Probing Lepton Flavour Universality with $Λ_b$ decays to $τ^+τ^-$ final states

TL;DR

The paper investigates Lepton Flavour Universality in the rare baryonic decay $\Lambda_b\to\Lambda\tau^+\tau^-$ as a probe of third-generation New Physics. It provides a precise Standard Model prediction for the LFU ratio $R_\Lambda^{\tau/\mu}$ (uncertainty $<10\%$) by combining lattice form factors with a dispersive treatment of long-distance charm contributions, and delivers a SM branching ratio $\mathcal{B}(\Lambda_b\to\Lambda\tau^+\tau^-)_{q^2>15\,\mathrm{GeV}^2}=(1.93^{+0.30}_{-0.23})\times 10^{-7}$. In the presence of NP coupled predominantly to third-generation fermions, $R_\Lambda^{\tau/\mu}$ can be enhanced by orders of magnitude and is correlated with anomalies in $R_D^{(*)}$ and in $b\to s\mu^+\mu^-$, via an effective field theory with $\Delta C^{\tau}_{9,10}$ tied to $\Delta C^{\mu}_{9}$ through loop effects. The analysis shows that future measurements of $R_\Lambda^{\tau/\mu}$ at LHCb would provide a decisive test of these NP scenarios and constrain or reveal new third-generation dynamics, with extensions to related channels such as $\Lambda_b\to pK\tau^+\tau^-$.

Abstract

We present a study of the rare baryonic decay $Λ_b \to Λτ^+ τ^-$ as a probe of new physics (NP) coupled preferentially to third-generation fermions. Within the Standard Model, we evaluate the branching ratio and the lepton-flavour-universality (LFU) ratio $R_Λ^{τ/μ}$, including both perturbative and long-distance charm contributions. We show that the LFU ratio can be predicted with an uncertainty below 10%. Possible NP effects arising from lepton non-universal dynamics are analysed within an effective field theory framework motivated by the current anomalies in $b \to cτν$ and $b \to sμ^+μ^-$ transitions. In this context, $R_Λ^{τ/μ}$ can be enhanced by several orders of magnitude, offering a clear target for upcoming searches. The implications for the related mode $Λ_b \to pKτ^+τ^-$ are also briefly discussed.

Figures (3)

• Figure 1: Predictions of the differential branching ratio of $\Lambda_b \rightarrow \Lambda \tau^+ \tau^-$ as a function of the di-lepton invariant mass $q^2$ in $\text{GeV}^2$. The band is the $1\sigma$ uncertainty region due to uncertainties from local form factors and resonance parameters. The latter includes varying the phases with a flat distribution within the interval $[0,2\pi)$.
• Figure 2: Dilepton spectrum of the $\Lambda_b\to\Lambda\mu^+\mu^-$ decay measured by LHCb. The gray areas are the original results reported in LHCb:2015tgy, while the blue ones are those obtained rescaling the normalization using the recent result for $\mathcal{B}(\Lambda_b\to \Lambda J/\psi)$ in LHCb:2025jva. The crosses denote our theory prediction in the SM case (violet) and with the NP shift to $C_9$ discussed in Section \ref{['sect:NPEFT']} (purple).
• Figure 3: Predictions of $R_\Lambda^{\tau/\mu}$ in extensions of the SM with NP predominantly coupled to third-generation fermions. Left: correlation $R_\Lambda^{\tau/\mu}$ vs. $R_{D^{(*)}}$ in the absence of right-handed currents (blue band); both LFU ratios are normalised to their SM value; the dark (light) gray region indicates the experimental value of $R_{D^{(*)}}$ at 68% CL (98% CL). Right: contours in the $C_9^\tau$--$C_{10}^\tau$ plane corresponding to different values of $R_\Lambda^{\tau/\mu}$ normalised to the SM (dashed circles); the brown and green areas are those currently favored at 68% CL by $b\to s\mu\bar{\mu}$ and $R_{D^{(*)}}$, respectively; the dotted line indicates the relation $C_9^\tau=-C_{10}^\tau$ expected for left-handed interactions.