Effective-range expansion of the $T_{cc}^{+}$ state at the complex $D^{\ast +}{D}^0$ threshold

Abstract

Evaluation of the effective-range parameters for the $T_{cc}^{+}$ state in the LHCb model is examined. The finite width of $D^{\ast }$ leads to a shift of the expansion point into the complex plane to match analytical properties of the expanded amplitude. We perform an analytic continuation of the three-body scattering amplitude to the complex plane in a vicinity of the branch point and develop a robust procedure for computation of the expansion coefficients. The results yield a nearly-real scattering length, and two contributions to the the effective range which have not been accounted before.

5 pages, 2 figures