Triangle singularities in the $T_{cc}^{+}\to D^{\ast +}{D}^0\to {\pi }^{+}{D}^0{D}^0$ decay width

Abstract

The values of the masses of the particles involved in the decay of $T_{cc}^{+}\to D^{\ast +}{D}^0\to {\pi }^{+}{D}^0{D}^0$ suggest that due to the final state interactions in the transition vertex $T_{cc}^{+}\to D^{\ast +}{D}^0$ there may be triangle logarithmic singularities. We discuss their possible role and show that the tree approximation for calculating the decay widths $T_{cc}^{+}\to (D^{\ast +}{D}^0+D^{\ast 0}{D}^{+})\to {\pi }^{+}{D}^0{D}^0$, ${\pi }^0{D}^0{D}^{+}$, $\gamma D^0{D}^{+}$ is quite sufficient at the current level of measurement accuracy.

Comments: 5 pages, 4 figures; v2: published version, elusidations and four references added