High-order perturbative calculations for thermodynamic quantities in QCD are complicated by the physics of dynamical screening that affects the soft, long-wavelength modes of the system. Here, we provide details for the evaluation of this soft contribution to the next-to-next-to-next-to-leading order () pressure of high-density, zero-temperature quark matter (QM), complementing our accompanying Letter [T. Gorda et al., Phys. Rev. Lett. 127, 162003 (2021)]. Our calculation requires the determination of the pressure of the hard-thermal-loop effective theory to full two-loop order at zero temperature, which we go through in considerable detail. In addition to this, we comprehensively discuss the structure of the weak-coupling expansion of the QM pressure, and lay out a roadmap towards the evaluation of the contributions missing from a full result for this quantity.
{ "_oai": { "updated": "2022-04-05T09:48:27Z", "id": "oai:repo.scoap3.org:65367", "sets": [ "PRD" ] }, "authors": [ { "raw_name": "Tyler Gorda", "affiliations": [ { "country": "Germany", "value": "Technische Universit\u00e4t Darmstadt, Department of Physics, D-64289 Darmstadt, Germany" }, { "country": "Germany", "value": "Helmholtz Research Academy for FAIR, D-64289 Darmstadt, Germany" } ], "surname": "Gorda", "given_names": "Tyler", "full_name": "Gorda, Tyler" }, { "raw_name": "Aleksi Kurkela", "affiliations": [ { "country": "Norway", "value": "Faculty of Science and Technology, University of Stavanger, 4036 Stavanger, Norway" } ], "surname": "Kurkela", "given_names": "Aleksi", "full_name": "Kurkela, Aleksi" }, { "raw_name": "Risto Paatelainen", "affiliations": [ { "country": "Finland", "value": "Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland" } ], "surname": "Paatelainen", "given_names": "Risto", "full_name": "Paatelainen, Risto" }, { "raw_name": "Saga S\u00e4ppi", "affiliations": [ { "country": "Italy", "value": "European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione Bruno Kessler, Strada delle Tabarelle 286, I-38123 Villazzano (TN), Italy" }, { "country": "Finland", "value": "Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland" } ], "surname": "S\u00e4ppi", "given_names": "Saga", "full_name": "S\u00e4ppi, Saga" }, { "raw_name": "Aleksi Vuorinen", "affiliations": [ { "country": "Finland", "value": "Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland" } ], "surname": "Vuorinen", "given_names": "Aleksi", "full_name": "Vuorinen, Aleksi" } ], "titles": [ { "source": "APS", "title": "Cold quark matter at <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>: Soft contributions" } ], "dois": [ { "value": "10.1103/PhysRevD.104.074015" } ], "publication_info": [ { "journal_volume": "104", "journal_title": "Physical Review D", "material": "article", "journal_issue": "7", "year": 2021 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2022-04-05T09:21:44.250600", "source": "APS", "method": "APS", "submission_number": "a0d20d20b4c111ec837fd6d834be26e1" }, "page_nr": [ 43 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2021" } ], "control_number": "65367", "record_creation_date": "2021-10-15T14:30:02.482454", "_files": [ { "checksum": "md5:4e62106fdf734746c4468d10d6af5f5e", "filetype": "pdf", "bucket": "31eed7cf-13da-48e9-bc82-cdc42936ad4a", "version_id": "a30862c5-b96a-4b78-99b8-14035ea368a5", "key": "10.1103/PhysRevD.104.074015.pdf", "size": 2306076 }, { "checksum": "md5:6aa5282170096f4885e4e34324c1da7d", "filetype": "xml", "bucket": "31eed7cf-13da-48e9-bc82-cdc42936ad4a", "version_id": "c6243ff0-e2e7-47d0-873a-756a74896b4c", "key": "10.1103/PhysRevD.104.074015.xml", "size": 1035783 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-ph", "nucl-th" ], "value": "2103.07427" } ], "abstracts": [ { "source": "APS", "value": "High-order perturbative calculations for thermodynamic quantities in QCD are complicated by the physics of dynamical screening that affects the soft, long-wavelength modes of the system. Here, we provide details for the evaluation of this soft contribution to the next-to-next-to-next-to-leading order (<math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>) pressure of high-density, zero-temperature quark matter (QM), complementing our accompanying Letter [T. Gorda et al., Phys. Rev. Lett. 127, 162003 (2021)]. Our calculation requires the determination of the pressure of the hard-thermal-loop effective theory to full two-loop order at zero temperature, which we go through in considerable detail. In addition to this, we comprehensively discuss the structure of the weak-coupling expansion of the QM pressure, and lay out a roadmap towards the evaluation of the contributions missing from a full <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math> result for this quantity." } ], "imprints": [ { "date": "2021-10-15", "publisher": "APS" } ] }