Final-state rescattering mechanism of the $\Delta (1232{)}^{++}$ production in ${\Lambda }_c^{+}\to K^{-}{\pi }^{+}p$ decay

Abstract

We investigate the production of the $\Delta (1232{)}^{++}$ resonance in the charmed baryon weak decay ${\Lambda }_c^{+}\to K^{-}{\pi }^{+}p$, focusing on the ${\pi }^{+}p$ final-state rescattering mechanism. The direct $W^{+}$ exchange diagram is expected to be suppressed, hence we adopt the $W^{+}$ internal emission process ${\Lambda }_c^{+}\to p{\bar{K}}^{\ast 0}(892)$ followed by the subsequent decay ${\bar{K}}^{\ast 0}\to K^{-}{\pi }^{+}$ as the dominant source of the final state particles. The $\Delta (1232{)}^{++}$ resonance is then generated via ${\pi }^{+}p$ rescattering within a triangle loop mechanism. Our calculations incorporate both the tree-level ${\bar{K}}^{\ast 0}(892)$ and the dynamically generated ${\bar{K}}_0^{\ast }(700)$ state arising from the $S$-wave $K\pi$ final state interaction. We find that our theoretical results can reproduce the bump and peak structures in the $K^{-}{\pi }^{+}$ invariant mass distributions for the ${\bar{K}}_0^{\ast }(700)$ and ${\bar{K}}^{\ast 0}(892)$, respectively. Meanwhile, the peak for the $\Delta (1232{)}^{++}$ in the ${\pi }^{+}p$ invariant mass distributions is also well described. The $\Delta (1232{)}^{++}$ signal naturally emerges from rescattering effects, and adopting the pole parameters of $\Delta (1232)$ resonance yields an improved description of the experimental data. In addition, we obtain a branching fraction ratio $\mathcal{B}[{\Lambda }_c^{+}\to \Delta (1232{)}^{++}{K}^{-}]/\mathcal{B}[{\Lambda }_c^{+}\to p{\bar{K}}^{\ast 0}(892)]\approx 0.5$, which is lower than the experimentally measured value. This discrepancy suggests that interference effects are likely significant in this decay process. Future high-precision measurements will further verify the proposed rescattering mechanism.

Comments: 9 pages, 5 figures