Lattice QCD calculation of charmed baryon decay constants at continuum limit and physical mass

TL;DR

This paper delivers the first-principles lattice-QCD determination of charmed-baryon decay constants using $2+1$ flavor ensembles and SU(3) flavor-based interpolating operators. It performs nonperturbative renormalization in the SYM3q/SMOM$_{\gamma_\mu}$ scheme and converts to $\overline{\mathrm{MS}}$ at $\mu=2$ GeV, followed by joint chiral and continuum extrapolations. The authors obtain renormalized decay constants for $\Lambda_c$, $\Xi_c$, $\Xi_c'$, $\Sigma_c$, and $\Omega_c$ with total uncertainties of about $8$–$16\%$, providing a robust set of inputs for charm phenomenology and CKM analyses and offering a benchmark for heavy-quark symmetry studies. This work thus strengthens the theoretical foundation for interpreting charm-decay processes and sets the stage for further lattice studies of baryonic observables in QCD.

Abstract

We present the first principle calculation of charmed baryon decay constants employing 2+1 flavor gauge ensembles with lattice spacings ranging from 0.05 to 0.1 fm and pion masses between 136 and 310 MeV. Under $SU(3)$ flavor symmetry, we construct the charmed baryon interpolating operators and compute the corresponding hadronic matrix elements to extract the bare decay constants for each ensemble. The non-perturbative renormalization is performed via the symmetric momentum-subtraction scheme. After performing systematic chiral and continuum extrapolations, we obtain the decay constants with a precision of $8\sim 16\%$ from first principles.

Figures (13)

• Figure 1: $SU(3)$ flavor classification of the $J^{P}=(1/2)^{+}$ charmed baryons. Green triangles denote the anti-triplet states, while blue inverted triangles denote the sextet states.
• Figure 2: The two-point correlation functions of charmed baryons, shown from top to bottom, correspond to the quark level and the hadron level, respectively.
• Figure 3: The chiral and continuum extrapolation results for the charmed baryon masses are shown as a function of the lattice spacing. The blue, red, green, purple and yellow error bands correspond to $\Lambda_{c}$, $\Xi_{c}$, $\Xi^{\prime}_{c}$, $\Sigma_{c}$ and $\Omega_{c}$ baryons, respectively.
• Figure 4: The left and right panels show the results for the ratios of renormalization constants $Z_{O_{1}}^{\overline{\mathrm{MS}}}/Z_{V}^{3/2}$ and $Z_{O_{2}}^{\overline{\mathrm{MS}}}/Z_{V}^{3/2}$ at the scale $\mu = 2\mathrm{GeV}$, where the black, brown, green, purple, red, and blue error bars correspond to the C24P29, C32P29, C32P23, C48P14, F32P30, and H48P32 ensembles, respectively. The solid lines show the fitting results of Eq. (\ref{['eq: a2p2 fit']}). The dashed lines show the extrapolation results for $a^2p^2=0$ after removing the $c^{-1}(a^{2}p^{2})^{-1}$ term in Eq. (\ref{['eq: a2p2 fit']}).
• Figure 5: The chiral and continuum extrapolation results for the charmed baryon decay constants are shown as a function of $m_{\pi}^{2}$. The red, green, and blue error bands correspond to lattice spacings of 0.10524 fm, 0.07753 fm, and 0.05199 fm, respectively, while the black error bar represents the physical point.