[Paper Review] The $a_0(980)$ in the single Cabibbo-suppressed process $Λ_c o π^0ηp$

Xue-Chao Feng, Le-Le Wei+3 more|arXiv (Cornell University)|Sep 18, 2020

Quantum Chromodynamics and Particle Interactions27 references4 citations

TL;DR

This study investigates the Cabibbo-suppressed decay $\Lambda_c \to \pi^0\eta p$ using the chiral unitary approach, where the $a_0(980)$ resonance is dynamically generated from $\pi^0\eta$ final-state interactions. A significant cusp structure near 980 MeV in the $\pi^0\eta$ invariant mass distribution is predicted, with a branching fraction estimated at $1.13\sim1.26\times10^{-4}$ for positive $C$ and $5.96\sim8.19\times10^{-4}$ for negative $C$, suggesting detectability at BESIII and Belle II experiments.

ABSTRACT

In this work, we have investigated the Cabibbo-suppressed process $Λ_c o π^0ηp$, by taking into account the intermediate scalar state $a_0(980)$, which could be dynamically generated from the $S$-wave pseudoscalar-pseudoscalar interaction within the chiral unitary approach. We have calculated the $π^0η$ invariant mass distribution, and found that there is a significant structure associated to the $a_0(980)$. We have also roughly estimated the branching fraction $\mathcal{B}(Λ_c o π^0ηp) \sim 10^{-4}$. We encourage our experimental colleagues to measure the process $Λ_c o π^0ηp$ for searching for the state $a_0(980)$ in this reaction.

Motivation & Objective

• To investigate the production mechanism of the $a_0(980)$ resonance in the Cabibbo-suppressed decay $\Lambda_c \to \pi^0\eta p$.
• To explore the role of final-state interactions involving $\pi^0\eta$, $K^+K^-$, and $K^0\bar{K}^0$ in generating the $a_0(980)$ resonance.
• To provide a theoretical prediction of the $\pi^0\eta$ invariant mass distribution and branching fraction for future experimental validation.
• To constrain the parameter $C$ in the weak transition amplitude through future precision measurements.

Proposed method

• The process is modeled in three steps: weak decay at the quark level, hadronization, and final-state interaction (FSI) via the chiral unitary approach.
• The $a_0(980)$ is dynamically generated from $S$-wave $\pi^0\eta$ and $K\bar{K}$ interactions using the chiral unitary framework.
• Transition amplitudes for $K^+K^- \to \pi^0\eta$, $K^0\bar{K}^0 \to \pi^0\eta$, and $\pi^0\eta \to \pi^0\eta$ are calculated to model the resonance formation.
• The $\pi^0\eta$ invariant mass distribution is computed by integrating the squared transition amplitude over the physical region.
• The branching fraction is estimated using the normalization factor $V_p^2 / \Gamma_{\Lambda_c} = 0.2$ MeV$^{-1}$ from prior work.
• The dependence of the lineshape on the sign of parameter $C$ is analyzed to assess sensitivity to dynamical inputs.

Experimental results

Research questions

• RQ1 Can the $a_0(980)$ resonance be observed in the $\Lambda_c \to \pi^0\eta p$ decay via final-state interactions?
• RQ2 What is the expected shape of the $\pi^0\eta$ invariant mass distribution in this decay channel?
• RQ3 How does the sign of the parameter $C$ affect the lineshape of the $\pi^0\eta$ mass distribution?
• RQ4 What is the predicted branching fraction of $\Lambda_c \to \pi^0\eta p$, and is it accessible at BESIII or Belle II?
• RQ5 Can this decay channel help disentangle the contributions of $a_0(980)$ and $f_0(980)$ in $K^+K^-$ final states?

Key findings

• A clear cusp structure near 980 MeV in the $\pi^0\eta$ invariant mass distribution is observed, corresponding to the $a_0(980)$ resonance.
• For positive $C$, the distribution exhibits a dip near 980 MeV; for negative $C$, a prominent cusp structure emerges.
• The branching fraction is estimated at $(1.13\sim1.26)\times10^{-4}$ for positive $C$ and $(5.96\sim8.19)\times10^{-4}$ for negative $C$.
• The predicted branching fraction is within the sensitivity reach of BESIII and Belle II experiments.
• The lineshape is sensitive to the sign of $C$, suggesting that future measurements could constrain this parameter and test $N_c$ scaling in weak decays.
• The model predicts a significant resonance structure in $\pi^0\eta$ channel, supporting the $a_0(980)$ as a dynamically generated state from meson-meson interactions.