Precise study of triply charmed baryons $Ω_{ccc}$

TL;DR

This work delivers the most precise lattice QCD predictions to date for the ground-state masses of the triply charmed baryon $\Omega_{ccc}$ in the $3/2^+$ and $3/2^-$ channels, using six $N_f=2+1+1$ MILC ensembles and two valence charm actions. By performing continuum extrapolations from five lattice spacings and two volumes and by subtracting the charm content (e.g., $\Delta M_{\Omega_{ccc}}=M_{\Omega_{ccc}}-\tfrac{3}{2}M_{c\bar c}$ with $c\bar c=J/\psi$ or $\overline{1S}$), the study controls discretization and scale uncertainties and yields robust predictions. The results are $M_{\Omega_{ccc}}(3/2^+)=4793(5)\left(^{+11}_{-8}\right)$ MeV and $M_{\Omega_{ccc}}(3/2^-)=5094(12)\left(^{+19}_{-17}\right)$ MeV, with a parity splitting of $\Delta_{\Omega_{ccc}}(3/2^+-3/2^-) =301(13)(14)$ MeV; electromagnetic, finite-volume, and sea-quark effects are carefully quantified in the total error. These precise lattice predictions provide a stringent target for experimental searches and offer valuable benchmarks for heavy-quark dynamics in triply charmed systems.

Abstract

We present the most precise results for the ground state mass of the triply-charmed spin-$3/2$ baryon using lattice quantum chromodynamics. The calculations are performed on six $N_f=2+1+1$ Highly Improved Staggered Quark (HISQ) lattice ensembles generated by the MILC collaboration. Two different lattice setups are employed: in the first one, a fully dynamical calculation with HISQ action is performed, while in the second calculation, an overlap action is utilized for the valence charm quark dynamics. Following the continuum extrapolation of our results, obtained at five different lattice spacings, two different volumes, and two different actions, our prediction for the mass of the lowest triply charmed spin-3/2 baryon, $Ω_{ccc} (3/2^{+})$, is $4793 (5) \left(^{+11}_{-8}\right)$ MeV. This is the most precise determination to date, fully addressing the systematic uncertainties. We also predict the $Ω_{ccc} (3/2^{-})$ mass to be $5094 (12) \left(^{+19}_{-17}\right)$ MeV.

Figures (18)

• Figure 1: Six lattice QCD ensembles used in this work and are labeled in the plot as S$_5$ ($96^3 \times 288$), S$_4$ ($64^3 \times 192$), S$_3$ ($48^3 \times 144$), S$_2$ ($32^3 \times 96$), S$_1$ ($24^3 \times 64$), and L$_1$ ($40^3 \times 64$).
• Figure 2: Representative effective mass plots for the lowest energy state of $\Omega_{cc}(3/2^+)$ baryon. Top: overlap action, lattice size: $64^3\times 192$, Bottom: HISQ action, lattice size $96^3\times 288$.
• Figure 3: Continuum extrapolations of the subtracted ground state masses $\Delta M^{\text{sub}}_{\Omega_{ccc}}(a)$ (Eq. \ref{['eq:sub']}). Top two: $\Omega_{ccc}(3/2^+)$ and bottom two: $\Omega_{ccc}(3/2^-)$. Subtraction of charm quark content is done with both $c\bar{c} \equiv J/\psi$ and $\overline{1S}$. Various fit forms with their respective color schemes are shown in the legends and more details on fits are provided in the supplement Suppl. The shaded bands represent $1\sigma$ uncertainties, estimated via the bootstrap method. Symbol star: continuum extrapolated values. Red solid square: final value by symmetrized averaging the linear fit results of overlap and HISQ quarks, while the extended errors include other fits results.
• Figure 4: Summary of results on the ground state mass of $\Omega_{ccc}(3/2^+)$ (left) and $\Omega_{ccc}(3/2^-)$ (right) baryons as obtained in various calculations (references on the side panels can be tracked through the faint horizontal lines). The results below the thick horizontal dashed line are from lattice calculations and above that are obtained using various models. Among the lattice results, those with orange circles are obtained with continuum extrapolations, while others (blue circles) are obtained at a single lattice spacing. The deviation of the results obtained in Refs. Alexandrou:2012xk and Alexandrou:2014sha are most possibly due to their errors in the charm quark mass tuning. Our results at the physical point are shown by the red circles (at the bottom).
• Figure 5: Effective mass plots corresponding to the positive (top) and negative (bottom) parity lowest energy levels of $\Omega_{ccc}(3/2)$ baryons for different lattice ensembles. The dashed lines are the fit results with one exponential fits, and the bands show the fit ranges with the corresponding $1\sigma$ errors.