LFV couplings of the extra gauge boson Z' and leptonic decay and production of pseudoscalar mesons

Abstract

Considering the constraints of the lepton flavor violating (LFV) processes $\mu \to 3e$ and $\tau \to 3\mu$ on the LFV couplings $Z^{\prime }{\ell }_i{\ell }_j$, in the contexts of the $E_6$ models, the left-right (LR) models, the "alternative" left-right (ALR) models and the 331 models, we investigate the contributions of the extra gauge boson $Z^{\prime }$ to the decay rates of the processes ${\ell }_i\to {\ell }_j{\nu }_{\ell }{\nu }_{\ell }$, $\tau \to \mu P$ and $P\to \mu e$ with $P={\pi }^0,\eta$ and ${\eta }^{\prime }$. Our numerical results show that the maximal values of the branching ratios for these processes are not dependent on the $Z^{\prime }$ mass $M_{Z^{\prime }}$ at leader order. The extra gauge boson $Z_X^{\prime }$ predicted by the $E_6$ models can make the maximum value of the branching ratio $Br(\tau \to \mu {\nu }_{\ell }{\nu }_{\ell })$ reach $1.1\times 10^{-7}$. All $Z^{\prime }$ models considered in this paper can produce significant contributions to the process $\tau \to \mu P$. However, the value of $Br(P\to \mu e)$ is far below its corresponding experimental upper bound.

Comments: 14 pages, 2 figures; matches published version