Abstract
Standard interpolating operators for charged mesons, e.g. JB = \( \overline{b} \)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, \( {\mathcal{J}}_B^{(0)} \) = 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 \( \mathcal{O} \)(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− → π0ℓ−\( \overline{\nu} \)).
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Nabeebaccus, S., Zwicky, R. Resolving charged hadrons in QED — gauge invariant interpolating operators. J. High Energ. Phys. 2022, 101 (2022). https://doi.org/10.1007/JHEP11(2022)101
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DOI: https://doi.org/10.1007/JHEP11(2022)101