Hadronic decays of the heavy-quark-spin molecular partner of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>
Zhao-Sai Jia, Mao-Jun Yan, Zhen-Hua Zhang, Pan-Pan Shi, Gang Li, Feng-Kun Guo
Abstract
Starting from the hypothesis that the ${T}_{cc}^{+}$ discovered at LHCb is a ${D}^{*+}{D}^{0}/{D}^{*0}{D}^{+}$ hadronic molecule, we consider the partial width of its heavy quark spin partner, the ${T}_{cc}^{*+}$ as a ${D}^{*+}{D}^{*0}$ shallow bound state, decaying into the ${D}^{*}D\ensuremath{\pi}$ final states including the contributions of the ${D}^{*}D$ and ${D}^{*}\ensuremath{\pi}$ final state interaction by using a nonrelativistic effective field theory. Because of the existence of the ${T}_{cc}^{+}$ pole, the $I=0$ ${D}^{*}D$ rescattering can give a sizeable correction up to about 40% to the decay widths considering only the tree diagrams, and the ${D}^{*}\ensuremath{\pi}$ rescattering correction is about 10%. The four-body partial widths of the ${T}_{cc}^{*+}$ into $DD\ensuremath{\pi}\ensuremath{\pi}$ are also explicitly calculated, and we find that the interference effect between different intermediate ${D}^{*}D\ensuremath{\pi}$ states is small. The total width of the ${T}_{cc}^{*+}$ is predicted to be about 41 keV.