Resolving Charged Hadrons in QED -- Gauge Invariant Interpolating Operators

Abstract

Standard interpolating operators for charged mesons, e.g. $J_B=\bar{b}i{\gamma }_{5}u$ 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 ${\Phi }_B$, ${\mathcal{J}}_B^{(0)}=J_B{\Phi }_B$, 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 $\mathcal{O}(\alpha )$, 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 $B^{-}\to {\ell }^{-}\bar{\nu }$ for which a numerical study is to follow. The formalism itself is valid for any spin, flavour and set of final states (e.g. $B^{-}\to {\pi }^0{\ell }^{-}\bar{\nu }$).

4 Fig, 17 pp + refs, version quasi identical to JHEP version (conclusions unchanged)

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Cited by in corpus (3)

• Structure-dependent QED effects in exclusive $B$-meson decays
• Isospin Mass Differences of the $B$, $D$ and $K$
• The Simplest B Decay, Precisely