The $D^{\ast }{D}^{\ast }\pi$ and $B^{\ast }{B}^{\ast }\pi$ couplings from light-cone sum rules

Abstract

We revisit the calculation of the strong couplings $D^{\ast }{D}^{\ast }\pi$ and $B^{\ast }{B}^{\ast }\pi$ from the light-cone sum rules (LCSR) using the pion light-cone distribution amplitudes. The accuracy of the underlying correlation function is upgraded by establishing the hard-collinear factorization formula at the leading power up to the next-to-leading order in ${\alpha }_s$. Furthermore, the next-to-leading power contributions are systematically incorporated at the leading order by evaluating the two-particle and three-particle higher-twist pion distribution amplitudes up to twist-4 accuracy. By matching the QCD-level spectral representations with the hadronic dispersion relations, we present a solid numerical analysis that accounts for the finite heavy quark masses and carefully evaluates the systematic uncertainty originating from the two-dimensional quark-hadron duality ansatz. We predict $g_{D^{\ast }{D}^{\ast }\pi }=5.71_{-0.53}^{+0.67}{\text{ GeV}}^{-1}$ and $g_{B^{\ast }{B}^{\ast }\pi }=4.90_{-0.44}^{+0.57}{\text{ GeV}}^{-1}$. Finally, by parameterizing the $1/m_H$ (with $H=D,B$) power corrections to extract the universal static coupling $\hat{g}=0.30\pm 0.04$, we compare our results with previous theoretical determinations and experimental data, highlighting the significance of heavy quark spin symmetry breaking effects.

Comments: 26 pages, 2 figures