The $H^{\ast }{H}^{\ast }V$ couplings from light-cone sum rules

Abstract

We present a determination of the strong charge couplings $g_{H^{\ast }{H}^{\ast }V}$ and magnetic couplings $f_{H^{\ast }{H}^{\ast }V}$ (with $H\in \{D,B\}$ and $V\in \{\rho ,\omega ,K^{\ast },\varphi \}$) using the framework of light-cone sum rules (LCSR). The theoretical precision is improved by establishing the leading-power hard-collinear factorization formulas with next-to-leading-order (NLO) ${\alpha }_s$ corrections, alongside the inclusion of power-suppressed contributions up to the next-to-next-to-leading power (NNLP) for both channels. By parameterizing the $\mathcal{O}(1/m_{H^{\ast }})$ power corrections, we extract the universal static couplings $\beta =0.73\pm 0.13$ and $\hat{\lambda }=0.23\pm 0.06{\text{ GeV}}^{-1}$, highlighting their distinct heavy-quark scaling behaviors. While our investigation into SU(3) flavor symmetry breaking shows that these effects are currently overwhelmed by uncertainties in the non-perturbative vector meson distribution amplitudes, our determinations of these spin-conserving and spin-flip parameters provide non-perturbative inputs for modeling the S-wave central potentials, as well as the tensor forces and D-wave mixing effects, in exotic heavy tetraquarks.

29 pages, 3 figures