Investigation of triply heavy spin-3/2 baryons in their ground and excited states

TL;DR

This work addresses the lack of experimental data on triply heavy spin-3/2 baryons by applying QCD sum rules with operators up to dimension eight to compute the masses and residues of the ground and first two excited states for $Ω^*_{ccc}$, $Ω^*_{ccb}$, $Ω^*_{bbc}$ and $Ω^*_{bbb}$ in both pole and $\overline{MS}$ schemes. The authors construct the two-point correlator $\Pi_{\mu\nu}(q)$ from the interpolating current $\eta_\mu$, perform OPE on the QCD side, and match to the hadronic representation, isolating the $g_{\mu\nu}$ structure to extract $m$ and $\lambda$ for the $1S$, $1P$, and $2S$ states through a three-step, $s_0$-dependent procedure. Numerical results show that the predicted masses align with other theoretical predictions within a few percent, while the residues exhibit larger discrepancies, underscoring the importance of the higher-dimension condensates for precise decay- and interaction-related inputs. These predictions provide valuable guidance for ongoing and future experimental searches at high-energy colliders and for studies of decay channels and interactions involving triply heavy baryons.

Abstract

We calculate the masses and residues of triply heavy baryons with spin-3/2, including $Ω^*_{ccc}$, $Ω^*_{ccb}$, $Ω^*_{bbc}$ and $Ω^*_{bbb}$, using the QCD sum rules method. Our calculations primarily focus on obtaining the masses of the first three resonances, that is, the ground state (1S), the first orbital excited state (1P), and the first radial excited state (2S), for the mentioned baryons. We additionally determine the residues of these baryons, which serve as key parameters for studying their possible decay channels and interactions with other particles. To achieve higher accuracy compared to previous studies, we consider nonperturbative operators up to eight mass dimensions. We present our calculated outcomes in two distinct energy schemes, referred to as pole and $\mathrm{\overline{MS}}$. Given the absence of experimental data for these states, we compare our results with previous theoretical calculations that are reported in relevant studies employing various approaches. These results may provide valuable insights for experimental groups searching for the triply heavy baryons.

Figures (3)

• Figure 1: Dependence of FTRC on $M^2$ for three distinct values of $s_0$ in the $\overline{\Omega}^*_{ccb}$ state.
• Figure 2: Left column: Mass dependence of $\overline{\Omega}^*_{ccc}$ for the first $(1S)$, second $(1P)$ and third $(2S)$ resonances with respect to $M^2$ for different values of $s_0$. Right column: Mass dependence of $\overline{\Omega}^*_{ccb}$ for the first $(1S)$, second $(1P)$ and third $(2S)$ resonances with respect to $M^2$ for different values of $s_0$..
• Figure 3: Left column: Mass dependence of $\overline{\Omega}^*_{ccc}$ for the first $(1S)$, second $(1P)$ and third $(2S)$ resonances with respect to $s_0$ for different values of $M^2$. Right column: Mass dependence of $\overline{ \Omega}^*_{ccb}$ for the first $(1S)$, second $(1P)$ and third $(2S)$ resonances with respect to $s_0$ for different values of $M^2$.