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

TL;DR

This paper develops an effective-range expansion method for the $T_{cc}^+$ state near the $D^{*+}D^0$ threshold, accounting for the finite width of $D^*$ and providing new insights into scattering parameters.

Contribution

It introduces a novel approach for the effective-range expansion that incorporates the complex nature of the $D^*$ width and analytically continues the scattering amplitude near the branch point.

Findings

Nearly-real scattering length obtained

Two previously unaccounted contributions to the effective range identified

Method successfully handles complex expansion points

Abstract

Evaluation of the effective-range parameters for the $T_{cc}^+$ state in the LHCb model is examined. The finite width of $D^*$ 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.