A viable model with violation

Marco Ardu; Fiona Kirk

doi:10.1140/epjc/s10052-023-11469-z

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 394
https://doi.org/10.1140/epjc/s10052-023-11469-z

Regular Article - Theoretical Physics

A viable $L_{e} - L_{μ}$ $L_e-L_\mu$ model with $μ \to e$ $\mu \rightarrow e$ violation

Marco Ardu¹ and Fiona Kirk²^,3^b

¹ LUPM, CNRS, Université Montpellier Place Eugene Bataillon, 34095, Montpellier Cedex 5, France
² Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland
³ Paul Scherrer Institut, 5232, Villigen PSI, Switzerland

^b fiona.kirk@itp.uni-hannover.de

Received: 4 December 2022
Accepted: 3 April 2023
Published online: 11 May 2023

Abstract

We extend the Standard Model gauge group by $U {(1)}_{L_{e} - L_{μ}}$ $U(1)_{L_e-L_\mu }$ and introduce two scalars, a doublet and a singlet, that are charged under this new group and have lepton flavour violating couplings. Since in this model $μ \to e$ $\mu \rightarrow e$ processes can only be mediated by $μ \to τ \times τ \to e$ $\mu \rightarrow \tau \times \tau \rightarrow e$ interactions, bounds from $μ \to e$ $\mu \rightarrow e$ transitions can be avoided while allowing for accessible new physics. We consider the case of a $Z^{'}$ $$Z'$$ boson with a mass of $M_{Z^{'}} ≃ 10$ $M_{Z'}\simeq 10~$ GeV and a gauge coupling $g^{'} ≃ 10^{- 4}$ $g'\simeq 10^{-4}$ , which is in reach of Belle-II, and a long-lived $Z^{'}$ $$Z'$$ boson with a mass of $MeV ≲ M_{Z^{'}} ≲ m_{μ} - m_{e}$ $\text {MeV}\lesssim M_{Z'}\lesssim m_\mu -m_e$ which can be probed by searching for $ℓ \to ℓ^{'} + inv .$ $\ell \rightarrow \ell ' +\mathrm {inv.}$ . Neutrino masses and mixing angles can also be accounted for if sterile neutrinos are added to the spectrum.

© The Author(s) 2023

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