Prospects for $P$ and $C\!P$ violation in $Λ_{c}^{+}$ decays with polarized beam at Super Tau-Charm Facility

TL;DR

This work assesses the prospects for parity and CP violation measurements in charmed-baryon decays at the Super Tau-Charm Facility using polarized $e^+e^-$ collisions that produce quantum-entangled $Λ_c^+\bar{Λ}_c^-$ pairs. It develops a spin-density-matrix formalism incorporating longitudinal and transverse beam polarization, and derives cascade-angular distributions for multiple decay chains. A fast Monte Carlo framework (OSCAR) with a single-tag analysis and an unbinned likelihood fit is employed to estimate sensitivities for $P$- and $Car{P}$-violating observables in $Λ_c^+$ decays to $pπ^0$, $pη$, $ΛK^+$, $Σ^0K^+$, and $Σ^+K^0_S$, under various polarization scenarios. The results indicate that longitudinal polarization substantially enhances precision, with potentially $\sim$order-of-magnitude improvements in certain parameters and reach to the $10^{-2}$ level for some channels at realistic luminosities. These findings position STCF as a uniquely powerful facility for probing symmetry-violating effects in charm baryons and complementing existing programs at LHCb and Belle II.

Abstract

Weak decays of the charmed baryons offer an ideal platform to study parity ($P$) and charge conjugation-parity ($C\!P$) violation in quark sector, to stringently test the Standard Model and search for new physics. It is a key goal in the next-generation positron-electron collider, such as the Super Tau-Charm Facility (STCF). Thanks to the quantum-entangled pair production with super high luminosity and the possibility of beam polarization, STCF provides a unique environment to probe such symmetry violations with unprecedented sensitivity. In this paper, we evaluate the precisions of the $P$-violating parameters and subsequently obtain the expected sensitivity of the $C\!P$-violating parameters in charmed baryon decays of $Λ_{c}^{+}\to pπ^0$, $pη$, $ΛK^+$, $Σ^0 K^+$, and $Σ^+ K^0_S$, regarding to different polarization setups in STCF. The study suggests that the implementation of longitudinal beam polarization in STCF would greatly enhance the experimental capability in studying $P$ and $C\!P$ violation.

Figures (9)

• Figure 1: Topological structure of the process $e^{+}e^{-} \to\Lambda_c^+\bar{\Lambda}_c^-$. The $z$-axis is defined along the momentum direction of the positron beam.
• Figure 2: Data taking plan of different experiments in high luminosity with similar physical goals.
• Figure 3: Uncertainty prediction of $P$-violating parameters $\alpha_{\Lambda K^+}$ for channel $\Lambda_c^+\to\Lambda K^+$ in different integrated luminosity with different polarized beam.
• Figure 4: Uncertainty prediction of parameters $\Delta_{\Lambda K^+}$ and $A^{\alpha_{\Lambda K^+}}_{C\!P}$ for channel $\Lambda_c^+\to\Lambda K^+$ in different integrated luminosity with different polarized beam.
• Figure 5: Uncertainty prediction of parameters $\alpha_{p\pi^0}$ and $A^{\alpha_{p\pi^0}}_{C\!P}$ for channel $\Lambda_c^+\to p\pi^0$ in different integrated luminosity with different polarized beam.