Subleading contributions to the decay width of the $T_{cc}^{+}$ tetraquark

Abstract

Recently the LHCb collaboration has announced the discovery of the $T_{cc}^{+}$ tetraquark. Being merely a few hundred $\mathrm{keV}$ below the $D^{\ast +}{D}^0$ threshold, the $T_{cc}^{+}$ is expected to have a molecular component, for which there is a good separation of scales that can be exploited to make reasonably accurate theoretical predictions about this tetraquark. Independently of its nature, the most important decay channels will be $D^{+}{D}^0{\pi }^0$, $D^0{D}^0{\pi }^{+}$ and $D^{+}{D}^0\gamma$. Its closeness to threshold suggests that the mass and particularly the width of the $T_{cc}^{+}$ tetraquark depend on the resonance profile. While the standard Breit-Wigner parametrization generates a $T_{cc}^{+}$ that is too broad for current theoretical calculations to reproduce, a three-body unitarized Breit-Wigner shape reveals instead a decay width (${\Gamma }_{\mathrm{pole}}=48\pm 2{}_{-12}^{+0}\mathrm{keV}$) consistent with theoretical expectations. Here we consider subleading order contributions to the decay amplitude, which though having at most a moderate impact in the width still indicate potentially significant differences with the experimental width that can be exploited to disentangle the nature of the $T_{cc}^{+}$. Concrete calculations yield ${\Gamma }^{\mathrm{LO}}=49\pm 16\mathrm{keV}$ and ${\Gamma }^{\mathrm{NLO}}=58_{-6}^{+7}\mathrm{keV}$, though we expect further corrections to the $\mathrm{NLO}$ decay widths from asymptotic normalization effects. We find that a detailed comparison of the $\mathrm{NLO}$ total and partial decay widths with experiment suggests the existence of a small (but distinguishable from zero) non-molecular component of the $T_{cc}^{+}$.

Comments: 13 pages, 1 figure; corresponds with the published version