Probing the inverse moment of Bₛ-meson distribution amplitude via Bₛ → ηₛ form factors

We investigate the inverse moment of the Bₛ-meson light-cone distribution amplitude (LCDA), denoted as λBₛ and defined within the heavy quark effective theory, through the calculation of Bₛ → ηₛ form factors. The presence of the s-quark inside the Bₛ-meson dictates a notable departure of approximately $20%$ in the λBₛ value compared to the non-strange case λBq, as computed within the QCD sum rule approach, albeit with significant uncertainty. First, we compute the decay constant of the ηₛ-meson utilizing two-point sum rules while retaining finite s-quark mass contributions. Next, we constrain the parameter λBₛ by calculating Bₛ → ηₛ form factors within the light-cone sum rule approach, using Bₛ-meson LCDAs, and leveraging Lattice QCD estimates at zero momentum transfer from the HPQCD collaboration. Our findings yield λBₛ = 480 ± 92 MeV when expressing the Bₛ-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 λBₛ value, with earlier analyses for other channels such as Bₛ → Dₛ and Bₛ → K.