The chiral symmetry of QCD requires energy-dependent pionic strong
interactions at low energies. This constraint, however, is not fulfilled by the
usual Breit--Wigner parameterization of pionic resonances, leading to masses
larger than the real ones. We derive relations between nonleptonic three-body
decays of the B-meson into a D-meson and a pair of light pseudoscalar
mesons based on SU(3) chiral symmetry. Employing effective field theory
methods, we demonstrate that taking into account the final-state interactions,
the experimental data of the decays B−→D+π−π−, Bs0→Dˉ0K−π+, B0→Dˉ0π−π+, B−→D+π−K− and
B0→Dˉ0π−K+ can all be described by the nonperturbative
π/η/K-D/Ds scattering amplitudes previously obtained from a
combination of chiral effective field theory and lattice QCD calculations. The
results provide a strong support of the scenario that the broad scalar charmed
meson D0∗(2400) should be replaced by two states, the lower one of which
has a mass of around 2.1 GeV, much smaller than that extracted from
experimental data using a Breit--Wigner parameterization.Comment: 26 pages, 9 figuere