We investigate the dynamics responsible for generating the potential of the η ′ , the (would-be) Goldstone boson associated with the anomalous axial U(1) symmetry of QCD. The standard lore posits that pure QCD dynamics generates a confining potential with a branched structure as a function of the θ angle, and that this same potential largely determines the properties of the η ′ once fermions are included. Here we test this picture by examining a supersymmetric extension of QCD with a small amount of supersymmetry breaking generated via anomaly mediation. For pure SU(N) QCD without flavors, we verify that there are N branches generated by gaugino condensation. Once quarks are introduced, the flavor effects qualitatively change the strong dynamics of the pure theory. For F flavors we find |N − F| branches, whose dynamical origin is gaugino condensation in the unbroken subgroup for F < N – 1, and in the dual gauge group for F > N + 1. For the special cases of F = N – 1, N, N + 1 we find no branches and the entire potential is consistent with being a one-instanton effect. The number of branches is a simple consequence of the selection rules of an anomalous U(1) R symmetry. We find that the η ′ mass does not vanish in the large N limit for fixed F/N, since the anomaly is non-vanishing. The same dynamics that is responsible for the η ′ potential is also responsible for the axion potential. We present a simple derivation of the axion mass formula for an arbitrary number of flavors.
{ "_oai": { "updated": "2024-01-24T15:32:29Z", "id": "oai:repo.scoap3.org:81098", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "USA", "value": "Laboratory for Elementary Particle Physics, Cornell University, Ithaca, NY, 14853, USA", "organization": "Cornell University" } ], "surname": "Cs\u00e1ki", "email": "csaki@cornell.edu", "full_name": "Cs\u00e1ki, Csaba", "given_names": "Csaba" }, { "affiliations": [ { "country": "France", "value": "Universit\u00e9 Paris-Saclay, CEA, CNRS, Institut de Physique Th\u00e9orique, Gif-sur-Yvette, 91191, France", "organization": "Institut de Physique Th\u00e9orique" }, { "country": "France", "value": "Laboratoire de Physique de l\u2019\u00c9cole normale sup\u00e9rieure, ENS, Universit\u00e9 PSL, CNRS, Sorbonne Universit\u00e9, Universit\u00e9 Paris Cit\u00e9, Paris, F-75005, France", "organization": "Universit\u00e9 PSL, CNRS, Sorbonne Universit\u00e9, Universit\u00e9 Paris Cit\u00e9" } ], "surname": "D\u2019Agnolo", "email": "raffaele-tito.dagnolo@ipht.fr", "full_name": "D\u2019Agnolo, Raffaele", "given_names": "Raffaele" }, { "affiliations": [ { "country": "India", "value": "Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Rd, Mumbai, 400005, India", "organization": "Department of Theoretical Physics, Tata Institute of Fundamental Research" } ], "surname": "Gupta", "email": "rsgupta@theory.tifr.res.in", "full_name": "Gupta, Rick", "given_names": "Rick" }, { "affiliations": [ { "country": "Israel", "value": "Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel", "organization": "Hebrew University of Jerusalem" } ], "surname": "Kuflik", "email": "eric.kuflik@mail.huji.ac.il", "full_name": "Kuflik, Eric", "given_names": "Eric" }, { "affiliations": [ { "country": "India", "value": "Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Rd, Mumbai, 400005, India", "organization": "Department of Theoretical Physics, Tata Institute of Fundamental Research" } ], "surname": "Roy", "email": "tuhin@theory.tifr.res.in", "full_name": "Roy, Tuhin", "given_names": "Tuhin" }, { "affiliations": [ { "country": "USA", "value": "Laboratory for Elementary Particle Physics, Cornell University, Ithaca, NY, 14853, USA", "organization": "Cornell University" } ], "surname": "Ruhdorfer", "email": "m.ruhdorfer@cornell.edu", "full_name": "Ruhdorfer, Maximilian", "given_names": "Maximilian" } ], "titles": [ { "source": "Springer", "title": "On the dynamical origin of the \u03b7 \u2032 potential and the axion mass" } ], "dois": [ { "value": "10.1007/JHEP10(2023)139" } ], "publication_info": [ { "page_end": "33", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2023", "artid": "JHEP10(2023)139", "year": 2023, "page_start": "1", "journal_issue": "10" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2024-01-24T15:30:53.591683", "source": "Springer", "method": "Springer", "submission_number": "6fb69724bacd11eea49c8e4864f4776e" }, "page_nr": [ 33 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2023" } ], "control_number": "81098", "record_creation_date": "2023-10-25T15:30:19.089262", "_files": [ { "checksum": "md5:6d5ef7d55c2e3f227a6c3f666b02e1b1", "filetype": "xml", "bucket": "7a98699d-bc62-42d3-9bd6-13ca1c93783e", "version_id": "70fd67c2-5113-43cb-895f-29bdf0eeee1e", "key": "10.1007/JHEP10(2023)139.xml", "size": 17331 }, { "checksum": "md5:de91af6b2c2b4eb4b19dac3efb93e6ff", "filetype": "pdf/a", "bucket": "7a98699d-bc62-42d3-9bd6-13ca1c93783e", "version_id": "6cc64059-a3da-420e-a699-c5769966a64a", "key": "10.1007/JHEP10(2023)139_a.pdf", "size": 756159 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-ph", "hep-th" ], "value": "2307.04809" } ], "abstracts": [ { "source": "Springer", "value": "We investigate the dynamics responsible for generating the potential of the \u03b7 \u2032 , the (would-be) Goldstone boson associated with the anomalous axial U(1) symmetry of QCD. The standard lore posits that pure QCD dynamics generates a confining potential with a branched structure as a function of the \u03b8 angle, and that this same potential largely determines the properties of the \u03b7 \u2032 once fermions are included. Here we test this picture by examining a supersymmetric extension of QCD with a small amount of supersymmetry breaking generated via anomaly mediation. For pure SU(N) QCD without flavors, we verify that there are N branches generated by gaugino condensation. Once quarks are introduced, the flavor effects qualitatively change the strong dynamics of the pure theory. For F flavors we find |N \u2212 F| branches, whose dynamical origin is gaugino condensation in the unbroken subgroup for F < N \u2013 1, and in the dual gauge group for F > N + 1. For the special cases of F = N \u2013 1, N, N + 1 we find no branches and the entire potential is consistent with being a one-instanton effect. The number of branches is a simple consequence of the selection rules of an anomalous U(1) R symmetry. We find that the \u03b7 \u2032 mass does not vanish in the large N limit for fixed F/N, since the anomaly is non-vanishing. The same dynamics that is responsible for the \u03b7 \u2032 potential is also responsible for the axion potential. We present a simple derivation of the axion mass formula for an arbitrary number of flavors." } ], "imprints": [ { "date": "2023-10-23", "publisher": "Springer" } ] }