is small, quadruplet Yukawa coupling can be order of one.

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Making perturbation to the above forms, one can get non - zero solutions, which is indicated by the results at T2K. For normal mass hierarchy, and keep the same with For inverted mass hierarchy

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2. →e and −e conversion The dominant contribution come at the one loop level due to possible large Yukawa coupling The effective Lagrangian is given by with being the electric charge of the q - quark, and

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The LFV →eγ decay branching ratio is easily evaluated by The strength of − e conversion is measured by the quantity,

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The current experimental upper limit is The μ−e conversion for Au nuclei is The near future MEG experimental The μ−e conversion, Mu2E/COMET Al PRISM Ti The relevant parameters for μ-e conversion processes.

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The current and future experimental constraints on the quadruplet Yukawa coupling from and conversion. The mass of quadruplet scalar is taken as

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V. Conclu sion 1. The heavy neutrinos are contained in leptonic triplet seesaw III model. 2. A quadruplet χ is introduced to get the new type of Yukawa couplings. Light neutrino masses can receive sizeable contribution from both the tree and loop level. 3. The mass matrix obtained can be made consistent with experimental data on mixing parameters. Large Yukawa coupling may have observable effects on lepton flavor violating processes, such as, → e and −e conversion.

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Thank you for your attention!

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