Probing the inverse moment of B s -meson distribution amplitude via B s → η s form factors

Abstract We investigate the inverse moment of the B s -meson light-cone distribution amplitude (LCDA), denoted as λ 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 λ B s $$ {\lambda}_{B_s} $$ value compared to the non-strange case λ 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 λ 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 λ 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 λ B s $$ {\lambda}_{B_s} $$ value, with earlier analyses for other channels such as B s → D s and B s → K.