Resolving charged hadrons in QED — gauge invariant interpolating operators
Abstract 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 $$...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP11(2022)101 |
| _version_ | 1797865684082884608 |
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| author | Saad Nabeebaccus Roman Zwicky |
| author_facet | Saad Nabeebaccus Roman Zwicky |
| author_sort | Saad Nabeebaccus |
| collection | DOAJ |
| description | Abstract Standard interpolating operators for charged mesons, e.g. J B = b ¯ $$ \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} $$ ). |
| first_indexed | 2024-04-09T23:13:15Z |
| format | Article |
| id | doaj.art-97eefc65d2334cbe9908b95bb0c4a009 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:13:15Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-97eefc65d2334cbe9908b95bb0c4a0092023-03-22T10:16:46ZengSpringerOpenJournal of High Energy Physics1029-84792022-11-0120221112010.1007/JHEP11(2022)101Resolving charged hadrons in QED — gauge invariant interpolating operatorsSaad Nabeebaccus0Roman Zwicky1Université Paris-Saclay, CNRS/IN2P3, IJCLabHiggs Centre for Theoretical Physics, School of Physics and Astronomy, University of EdinburghAbstract Standard interpolating operators for charged mesons, e.g. J B = b ¯ $$ \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} $$ ).https://doi.org/10.1007/JHEP11(2022)101Precision QEDBottom Quarks |
| spellingShingle | Saad Nabeebaccus Roman Zwicky Resolving charged hadrons in QED — gauge invariant interpolating operators Journal of High Energy Physics Precision QED Bottom Quarks |
| title | Resolving charged hadrons in QED — gauge invariant interpolating operators |
| title_full | Resolving charged hadrons in QED — gauge invariant interpolating operators |
| title_fullStr | Resolving charged hadrons in QED — gauge invariant interpolating operators |
| title_full_unstemmed | Resolving charged hadrons in QED — gauge invariant interpolating operators |
| title_short | Resolving charged hadrons in QED — gauge invariant interpolating operators |
| title_sort | resolving charged hadrons in qed gauge invariant interpolating operators |
| topic | Precision QED Bottom Quarks |
| url | https://doi.org/10.1007/JHEP11(2022)101 |
| work_keys_str_mv | AT saadnabeebaccus resolvingchargedhadronsinqedgaugeinvariantinterpolatingoperators AT romanzwicky resolvingchargedhadronsinqedgaugeinvariantinterpolatingoperators |