| Summary: | Abstract Standard interpolating operators for charged mesons, e.g. J B = 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 , J B 0 $$ {\mathcal{J}}_B^{(0)} $$ = 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 O $$ \mathcal{O} $$ (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 − ν ¯ $$ \overline{\nu} $$ 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 − ν ¯ $$ \overline{\nu} $$ ).
|
|---|