Singly Cabibbo-suppressed hadronic decays of $\Lambda_c^+$

TL;DR

This paper analyzes singly Cabibbo-suppressed two-body hadronic decays of the $\\Lambda_c^+$ baryon using current algebra and experimental data to predict decay rates, interference effects, and asymmetries, with results aligning well with measurements.

Contribution

It introduces a method combining current algebra and experimental data to predict decay amplitudes and asymmetries for $\\Lambda_c^+$ decays, improving understanding of nonfactorizable effects.

Findings

Predicted $\\Lambda_c^+\to p\eta$ rate matches BESIII data.

Found large constructive interference in $p\eta$ mode.

Branching ratio of $n\pi^+$ is about 3.5 times that of $p\pi^0$.

Abstract

We study singly Cabibbo-suppressed two-body hadronic decays of the charmed baryon $\Lambda_c^+$, namely, $\Lambda_c^+\to \Lambda K^+, p\pi^0, p\eta, n\pi^+,\Sigma^0K^+,\Sigma^+ K^0$. We use the measured rate of $\Lambda_c^+\to p\phi$ to fix the effective Wilson coefficient $a_2$ for naive color-suppressed modes and the effective number of color $N_c^{\rm eff}$. We rely on the current-algebra approach to evaluate $W$-exchange and nonfactorizable internal $W$-emission amplitudes, that is, the commutator terms for the $S$-wave and the pole terms for the $P$-wave. Our prediction for $\Lambda_c^+\to p\eta$ is in excellent agreement with the BESIII measurement. The $p\eta$ ($p\pi^0$) mode has a large (small) rate because of a large constructive (destructive) interference between the factorizable and nonfactorizable amplitudes for both $S$- and $P$-waves. Some of the SU(3) relations such as $M(\Lambda_c^+\to n\pi^+)=\sqrt{2}M(\Lambda_c^+\to p\pi^0)$ derived under the assumption of sextet dominance are not valid for decays with factorizable terms. Our calculation indicates that the branching fraction of $\Lambda_c^+\to n\pi^+$ is about 3.5 times larger than that of $\Lambda_c^+\to p\pi^0$. Decay asymmetries are found to be negative for all singly Cabibbo-suppressed modes and range from $-0.56$ to $-0.96$.