$D^{\ast }D\ddot{I}€$ and $B^{\ast }B\ddot{I}€$ couplings from Dyson-Schwinger equations framework

Abstract

Employing a unified Dyson-Schwinger/Bethe-Salpeter equations approach, we calculate the strong decay couplings $D^{\ast }D\ddot{I}€$ and $B^{\ast }B\ddot{I}€$ within the so-called impulse-approximation in the moving frame. The $B^{\ast }B\ddot{I}€$ estimation is reported for the first time based on a Poincaré invariant computation of the associated Bethe-Salpeter amplitudes. Our predictions yield $g_{D^{\ast }D\ddot{I}€}=16.22_{-0.01}^{+0.03}$ and $g_{B^{\ast }B\ddot{I}€}=40.09_{-1.37}^{+1.51}$, along with corresponding static strong couplings of ${\hat{g}}_D=0.55_{-<0.01}^{+<0.01}$, ${\hat{g}}_B=0.50_{-0.02}^{+0.02}$, which are consistent with recent experimental and lattice data.

12 pages, 4 figures. Close to published version