Probing the inverse moment of $B_s$meson distribution amplitude via $B_s \to \eta_s$ form factors
Abstract
We investigate the inverse moment of the $B_s$meson lightcone distribution amplitude (LCDA), denoted as $\lambda_{B_s}$ and defined within the heavy quark effective theory, through the calculation of $B_s \to \eta_s$ form factors. The presence of the $s$quark inside the $B_s$meson dictates a notable departure of approximately $20\%$ in the $\lambda_{B_s}$ value compared to the nonstrange case $\lambda_{B_q}$, as computed within the QCD sum rule approach, albeit with significant uncertainty. First, we compute the decay constant of the $\eta_s$meson utilizing twopoint sum rules while retaining finite $s$quark mass contributions. Next, we constrain the parameter $\lambda_{B_s}$ by calculating $B_s \to \eta_s$ form factors within the lightcone sum rule approach, using $B_s$meson LCDAs, and leveraging Lattice QCD estimates at zero momentum transfer from the HPQCD collaboration. Our findings yield $\lambda_{B_s}$ = 480 $\pm$ 92 MeV when expressing the $B_s$meson LCDAs in the Exponential model, consistent with previous QCD sum rule estimate yet exhibiting a 1.5fold improvement in uncertainty. Furthermore, we compare the form factor predictions, based on the extracted $\lambda_{B_s}$ value, with earlier analyses for other channels such as $B_s \to D_s$ and $B_s \to K$.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.16737
 arXiv:
 arXiv:2402.16737
 Bibcode:
 2024arXiv240216737M
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Experiment;
 High Energy Physics  Lattice
 EPrint:
 Some additional texts and references added