Elastic s-wave B pi, D pi, DK and K pi scattering from lattice calculations of scalar form factors in semileptonic decays

We show how theoretical, principally lattice calculations of the scalar form factors in semileptonic pseudoscalar-to-pseudoscalar decays can be used to extract information about the corresponding elastic s-wave scattering channels. We find values for the scattering lengths m(pi)a=0.179(17)(14), 0.26(26) and 0.29(4) for elastic s-wave isospin-1/2 K pi, B pi and D pi channels, respectively. We also determine phase shifts. For the DK channel we find hints that there is a bound state which can be identified with the recently discovered D-s0(+)(2317).