Analysis of the semileptonic decays of $Ξ_{cc}$ and $Ω_{cc}$ baryons in QCD sum rules

TL;DR

This work uses three-point QCD sum rules to study $J^{P}=\frac{1}{2}^{+}\rightarrow\frac{3}{2}^{+}$ weak transitions in doubly charmed baryons, extracting 16 form factors $F_i(Q^{2})$ and $G_i(Q^{2})$ from a carefully constructed correlator $\Pi_{\mu\nu}(p,p')$ and its hadronic and QCD representations. A double Borel transform and quark-hadron duality yield linear equations whose solutions provide the $Q^{2}$-dependent form factors, which are then fitted with a $z$-series to extrapolate to the time-like region. These form factors are employed to compute differential and total decay widths for ${\Xi_{cc}^{++}\rightarrow \Sigma_{c}^{*+}l^{+}\nu_{l}}$, ${\Xi_{cc}^{++}\rightarrow \Xi_{c}^{\prime*+}l^{+}\nu_{l}}$, ${\Omega_{cc}^{+}\rightarrow \Xi_{c}^{\prime*0}l^{+}\nu_{l}}$, and ${\Omega_{cc}^{+}\rightarrow \Omega_{c}^{*0}l^{+}\nu_{l}}$ with $l=e,\mu$. While the $F_i(0)$ values differ from some prior results, the time-like extrapolation brings the widths into reasonable agreement with other models, and the results show identifiable SU(3) breaking and dominance patterns among the decay channels, providing insights for heavy-baryon dynamics and potential new-physics probes.

Abstract

We firstly carry out a systematic analysis on the spin $\frac{1}{2}^{+}\rightarrow\frac{3}{2}^{+}$ weak transition process in the framework of three-point QCD sum rules, where the initial and final states are doubly and singly charmed baryons. In the phenomenological side, all possible couplings of interpolating current to hadronic states are considered. In doing operator production expansion at QCD side, the contributions of the perturbative part, vacuum condensate terms of $\langle{\bar qq}\rangle$, $\langle g_{s}^{2}GG\rangle$, $\langle \bar q g_{s}σGq\rangle$ and $g_{s}^{2}\langle{\bar qq}\rangle^{2}$ are all considered. After the form factors in space-like region ($Q^2>0$) are obtained, the numerical results are extrapolated into time-like region ($Q^2<0$) by a fitting function. Using the predicted form factors, we finally analyze the semileptonic decays of $Ξ_{cc}^{++}\rightarrow Σ_{c}^{*+}l^{+}ν_{l}$, $Ξ_{cc}^{++}\rightarrow Ξ_{c}^{\prime*+}l^{+}ν_{l}$, $Ω_{cc}^{+}\rightarrowΞ_{c}^{\prime*0}l^{+}ν_{l}$ and $Ω_{cc}^{+}\rightarrow Ω_{c}^{*0}l^{+}ν_{l}$ with $l=e,μ$. The predictions in this work can deepen our understanding of the dynamics in the decay processes of doubly heavy baryons and provide useful information to explore the possibility of new physics in heavy baryonic decay channels.

Figures (5)

• Figure 1: Feynman diagram of semileptonic decay process $\mathcal{B}_{1}\rightarrow \mathcal{B}_{2}^{*}l\nu_{l}$.
• Figure 2: The Feynman diagrams for the perturbative part and vacuum condensate terms, where the doubly-solid line denotes a charm quark, and the ordinary solid line represents a light quark.
• Figure 3: Variations of the pole contributions and contributions of perturbative term, different vacuum condensates with respect to the Borel parameter $\mathrm{M}_{2}^{2}$. These results are for the form factors $F_{1}$ and $F_{4}$ of transition $\Xi_{cc}^{++}\rightarrow\Sigma_{c}^{*+}$. The blue bounds denote the Borel platform.
• Figure 4: The fitting results of the form factors for transition processes $\Xi_{cc}^{++}\rightarrow\Sigma_{c}^{*+}$ and $\Xi_{cc}^{++}\rightarrow\Xi_{c}^{\prime*+}$.
• Figure 5: The fitting results of the form factors for transition processes $\Omega_{cc}^{+}\rightarrow\Xi_{c}^{\prime*0}$ and $\Omega_{cc}^{+}\rightarrow\Omega_{c}^{*0}$.