Lepton flavor violating decays $l_j\rightarrow{l_i\gamma}$ in the $U(1)_X$SSM model within the Mass Insertion Approximation

TL;DR

This paper investigates lepton flavor violating decays within the $U(1)_X$SSM model, providing analytical formulas and identifying key parameters influencing these rare processes, which could signal new physics beyond the Standard Model.

Contribution

It introduces a set of simple analytical formulas for LFV decay form factors in the $U(1)_X$SSM using the Mass Insertion Approximation, highlighting sensitive parameters affecting these decays.

Findings

Non-diagonal elements are main sensitive parameters.

Analytical formulas facilitate future phenomenological studies.

LFV decays can serve as signals of new physics.

Abstract

Three singlet new Higgs superfields and right-handed neutrinos are added to MSSM to obtain $U(1)_X$SSM model. Its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. In the framework of $U(1)_X$SSM, we study muon anomalous magnetic moment and lepton flavor violating decays $l_j\rightarrow{l_i\gamma}(j=2,3;i=1,2)$ within the Mass Insertion Approximation(MIA). Through the MIA method, we can find the parameters that directly affect the analytical result of the lepton flavor violating decays $l_j\rightarrow{l_i\gamma}$, which make our work more convenient. We want to provide a set of simple analytic formulas for the form factors and the associated effective vertices, that may be very useful for future phenomenological studies of the lepton flavor violating decays. According to the accuracy of the numerical results which the influence of different sensitive parameters, we come to the conclusion that the non-diagonal elements which correspond to the generations of the initial lepton and final lepton are main sensitive parameters and lepton flavor violation(LFV) sources. This work can provide a clear signal of new physics(NP).