Abstract
Recently the LHCb collaboration has announced the discovery of the $T_{cc}^+$ tetraquark. Being merely a few hundred ${\rm keV}$ below the $D^{*+} D^0$ 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 ($\Gamma_{\rm pole} = 48\pm 2\,{}^{+0}_{-12}\,{\rm keV}$) 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 $\Gamma^{\rm LO} = 49 \pm 16\,{\rm keV}$ and $\Gamma^{\rm NLO} = 58^{+7}_{-6}\,{\rm keV}$, though we expect further corrections to the ${\rm NLO}$ decay widths from asymptotic normalization effects. We find that a detailed comparison of the ${\rm NLO}$ total and partial decay widths with experiment suggests the existence of a small (but distinguishable from zero) non-molecular component of the $T_{cc}^+$.
Highlights
The LHCb Collaboration has recently observed [1] a tetraquark in the D0D0πþ mass spectrum
We find that a detailed comparison of the NLO total and partial decay widths with experiment suggests the existence of a small nonmolecular component of the Tþcc
[16] and Törnqvist [17] considering it unlikely, but Ericson and Karl [18] realizing that this conclusion might change if other meson exchanges are considered, an observation later confirmed in Ref. [19] for
Summary
The LHCb Collaboration has recently observed [1] a tetraquark in the D0D0πþ mass spectrum. This in turn allows us to use the existent theoretical toolbox for shallow bound states [29,30], from which in principle it would be possible to make predictions accurate enough as to analyze its structure In this regard, the important (and it has already received due attention [31,32,33]); if the experimental measurements and theoretical predictions are on par with each other in terms of accuracy, we will be able to determine whether the Tþcc is purely molecular or compact, or what the degree of admixture is between these two explanations. A calculated decay width that is too small or too large in comparison with the experiment might point to (or even determine) the existence of physics beyond the naive molecular explanation, like a tetraquark component or unobserved states This might prove difficult; the wave function of a tetraquark close to the DÃD threshold might be indistinguishable from that of two separate DÃ and D mesons, as noted in Ref. This might prove difficult; the wave function of a tetraquark close to the DÃD threshold might be indistinguishable from that of two separate DÃ and D mesons, as noted in Ref. [8], which already considered the possibility of a tetraquark lying between the DÃD and DDπ thresholds (see the discussion in Ref. [34])
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