Cold quark matter at N3LO: Soft contributions

Tyler Gorda (Technische Universität Darmstadt, Department of Physics, D-64289 Darmstadt, Germany; Helmholtz Research Academy for FAIR, D-64289 Darmstadt, Germany) ; Aleksi Kurkela (Faculty of Science and Technology, University of Stavanger, 4036 Stavanger, Norway) ; Risto Paatelainen (Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland) ; Saga Säppi (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; Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland) ; Aleksi Vuorinen (Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland)

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 (N3LO) 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 N3LO result for this quantity.

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      "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"
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      "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."
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Published on:
15 October 2021
Publisher:
APS
Published in:
Physical Review D , Volume 104 (2021)
Issue 7
DOI:
https://doi.org/10.1103/PhysRevD.104.074015
arXiv:
2103.07427
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: