Dressing L_mu - L_tau in Color

TL;DR

The study investigates a $Z'$ boson coupling to leptons through the anomaly-free $L_\mu-L_\tau$ current and to quarks via effective operators generated by heavy vector-like quarks, aiming to explain the $B\to K^*\mu^+\mu^-$ anomaly. It provides a renormalizable UV completion and derives the corresponding Wilson coefficients, showing that appropriate Yukawa textures and vector-like masses can reproduce the needed $C_9$ and $C_9'$ while satisfying flavor constraints such as $B_s$ and Kaon mixing. Precision leptonic observables, especially neutrino trident production, impose strong bounds that compete with or surpass collider constraints, ruling out large portions of the $(g-2)_\mu$–favored region for many $Z'$ masses. The work highlights Z decays to four leptons and neutrino trident production as decisive tests, advocating for future measurements to further probe this $L_\mu-L_\tau$ portal and its connection to flavor anomalies. Overall, it presents a coherent, testable framework in which a light to sub-TeV $Z'$ can address the LHCb anomaly under tight, complementary constraints from leptonic processes.

Abstract

We consider a new massive vector-boson Z' that couples to leptons through the L_mu - L_tau current, and to quarks through an arbitrary set of couplings. We show that such a model can be obtained from a renormalizable field theory involving new heavy fermions in an anomaly-free representation. The model is a candidate explanation for the discrepancy observed recently by the LHCb collaboration in angular distributions of the final state particles in the rare decay B \to K* mu^+ mu^-. Interestingly, the new vector-boson contribution to the decay tau \to mu nu_tau \bar nu_mu can also remove a small tension in the measurement of the corresponding branching ratio. Constraints from light flavor meson-mixing restrict the coupling to the up- and down-quarks to be very small and thus direct production of the vector-boson at hadron colliders is strongly suppressed. The most promising ways to test the model is through the measurement of the Z decay to four leptons and through its effect on neutrino trident production of muon pairs. This latter process is a powerful but little-known constraint, which surprisingly rules out explanations of (g-2)_mu based on Z' gauge bosons coupled to muon number, with mass of at least a few GeV.

Figures (6)

• Figure 1: Example diagrams in the high energy theory that lead to flavor-changing effective couplings of the $Z^\prime$ to SM quarks.
• Figure 2: Constraints from $B_s$ mixing on the $U(1)^\prime$ breaking VEV, $v_\Phi$, in the plane of the vector-like quark masses $m_Q$ and $m_D$. In the left plot all relevant mixing Yukawas are set to 1. In the right plot, we assume a non trivial flavor structure that leads to $Y_{Qs} \simeq Y_{Ds} \simeq \lambda^2$, where $\lambda \simeq 0.23$ is the Cabibbo angle. The green region is preferred by an explanation of the $B \to K^* \mu^+\mu^-$ anomaly. The light gray regions are excluded by experimental results on neutrino trident production (see Eq. (\ref{['eq:trident_bound']}) below). The dark gray region in the left plot cannot be made compatible with $B_s$ mixing bounds.
• Figure 3: Constraints on the model parameter space from the different leptonic processes discussed in Section \ref{['sec:lep']}. The region in white is the allowed region. The anomaly in $B\rightarrow K^* \mu^+\mu^-$ can be accommodated everywhere to the left of the bottom-right triangle, see Eq. (\ref{['eq:18TeVbound']}). Note that the constraint from the neutrino trident production of muon pairs (red region) completely excludes the region favored by $(g-2)_\mu$. The dotted lines in the allowed region denote $(5-10)\%$ NP effects in $B_s$ mixing.
• Figure 4: Example one-loop box diagram that gives a correction to the $\tau \to \mu \nu_\tau \bar{\nu}_\mu$ decay. In total there are four box diagrams with the $Z^\prime$ connected to the lepton legs.
• Figure 5: The main NP contribution to the $Z\to 4\ell$ process at the LHC.