Resolving charged hadrons in QED — gauge invariant interpolating operators
Saad Nabeebaccus (Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, 91405, France); Roman Zwicky (Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh, Scotland, EH9 3JZ, UK)
Standard interpolating operators for charged mesons, e.g. J B = $$ \overline{b} $$ iγ 5 u 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 Φ B , $$ {\mathcal{J}}_B^{(0)} $$ = J B Φ B , 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 $$ \mathcal{O} $$ (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 − $$ \overline{\nu} $$ 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 − → π 0 ℓ − $$ \overline{\nu} $$ ).