Lattice outlook on $B\to \rho \mathrm{\ell }\bar{\nu }$ and $B\to K^{\star }\mathrm{\ell }\mathrm{\ell }$

Lattice Quantum Chromodynamics (QCD) has significantly contributed to our understanding of the CKM matrix through precise determinations of hadronic matrix elements. With advancements in theoretical methodologies and computational resources, investigations can now extend to processes involving QCD-unstable hadrons such as the $\rho$ and $K^{\star }(892)$. These resonances play vital roles in processes such as weak decays of $B$ mesons, opening new avenues for exploration. Finite-volume lattice QCD techniques involving complex computational methods are used to determine the transition amplitudes. Here, we present preliminary results for $B\to \rho \mathrm{\ell }\bar{\nu }$.