The nonleptonic decays of double-charmed baryon $Ω_{cc}^{+}$ within the nonrelativistic quark model

TL;DR

The paper addresses the weak two-body nonleptonic decays of the double-charmed baryon $Ω_{cc}^{+}$, a regime where nonfactorizable contributions from $W$-exchange are significant. It adopts a nonrelativistic quark framework (NRQM) and separates $W$-emission and $W$-exchange topologies, computing nonfactorizable amplitudes via a pole model while using baryon wave functions obtained from a Schrödinger-equation potential to reduce dependence on ill-defined spatial forms. The study finds that Cabibbo-favored decays and several singly Cabibbo-suppressed channels achieve branching fractions at the percent level, with $Ω_{cc}^{+} oΩ_{c}^{0}K^{+}$ notably competitive with CF modes due to large factorizable and pole contributions. These results provide concrete discovery channels for $Ω_{cc}^{+}$ at LHCb and Belle II and illustrate the importance of nonfactorizable dynamics in charmed-baryon weak decays, while also highlighting potential long-distance final-state interaction effects in some channels.

Abstract

In this work, we investigate the two-body nonleptonic decays of double-charmed baryon $Ω_{cc}^{+}$ within a nonrelativistic quark model, in which the nonfactorizable amplitudes contributed by $W$-exchange diagrams are evaluated under pole model assumption. To reduce sensitivity of decay amplitudes to arbitrary choice of baryon wave functions, we adopted charmed baryon wave functions obtained by solving the Schrödinger equation with a nonrelativistic quark potential model. Our results show that the branching fractions of CF decays $Ω_{cc}^{+}\toΩ_{c}^{0}π^{+}$ and $Ξ_{c}^{(\prime)+}π^{+}$, as well as the SCS decays $Ω_{cc}^{+}\toΩ_{c}^{0}K^{+}$, $Σ_{cc}^{++}K^{-}$, $Ξ_{c}^{\prime+}η$ and $Λ_{c}^{+}\bar{K}^{0}$ can reach up to a few percents. Particularly for the $Ω_{cc}^{+}\toΩ_{c}^{0}K^{+}$ mode, owing to the large factorizable amplitude and constructive pole contributions, the branching fraction is comparable to CF decays. These decay modes can serve as the discovery channels for the double-charmed baryon $Ω_{cc}^{+}$ in future experiments like LHCb and Belle II.

Figures (5)

• Figure 1: The Feynman diagrams for nonleptonic decays of double-charmed baryon $\Omega_{cc}^{+}$.
• Figure 2: The kinematic conventions of $W$-emission process.
• Figure 3: The kinematic conventions of $W$-exchange process.
• Figure 4: The corresponding pole diagrams of $W$-exchange processes.
• Figure 5: The definition of Jacobi coordinates of $\rho$-mode and $\lambda$-mode of charmed baryon. We set $q_{1}q_{2}q_{3}=(qqc)$ for single-charmed baryons and $q_{1}q_{2}q_{3}=(ccq)$ for double charmed baryons.