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We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlins representation based on current algebra relations permits a clear separation between the perturbatively-calculable and incalculable pieces in the $mathcal{O}(G_Falpha)$ radiative corrections. The latter are expressed as compact hadronic matrix elements that allow systematic non-perturbative analysis such as dispersion relation and lattice QCD. This brings substantial improvements to the precision of the electroweak radiative corrections in semileptonic decays of pion, kaon, free neutron and $J^P=0^+$ nuclei that are important theory inputs in precision tests of the Standard Model. Unresolved issues and future prospects are discussed.
Two of the elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix, $|V_{ub}|$ and $|V_{cb}|$, are extracted from semileptonic B decays. The results of the B factories, analysed in the light of the most recent theoretical calculations, remain p
We revisit QCD calculations of radiative heavy meson decay form factors by including the subleading power corrections from the twist-two photon distribution amplitude at next-to-leading-order in $alpha_s$ with the method of the light-cone sum rules (
Inclusive semileptonic decays of beauty baryons are studied using the heavy quark expansion to ${cal O}(1/m_b^3)$, at leading order in $alpha_s$. The case of a polarized decaying baryon is examined, with reference to $Lambda_b$. An extension of the S
We discuss the theoretical framework required for the computation of radiative corrections to semileptonic decay rates in lattice simulations, and in particular to those for $K_{ell3}$ decays. This is an extension of the framework we have developed a
Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic $B to gamma ell u$ decay, at next-to-leading order in QCD for the twist-two contribution and at lea