Continuum limit of the $D$ meson, $D_s$ meson and charmonium spectrum from $N_f=2+1+1$ twisted mass lattice QCD

TL;DR

This study calculates the masses of $D$, $D_s$, and charmonium mesons using $N_f=2+1+1$ twisted mass lattice QCD, extrapolating to physical quark masses and continuum, and compares results with experimental data.

Contribution

First comprehensive lattice QCD analysis of $D$, $D_s$, and charmonium spectra with systematic error quantification and continuum extrapolation.

Findings

Results agree with experimental data within 3% error.

Systematic errors include finite volume, isospin breaking, and fitting uncertainties.

Discrepancies discussed and potential reasons analyzed.

Abstract

We compute masses of $D$ meson, $D_s$ meson and charmonium states using $N_f=2+1+1$ Wilson twisted mass lattice QCD. All results are extrapolated to physical light quark masses, physical strange and charm quark masses and to the continuum. Our analysis includes states with spin $J = 0,1,2$, parity $\mathcal{P} = -,+$ and in case of charmonium also charge conjugation $\mathcal{C} = -,+$. Computations are based on a large set of quark-antiquark meson creation operators. We investigate and quantify all sources of systematic errors, including fitting range uncertainties, finite volume effects, isospin breaking effects and the choice of the fitting ansatz for the combined chiral and continuum extrapolation such that the resulting meson masses can be compared directly and in a meaningful way to experimental results. Within combined statistical and systematic errors, which are between below two per mille and three percent, our results agree with available experimental results for most of the states. In the few cases where we observe discrepancies, we discuss possible reasons.