Resolving charged hadrons in QED — gauge invariant interpolating operators

Abstract

Abstract Standard interpolating operators for charged mesons, e.g. JB = $$ \overline{b} $$ b ¯ iγ5u for B−, are not gauge invariant in QED and therefore problematic for perturbative methods. We propose a gauge invariant interpolating operator by adding an auxiliary charged scalar ΦB, $$ {\mathcal{J}}_B^{(0)} $$ J B 0 = JB ΦB, which reproduces all the universal soft and collinear logs. The modified LSZ-factor is shown to be infrared finite which is a necessary condition for validating the approach. At $$ \mathcal{O} $$ O (α), this is equivalent to a specific Dirac dressing of charged operators. A generalisation thereof, using iterated integrals, establishes the equivalence to all orders and provides a transparent alternative viewpoint. The method is discussed by the example of the leptonic decay B−→ ℓ−$$ \overline{\nu} $$ ν ¯ for which a numerical study is to follow. The formalism itself is valid for any spin, flavour and set of final states (e.g. B−→ π0ℓ−$$ \overline{\nu} $$ ν ¯ ).