Pseudoscalar meson $P\to τ(\to πν_τ, ρν_τ, \ell \barν_\ell ν_τ) \barν_τ$ decays in the Standard Model and beyond

TL;DR

This work analyzes the full cascade decays $P \to τ ν_τ$ of charged pseudoscalar mesons $P \in \{D_s, D, B, B_c\}$, followed by $τ$ decays into $π ν_τ$, $ρ ν_τ$, $e \bar{ν}_e ν_τ$, or $μ \bar{ν}_μ ν_τ$, within a model‑independent low‑energy EFT that includes the most general four‑fermion operators with right‑handed neutrinos. It provides precise Standard Model predictions for the differential decay rates $d\Gamma/dE$ as a function of the final-state charged-particle energy and develops an energy‑moments methodology to extract NP couplings $|g_L^{q_1 q_2}|^2$ and $|g_R^{q_1 q_2}|^2$ from $M_a^{(0)}$ and $M_a^{(1)}$, with explicit formulas for all cascade channels. A key theoretical finding is that the normalized spectra $d\Gamma/(\Gamma dE)$ possess fixed points that are invariant under NP contributions described by the EFT, providing a robust experimental cross‑check. The framework enables stringent tests of NP involving right‑handed neutrinos and offers concrete avenues for measurement at current and future facilities such as BESIII, Belle II, CEPC, and FCC‑ee.

Abstract

In this work, we have conducted a comprehensive and systematic theoretical investigation of the full cascade decays of charged pseudoscalar mesons, specifically $D_s$, $D$, $B$, and $B_c$, into $τν_τ$, followed by the subsequent decay of the $τ$ via its dominant experimentally reconstructible channels: $τ\to πν_τ$, $τ\to ρν_τ$, $τ\to e \barν_e ν_τ$, and $τ\to μ\barν_μν_τ$. Our study is framed within the model-independent low-energy effective field theory approach, which incorporates the most general set of four-fermion operators, including those coupling to right-handed neutrinos. We provide precise Standard Model predictions for differential decay rate as a function of the final-state charged particle energy, develop an innovative and robust methodology for extracting the magnitudes of the new physics couplings using energy moments, and identify and characterize fixed points in the normalized energy distributions. The fixed points are invariant under new physics contributions described by the considered effective Hamiltonian.

Figures (1)

• Figure 1: Numerical results for differential distributions $d\Gamma/dE_a$ ($a=\pi,\rho,e,\mu$) within the SM. From left to right are the results of the cascade decays of the $D_s$, $D$, and $B$ mesons, respectively.