Resolving Charged Hadrons in QED -- Gauge Invariant Interpolating Operators

Abstract

Standard interpolating operators for charged mesons, e.g. J B = biγ 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 (0) B = 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(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 − → − 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 − → π 0 − ν).

QED in $$ \overline{B} $$ → $$ \overline{K} $$ℓ+ℓ− LFU ratios: theory versus experiment, a Monte Carlo study

“…In fact, in a decay like B → K + − the (hard)-collinear and soft-collinear logs in the lepton mass can be reproduced from the lepton to lepton-photon splitting function. 7,8 7 The specific details are postponed to a future publication [8] and for more generic remarks we refer the reader to [9]. Although, note that the kinematic relations, to follow below, can be found in our previous work [5] (cf.…”

“…section 3.4 [5]). When going to the structure dependent level, which necessitates the introduction of new gauge invariant interpolating operators [8] and or new gauge invariant distribution amplitudes [11], new sizeable ln m K(π) -effects can be expected to be present for K(π) final states. However, they would cancel in LFU ratios [4,5], along with (other) structure dependent effects, for the reasons mentioned above.…”