Masses of $D$ mesons, $D_s$ mesons and charmonium states from twisted mass lattice QCD

TL;DR

This study calculates the masses of various $D$, $D_s$, and charmonium mesons using twisted mass lattice QCD, achieving results consistent with experiments and providing insights into the structure of $J^P=1^+$ states relevant for decay processes.

Contribution

First lattice QCD calculation to classify $J^P=1^+$ $D$ mesons by light angular momentum, aiding understanding of semileptonic $B$ decays and resolving theoretical-experimental discrepancies.

Findings

Results agree with experimental meson masses within 2-3%

Successfully classify $D_1(2430)$ and $D_1(2420)$ states by light degrees of freedom

Provides a foundation for studying $B$ meson decay channels

Abstract

We compute masses of $D$ mesons, $D_s$ mesons and charmonium states using Wilson twisted mass lattice QCD. We present results for spin $J = 0,1,2,3$, parity $\mathcal{P} = -,+$ and in case of charmonium also charge conjugation $\mathcal{C} = -,+$. Computations are based on quark-antiquark creation operators and performed at three different unphysically heavy $u/d$ quark masses allowing an extrapolation to the physical $u/d$ quark mass. Within combined statistical and systematic errors, which are around $2 \% \ldots 3 \%$, our results agree with available experimental results. Particular focus is put on the $J^\mathcal{P} = 1^+$ mesons $D_1(2430)$ and $D_1(2420)$. We separate and classify these close-by states according to the total angular momentum of their light degrees of freedom, $j \approx 1/2$ and $j \approx 3/2$. This is a first important step to study decays $B^{(\ast)} \rightarrow D_1 + l + \nu$, for which a long-standing conflict between theory and experiment exists.