Off-shell vertices in heavy particle effective theories and $B\rightarrow D\pi \ell \nu$

TL;DR

This paper investigates how off-shell effects of intermediate heavy hadrons modify decay amplitudes in heavy-to-heavy semileptonic decays, revealing important $O(1/M)$ corrections that can be computed without new form factors.

Contribution

It combines HH$ ext{ ext{}}$χPT with BCFW on-shell techniques to determine off-shell corrections in heavy meson decays, introducing a novel method for boundary term calculations.

Findings

Off-shell effects induce $O(1/M)$ corrections to decay amplitudes.

Corrections are fully determined by known Isgur-Wise functions.

The techniques are applicable to a broad class of effective field theories.

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 (HH$\chi$PT) with a BCFW on-shell factorization formula, we show that these effects induce $O(1/M)$ 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 $\bar B\rightarrow D\pi \ell\nu$ decay as an example, these techniques can generally be applied to effective field theories with (multiple) distinct reference vectors.