Off-shell vertices in heavy particle effective theories and B → Dπℓν - Michele Papucci; Ryan Plestid (Journal of High Energy Physics)
Abstract We study the modifications to decay amplitudes in heavy to heavy semileptonic decays with multiple hadrons in the final state due to intermediate heavy hadrons being off-shell or having a finite width. Combining Heavy Hadron Chiral Perturbation Theory (HHχPT) with a BCFW on-shell factorization formula, we show that these effects induce O $$ \mathcal{O} $$ (1/M) corrections to the standard results computed in the narrow-width approximation and therefore are important in extracting form factors from data. A combination of perturbative unitarity, analyticity, and reparameterization invariance fully determine these corrections in terms of known Isgur-Wise functions without the need to introduce new form factors. In doing so, we develop a novel technique to compute the boundary term at complex infinity in the BCFW formula for theories with derivatively coupled scalars. While we have used the B ¯ $$ \overline{B} $$ → Dπℓν decay as an example, these techniques can generally be applied to effective field theories with (multiple) distinct reference vectors.