Standard interpolating operators for charged mesons, e.g. J 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 , $$ {\mathcal{J}}_B^{(0)} $$ = 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 $$ \mathcal{O} $$ (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 − → π 0 ℓ − $$ \overline{\nu} $$ ).
{ "_oai": { "updated": "2023-02-24T00:31:56Z", "id": "oai:repo.scoap3.org:73971", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "France", "value": "Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, 91405, France", "organization": "Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab" } ], "surname": "Nabeebaccus", "email": "saad.nabeebaccus@ijclab.in2p3.fr", "full_name": "Nabeebaccus, Saad", "given_names": "Saad" }, { "affiliations": [ { "country": "UK", "value": "Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh, Scotland, EH9 3JZ, UK", "organization": "University of Edinburgh" } ], "surname": "Zwicky", "email": "roman.zwicky@ed.ac.uk", "full_name": "Zwicky, Roman", "given_names": "Roman" } ], "titles": [ { "source": "Springer", "title": "Resolving charged hadrons in QED \u2014 gauge invariant interpolating operators" } ], "dois": [ { "value": "10.1007/JHEP11(2022)101" } ], "publication_info": [ { "page_end": "20", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2022", "artid": "JHEP11(2022)101", "year": 2022, "page_start": "1", "journal_issue": "11" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-02-24T00:31:01.714623", "source": "Springer", "method": "Springer", "submission_number": "5f487fa6b3da11eda920065bd8dc6b20" }, "page_nr": [ 20 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2022" } ], "control_number": "73971", "record_creation_date": "2022-11-18T09:30:20.519736", "_files": [ { "checksum": "md5:30be920485df40a7fd9a952e1bc49a3b", "filetype": "xml", "bucket": "8c7d3049-f58f-4747-bd1c-0c6e8c6c74ca", "version_id": "c7c96aa9-864d-460a-abac-fa3f13e0ff78", "key": "10.1007/JHEP11(2022)101.xml", "size": 15690 }, { "checksum": "md5:57a13dd20f8f4629ea725d39bc194203", "filetype": "pdf/a", "bucket": "8c7d3049-f58f-4747-bd1c-0c6e8c6c74ca", "version_id": "66177c5d-c720-4811-a29c-7f8f32af8817", "key": "10.1007/JHEP11(2022)101_a.pdf", "size": 538094 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-ph", "hep-lat" ], "value": "2209.06925" } ], "abstracts": [ { "source": "Springer", "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> $$ \\overline{\\nu} $$ )." } ], "imprints": [ { "date": "2022-11-17", "publisher": "Springer" } ] }