Resolving charged hadrons in QED — gauge invariant interpolating operators

Abstract

Standard interpolating operators for charged mesons, e.g. JB = $$ \overline{b} $$ 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, $$ {\mathcal{J}}_B^{(0)} $$ 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 $$ \mathcal{O} $$ 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−$$ \overline{\nu} $$ 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−→ π0ℓ−$$ \overline{\nu} $$ ν ¯ ).

Structure-dependent QED effects in exclusive B-meson decays

“…In anticipation of the high-precision measurements from LHCb and BELLE II, the investigation of electromagnetic effects in B -meson decays has become an active research field in recent years (besides the articles which have already been mentioned in the main text, more examples can be found in Refs. [55][56][57][58][59][60][61][62][63][64][65]). In this review, we have summarized recent developments in the calculation of structure-dependent QED corrections to exclusive B -meson decays with effective field theory methods.…”

Isospin Mass Differences of the $B$, $D$ and $K$

“…This is the case since the particles are put on the mass shell and it is important that the quantity is infrared safe. Otherwise, as previously stated, one needs to introduce extra machinery [20].…”

“…same hadronic input). 4 To the best of our knowledge this has not been done previously with sum rules, presumably due to the subtleties of non gauge-invariant interpolating currents [19,20]. For example, in leptonic decays this requires the introduction of a non-local interpolating operator (or an auxiliary scalar field carrying the charge to infinity) for gauge invariance and reproduction of all infrared sensitive logs [20].…”

Isospin mass differences of the B, D and K

“…4 Note that the double dispersion is necessity since each B-meson requires an (approximate dispersive) LSZ procedure. To the best of our knowledge this has not been done previously with sum rules, presumably due to the subtleties of non gauge-invariant interpolating currents [23,24]. For example, in leptonic decays this requires the introduction of a non-local interpolating operator (or an auxiliary scalar field carrying the charge to infinity) for gauge invariance and reproduction of all infrared sensitive logs [24].…”

“…To the best of our knowledge this has not been done previously with sum rules, presumably due to the subtleties of non gauge-invariant interpolating currents [23,24]. For example, in leptonic decays this requires the introduction of a non-local interpolating operator (or an auxiliary scalar field carrying the charge to infinity) for gauge invariance and reproduction of all infrared sensitive logs [24]. However, in the case at hand this is not necessary, as verified by explicit computation, since ∆m B is an infrared safe quantity.…”