Resolving charged hadrons in QED — gauge invariant interpolating operators

Saad Nabeebaccus (Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, 91405, France) ; Roman Zwicky (Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh, Scotland, EH9 3JZ, UK)

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 ¯ $$ \overline{\nu} $$ ).

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      "title": "Resolving charged hadrons in QED \u2014 gauge invariant interpolating operators"
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      "value": "Standard interpolating operators for charged mesons, e.g. J  B  =   <math> <mover> <mi>b</mi> <mo>\u00af</mo> </mover> </math>  $$ \\overline{b} $$  i\u03b3 5 u for B  \u2212 , 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 \u03a6 B ,   <math> <msubsup> <mi>J</mi> <mi>B</mi> <mfenced> <mn>0</mn> </mfenced> </msubsup> </math>  $$ {\\mathcal{J}}_B^{(0)} $$  = J  B  \u03a6 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   <math> <mi>O</mi> </math>  $$ \\mathcal{O} $$ (\u03b1), 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  \u2212  \u2192 \u2113  \u2212    <math> <mover> <mi>\u03bd</mi> <mo>\u00af</mo> </mover> </math>  $$ \\overline{\\nu} $$  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  \u2212  \u2192 \u03c0 0 \u2113  \u2212    <math> <mover> <mi>\u03bd</mi> <mo>\u00af</mo> </mover> </math>  $$ \\overline{\\nu} $$ )."
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Published on:
17 November 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 11
Pages 1-20
DOI:
https://doi.org/10.1007/JHEP11(2022)101
arXiv:
2209.06925
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: