Constraints on lepton-flavor mixing with third-generation new physics

TL;DR

The paper investigates lepton-flavor mixing in a framework where new physics at the TeV scale couples predominantly to the third generation under an approximate $U(2)^5$ flavor symmetry. It extends previous SMEFT analyses by introducing a lepton-sector spurion $\tilde V_\ell$ that breaks $U(2)_\ell$, parameterized by $\delta$, and runs the Wilson coefficients through a combined RGE/matching procedure to connect high-scale NP to low-energy observables. A fit to current LFV and LFU data yields a robust bound $|\delta|<0.051$ (95% CL), with $R_{K^{(*)}}$ and $\mathcal{B}(B_s\to\mu\mu)$ driving the constraint; it also establishes $|\tilde V_\ell|/|\tilde V_q|<0.69$. Prospects for future measurements indicate that LFV tau decays and LFU tests could tighten the bound on $\delta$ to around $0.03$–$0.03$, significantly constraining NP scenarios with a $U(2)^5$ flavor structure and predominantly third-generation couplings.

Abstract

We study the implications of an approximate $U(2)^5$ flavor symmetry at the TeV scale, under the assumption of new physics predominantly coupled to the third-generation fermions, focusing on the breaking of the $U(2)_\ell$ subgroup governing the mixing between second- and third-generation left-handed leptons. We derive constraints on the corresponding spurion parameter $δ$ from current data on lepton flavor violating (LFV) and lepton flavor universality (LFU) observables, finding that $R_{K^{(*)}}$ and $\mathcal{B}(B_s \to μμ)$ give the most stringent bound on $δ$, yielding ${|δ|<0.051}$ at 95% CL. In addition, we provide updated bounds for LFV decay rates and discuss prospects for future sensitivity improvements, finding that future LFV searches could further tighten constraints on the mixing between second- and third-generation leptons.

Figures (2)

• Figure 1: Main results of our fit in the $\{\delta,C_{\ell q}^+\}$ plane. The $1\sigma$ and $2\sigma$ regions from the results in Allwicher:2024ncl provide horizontal bands (blue). The $1\sigma$ and $2\sigma$ bounds imposed by $\mathcal{B}(B_s\to\mu\mu)$ and $R_{K^{(*)}}$, with $C_{\ell q}^-$ and $\epsilon$ fixed to their best-fit values, provide a cross-shaped region (orange). The gray dashed contours represent the $2\sigma$ CL regions with fixed $\epsilon = 1.0$ (inner), and $\epsilon=3.6$ (outer). The $1\sigma$ and $2\sigma$ regions from the combined fit yield the central region in pink.
• Figure 2: Main results of our fit in the $\{\delta,\epsilon\}$ plane. The $1\sigma$ and $2\sigma$ region from the results in Allwicher:2024ncl provide horizontal bands (blue). The $1\sigma$ and $2\sigma$ bounds imposed by $\mathcal{B}(B_s\to\mu\mu)$ and $R_{K^{(*)}}$, with $C_{\ell q}^\pm$ fixed to their best-fit values, provide a cross-shaped region (orange). The gray dashed contours represent the $2\sigma$ CL regions with fixed $C_{\ell q} = -0.77$ (inner), and $C_{\ell q} = -0.05$ (outer). The $1\sigma$ and $2\sigma$ regions from the combined fit yield the central region in pink.