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

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