Radiative decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$

Abstract

With the assumptions that the $T_{cc}^{+}$ discovered at LHCb is a $D^{\ast }D$ hadronic molecule, using a nonrelativistic effective field theory we calculate the radiative partial widths of $T_{cc}^{\ast }\to D^{\ast }D\gamma$ with $T_{cc}^{\ast }$ being a $D^{\ast }{D}^{\ast }$ shallow bound state and the heavy-quark-spin partner of $T_{cc}^{+}$. The $I=0$ $D^{\ast }D$ rescattering effect with the $T_{cc}$ pole is taken into account. The results show that the isoscalar $D^{\ast }D$ rescattering can increase the tree-level decay width of $T_{cc}^{\ast +}\to D^{\ast +}{D}^0\gamma$ by about $50\%$, while decrease that of $T_{cc}^{\ast +}\to D^{\ast 0}{D}^{+}\gamma$ by a similar amount. The two-body partial decay widths of the $T_{cc}^{\ast +}$ into $T_{cc}^{+}\gamma$ and $T_{cc}^{+}{\pi }^0$ are also calculated, and the results are about $6\mathrm{keV}$ and $3\mathrm{keV}$, respectively. Considering that the $D^{\ast }$ needs to be reconstructed from the $D\pi$ or $D\gamma$ final state in an experimental measurement, the four-body partial widths of the $T_{cc}^{\ast +}$ into $DD\gamma \gamma$ and $DD\pi \gamma$ are explicitly calculated, and we find that the interference effect between different intermediate $D^{\ast }D\gamma$ states is small. The total radiative decay width of the $T_{cc}^{\ast }$ is predicted to be about $24\mathrm{keV}$. Adding the hadronic decay widths of $T_{cc}^{\ast }\to D^{\ast }D\pi$, the total width of the $T_{cc}^{\ast }$ is finally predicted to be $(65\pm 2)$ keV.

27 pages, 13 figures. Published in Phys. Rev. D. arXiv admin note: text overlap with arXiv:2211.02479

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