Antonino D'Anna, "Towards $B_s \to K \ell \nu$ and $B \to \pi \ell \nu$ semileptonic decay form factors from the ALPHA Collaboration"
We present the current status on our determination of the $B_s \to K$ and $B \to \pi$ semileptonic decay form factors. The ALPHA Collaboration aims to compute these form factors by interpolating continuum-limit observables in $1/m_h$, constructed so that the matching and renormalisation cancel. Relativistic continuum data at and above the charm mass are interpolated with their static-limit counterparts. This talk concentrates on the relativistic data obtained on CLS ensembles. Using five lattice spacings, down to $a \approx 0.04 \text{ fm}$, we investigate the continuum-limit extrapolation at the $\mathrm{SU}(3)$-symmetric point ($m_\pi = m_K \approx 420 \text{ MeV}$). Furthermore, at a fixed fine lattice spacing, $a \approx 0.05~\text{ fm}$, we explore the approach to the physical pion mass, where multi-particle excited-state contributions -- in particular $B^{*}\pi$ -- become increasingly significant for $B \to \pi$. Systematic effects in the extraction of the ground-state matrix elements at finite Euclidean time are reduced by employing summed ratios, together with a heavy-meson-ChPT-guided model treatment of the $B^{*}\pi$ excited-state contributions.