Probing the inverse moment of B_s-meson distribution amplitude via B_s → η_s form factors

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