Baryon spectrum with $N_f=2+1+1$ twisted mass fermions

TL;DR

This work computes the low-lying baryon spectrum using $N_f=2+1+1$ twisted mass fermions across three lattice spacings, controlling finite-volume and discretization effects, and performs chiral extrapolations to the physical point with SU(2) HB$oldsymbol{χ}$PT. By tuning strange and charm masses via $Ω^-$ and $Λ_c^+$ and using Osterwalder-Seiler valence quarks for the heavy sector, the authors obtain continuum-extrapolated baryon masses in good agreement with experiment and provide predictions for unobserved doubly/triply charmed states such as $Ξ_{cc}^*$, $Ω_{cc}$, $Ω_{cc}^*$, and $Ω_{ccc}$. They report small isospin-breaking effects at finite lattice spacing that vanish in the continuum, and demonstrate that discretization errors are largely $O(a^2)$ with the dominant uncertainty arising from chiral extrapolation. The results offer a robust lattice QCD determination of the baryon spectrum and valuable predictions for the charm sector that can guide experimental searches and phenomenology.

Abstract

The masses of the low lying baryons are evaluated using a total of ten ensembles of dynamical twisted mass fermion gauge configurations. The simulations are performed using two degenerate flavors of light quarks, and a strange and a charm quark fixed to approximately their physical values. The light sea quarks correspond to pseudo scalar masses in the range of about 210~MeV to 430~MeV. We use the Iwasaki improved gluonic action at three values of the coupling constant corresponding to lattice spacing $a=0.094$~fm, 0.082~fm and 0.065~fm determined from the nucleon mass. We check for both finite volume and cut-off effects on the baryon masses. We examine the issue of isospin symmetry breaking for the octet and decuplet baryons and its dependence on the lattice spacing. We show that in the continuum limit isospin breaking is consistent with zero, as expected. We performed a chiral extrapolation of the forty baryon masses using SU(2) $χ$PT. After taking the continuum limit and extrapolating to the physical pion mass our results are in good agreement with experiment. We provide predictions for the mass of the doubly charmed $Ξ_{cc}^*$, as well as of the doubly and triply charmed $Ω$s that have not yet been determined experimentally.

Figures (27)

• Figure 1: Representative effective mass plots for $\Xi^0$ (left) and $\Omega_c^0$ (right) at $\beta=2.10$, $a\mu_l=0.0015$. Both the constant and the exponential fits are displayed.
• Figure 2: The $20^\prime$-plet of spin-1/2 baryons classified according to their charm content. The lowest level represents the $c=0$ SU(3) octet.
• Figure 3: The 20-plet of spin-3/2 baryons classified according to their charm content. The lowest level represents the $c=0$ decuplet sub-group.
• Figure 4: Comparison of effective masses extracted using $\mathcal{J}_{\Sigma^{*+}}$ at $\beta=2.10$, $a\mu_l=0.0015$ (left) and using $\mathcal{J}_{\Sigma_c^{*++}}$ at $\beta=1.95$, $a\mu_l=0.0055$ (right) obtained with the spin-3/2 projection (red filled circles), spin-1/2 projection (green triangles) and without projection (blue open squares, shifted to the right for clarity).
• Figure 5: Comparison of effective masses extracted using for $\mathcal{J}_{\Xi^{*-}}$ at $\beta=1.95$, $a\mu_l=0.0025$ obtained with the spin-3/2 projection (red filled circles), without projection (blue open squares, shifted to the right for clarity) and with spin-1/2 projection (green triangles). Also plotted is the effective mass using $\mathcal{J}_{\Xi^-}$ (magenta diamonds).