Neutrino mass and neutrinoless double beta decay in SO(10) GUT with Pati–Salam symmetry

Abstract

We demonstrate how a class of non-supersymmetric SO(10) GUT with asymmetric left–right theory SU(2)L × U(1)R × U(1)B−L × SU(3)C and Pati–Salam theory SU(2)L × SU(2)R × SU(4)C as intermediate symmetry breaking steps leads to successful gauge coupling unification satisfying proton decay constraints. The motivation behind this work is two fold: firstly to study the renormalization group evolution equations for gauge couplings by keeping right-handed neutral gauge boson ZR around LHC energy range leading interesting dilepton searches at collider while fixing charge partner of the gauge boson WR at very high scale; secondly to explain neutrino masses and associated lepton number violating process like neutrinoless double beta decay in three possible cases depending on how SU(2)L × U(1)R × U(1)B−L × SU(3)C breaks down to SM. The presence of Pati–Salam symmetry and Pati–Salam symmetry with D-parity (discrete left–right symmetry leading to gL = gR) at highest scale is to allow two gauge couplings and thereby ensuring precision unification for gauge couplings. We focus on neutrino mass and neutrinoless double beta decay for one particular case where TeV scale asymmetric left–right theory is spontaneously broken down to SM with non-zero VEV of both Higgs doublets with B − L = −1 and Higgs triplets with B − L = 2. We include one extra fermion singlet per generation in order to implement gauged extended seesaw where light neutrino mass is governed by dominant type-II seesaw mechanism whereas type-I seesaw contribution is cancelled out. Since light neutrino mass formula is independent of Dirac neutrino mass matrix, the value of Dirac neutrino mass is taken to be up-type quark mass matrix which is a characteristics of Pati–Salam symmetry relating quarks with leptons. This can lead to non-unitarity effects in leptonic sector and induce lepton flavor violation. We present analytic relation for effective Majorana mass parameter and corresponding half-life arising from new physics contributions due to purely left-handed currents through exchange of heavy right-handed neutrinos and sterile neutrinos. We numerically estimate effective Majorana mass parameter and half-life versus lightest neutrino mass and derive lower bound on lightest neutrino mass by saturating with experimental bounds like GERDA Phase-II, KamLANDZen and EXO.