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Probing New Physics and CP Violation in $ν_τn \to Λ_c τ^- (π^- ν_τ)$ and $\barν_τp \to Λτ^+ (π^+ \barν_τ)$

E. Hernández, J. Nieves, J. E. Sobczyk

TL;DR

The paper develops a model‑independent EFT description of ν_τ(n) and ¯ν_τ(p) charged‑current transitions to Λ hyperons, incorporating all dimension‑six operators and allowing complex Wilson coefficients that can induce CP violation. A genuine CP‑odd signal is proposed: the azimuthal asymmetry of the pion from τ→πν in τ decays, which probes the transverse CP component P_{TT} of the τ polarization. Using lattice QCD form factors for the hadronic transitions and current experimental constraints on Wilson coefficients, the authors predict differential and total cross sections for ν_τ n → Λ_c τ^− (π^− ν_τ) and ¯ν_τ p → Λ τ^+ (π^+ ¯ν_τ), finding NP effects at the percent level and CP asymmetries Δσ that are small but nonzero when complex phases are present. The CP‑odd observable Δσ benefits from cancellations of hadronic uncertainties, making it a clean probe for NP that could be explored at facilities like DUNE, while future work will address nuclear effects and additional hyperon channels.

Abstract

We study the processes $ν_τn \to Λ_c τ^- (π^- ν_τ)$ and $\barν_τp \to Λτ^+ (π^+ \barν_τ)$, with particular emphasis on the pion energy and angular distributions, as a possible signal for lepton flavor universality violation, and in general of physics beyond the Standard Model (SM), as well as a sensitive probe of the $τ$ polarization vector. We work within an effective low-energy extension of the SM with all dimension-six four-fermion operators. In this framework, complex Wilson coefficients which encode new physics can generate CP-violating contributions. We propose an observable that provides a genuine CP-odd signal due to its sensitivity to particular transverse components of the $τ$ polarization vector. Namely, we show that the asymmetry in the azimuthal-angle distribution of the pion in the decay $τ^\pm\to π^\pm ν_τ$ constitutes a smoking-gun prediction of such a beyond the SM scenario. We estimate the strength of this effect extrapolating nucleon-hyperon form factors recently obtained from lattice QCD calculations.

Probing New Physics and CP Violation in $ν_τn \to Λ_c τ^- (π^- ν_τ)$ and $\barν_τp \to Λτ^+ (π^+ \barν_τ)$

TL;DR

The paper develops a model‑independent EFT description of ν_τ(n) and ¯ν_τ(p) charged‑current transitions to Λ hyperons, incorporating all dimension‑six operators and allowing complex Wilson coefficients that can induce CP violation. A genuine CP‑odd signal is proposed: the azimuthal asymmetry of the pion from τ→πν in τ decays, which probes the transverse CP component P_{TT} of the τ polarization. Using lattice QCD form factors for the hadronic transitions and current experimental constraints on Wilson coefficients, the authors predict differential and total cross sections for ν_τ n → Λ_c τ^− (π^− ν_τ) and ¯ν_τ p → Λ τ^+ (π^+ ¯ν_τ), finding NP effects at the percent level and CP asymmetries Δσ that are small but nonzero when complex phases are present. The CP‑odd observable Δσ benefits from cancellations of hadronic uncertainties, making it a clean probe for NP that could be explored at facilities like DUNE, while future work will address nuclear effects and additional hyperon channels.

Abstract

We study the processes and , with particular emphasis on the pion energy and angular distributions, as a possible signal for lepton flavor universality violation, and in general of physics beyond the Standard Model (SM), as well as a sensitive probe of the polarization vector. We work within an effective low-energy extension of the SM with all dimension-six four-fermion operators. In this framework, complex Wilson coefficients which encode new physics can generate CP-violating contributions. We propose an observable that provides a genuine CP-odd signal due to its sensitivity to particular transverse components of the polarization vector. Namely, we show that the asymmetry in the azimuthal-angle distribution of the pion in the decay constitutes a smoking-gun prediction of such a beyond the SM scenario. We estimate the strength of this effect extrapolating nucleon-hyperon form factors recently obtained from lattice QCD calculations.
Paper Structure (13 sections, 50 equations, 5 figures, 2 tables)

This paper contains 13 sections, 50 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Effective Hamiltonian
  3. The $\nu_\tau n\to \Lambda_c\tau^-(\pi^-\nu_\tau$) reaction
  4. The $\bar{\nu}_\tau p\to\Lambda \tau^+(\pi^+\bar{\nu}_\tau)$ reaction
  5. Results
  6. $\nu_\tau n\to\Lambda_c \tau^-(\pi^-\nu_\tau)$
  7. $\bar{\nu}_\tau p\to\Lambda \tau^+(\pi^+\bar{\nu}_\tau)$
  8. Conclusions
  9. Lepton Tensor, $\tau$ Polarization Vector, and Phase-Space Integration in $\nu_\tau n \to \Lambda_c \tau^- (\pi^- \nu_\tau)$
  10. Lepton Tensor
  11. Polarization vector
  12. Phase-Space Integration
  13. Correspondence between the $\bar{\nu}_\tau p\to\Lambda \tau^+(\pi^+\bar{\nu}_\tau)$ and $\nu_\tau n \to \Lambda_c \tau^- (\pi^- \nu_\tau)$ cross sections.

Figures (5)

  • Figure 1: Neutron-LAB kinematics for $\nu_\tau n \to \Lambda_c \tau^- (\pi^- \nu_\tau)$, showing the three-momenta $\vec{k}$, $\vec{k}'$, $\vec{p},'$ and $\vec{p}_\pi$ of the incoming neutrino, intermediate $\tau$, outgoing $\Lambda_c$, and pion. We also display the longitudinal unit vector $\vec{n}_L = \vec{k}'/|\vec{k}'|$ and the transverse unit vectors $\vec{n}_T$ and $\vec{n}_{TT}$ entering the definition of $N_L^\mu$, $N_T^\mu$, and $N_{TT}^\mu$ in Eq. \ref{['eq:nvecpol']}.
  • Figure 2: Double-differential cross section $d^2\sigma/(dE_\pi\, d\cos\theta_\pi)$ for the $\nu_\tau n \to \Lambda_c \tau^- (\pi^- \nu_\tau)$ reaction at $E_{\nu_\tau}=10\,\mathrm{GeV}$, evaluated within the SM for a fully left-handed polarized $\nu_\tau$ beam. The form factors have been taken from Ref. Meinel:2017ggx.
  • Figure 3: Differential cross sections $d\sigma/dE_\pi$ (left) and $d\sigma/d\cos\theta_\pi$ (right) for the $\nu_\tau n \to \Lambda_c \tau^- (\pi^- \nu_\tau)$ reaction evaluated at $E_\nu = 10\,\mathrm{GeV}$, for a fully left-handed polarized $\nu_\tau$ beam. The SM prediction (red curve) is shown together with results including NP effects (orange-shaded band) induced by a nonzero Wilson coefficient $C^V_{dc\tau RL}=0.04+0.12e^{i\phi}$. In both panels, the upper limit of the band is reached for $\phi=0$, while for the lower limit $\phi=\pi$.
  • Figure 4: Double-differential cross section $d^2\sigma/(dE_\pi\, d\cos\theta_\pi)$ for the $\bar{\nu}_\tau p \to \Lambda \tau^+ (\pi^+ \bar{\nu}_\tau)$ reaction, evaluated at $E_{\bar{\nu}_\tau} = 5\,\mathrm{GeV}$ within the SM for a fully right-handed $\bar{\nu}_\tau$ beam. The left panel shows results using the LQCD form factors from Ref. Bacchio:2025auj, while the right panel is evaluated with the phenomenological form factors from Ref. Mintz:2004hm.
  • Figure 5: SM differential cross sections $d\sigma/dE_\pi$ (left panel) and $d\sigma/d\cos\theta_\pi$ (right panel) for the $\bar{\nu}_\tau p \to \Lambda \tau^+ (\pi^+ \bar{\nu}_\tau)$ reaction, evaluated at $E_{\bar{\nu}_\tau} = 5\,\mathrm{GeV}$ for a fully right-handed polarized $\bar{\nu}_\tau$ beam. Results obtained using the LQCD form factors from Ref. Bacchio:2025auj (red curve) and the phenomenological form factors from Ref. Mintz:2004hm (black curve) are shown. The dotted curve corresponds to the latter prediction rescaled to reproduce the total cross section obtained with the LQCD form factors.