2000 character limit reached
Pressure and speed of sound in two-flavor color-superconducting quark matter at next-to-leading order (2403.18010v2)
Published 26 Mar 2024 in hep-ph and nucl-th
Abstract: Deconfined quark matter at asymptotically high densities is weakly coupled, due to the asymptotic freedom of Quantum Chromodynamics. In this weak-coupling regime, bulk thermodynamic properties of quark matter, assuming a trivial ground state, are currently known to partial next-to-next-to-next-to-leading order. However, the ground state at high densities is expected to be a color superconductor, in which the excitation spectrum of (at least some) quarks exhibit a gap with a non-perturbative dependence on the strong coupling. In this work, we calculate the thermodynamic properties of color-superconducting quark matter at high densities and zero temperature at next-to-leading order (NLO) in the coupling in the presence of a finite gap. We work in the limit of two massless quark flavors, which corresponds to deconfined symmetric nuclear matter, and further assume that the gap is small compared to the quark chemical potential. In these limits, we find that the NLO corrections to the pressure and speed of sound are comparable in size to the leading-order effects of the gap, and further increase both quantities above their values for non-superconducting quark matter. We also provide a parameterization of the NLO speed of sound to guide phenomenology in the high-density region, and we furthermore comment on whether our findings should be expected to extend to the case of three-flavor quark matter of relevance to neutron stars.
- A. Bazavov et al. (HotQCD), Equation of state in ( 2+1 )-flavor QCD, Phys. Rev. D 90, 094503 (2014), arXiv:1407.6387 [hep-lat] .
- P. de Forcrand, Simulating QCD at finite density, PoS LAT2009, 010 (2009), arXiv:1005.0539 [hep-lat] .
- O. Philipsen, The QCD equation of state from the lattice, Prog. Part. Nucl. Phys. 70, 55 (2013), arXiv:1207.5999 [hep-lat] .
- G. Aarts, Introductory lectures on lattice QCD at nonzero baryon number, J. Phys. Conf. Ser. 706, 022004 (2016), arXiv:1512.05145 [hep-lat] .
- C. Gattringer and K. Langfeld, Approaches to the sign problem in lattice field theory, Int. J. Mod. Phys. A 31, 1643007 (2016), arXiv:1603.09517 [hep-lat] .
- K. Nagata, Finite-density lattice QCD and sign problem: Current status and open problems, Prog. Part. Nucl. Phys. 127, 103991 (2022), arXiv:2108.12423 [hep-lat] .
- C. Drischler, K. Hebeler, and A. Schwenk, Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation, Phys. Rev. Lett. 122, 042501 (2019), arXiv:1710.08220 [nucl-th] .
- J. Keller, K. Hebeler, and A. Schwenk, Nuclear Equation of State for Arbitrary Proton Fraction and Temperature Based on Chiral Effective Field Theory and a Gaussian Process Emulator, Phys. Rev. Lett. 130, 072701 (2023), arXiv:2204.14016 [nucl-th] .
- A. Kurkela, P. Romatschke, and A. Vuorinen, Cold Quark Matter, Phys. Rev. D 81, 105021 (2010), arXiv:0912.1856 [hep-ph] .
- A. Kurkela and A. Vuorinen, Cool quark matter, Phys. Rev. Lett. 117, 042501 (2016), arXiv:1603.00750 [hep-ph] .
- T. Gorda and S. Säppi, Cool quark matter with perturbative quark masses, Phys. Rev. D 105, 114005 (2022), arXiv:2112.11472 [hep-ph] .
- J. Braun and B. Schallmo, From quarks and gluons to color superconductivity at supranuclear densities, Phys. Rev. D 105, 036003 (2022a), arXiv:2106.04198 [hep-ph] .
- J. Braun, A. Geißel, and B. Schallmo, Speed of sound in dense strong-interaction matter, arXiv:2206.06328 [nucl-th] (2022).
- O. Komoltsev and A. Kurkela, How Perturbative QCD Constrains the Equation of State at Neutron-Star Densities, Phys. Rev. Lett. 128, 202701 (2022), arXiv:2111.05350 [nucl-th] .
- T. Gorda, O. Komoltsev, and A. Kurkela, Ab-initio QCD Calculations Impact the Inference of the Neutron-star-matter Equation of State, Astrophys. J. 950, 107 (2023c), arXiv:2204.11877 [nucl-th] .
- R. Somasundaram, I. Tews, and J. Margueron, Perturbative QCD and the neutron star equation of state, Phys. Rev. C 107, L052801 (2023), arXiv:2204.14039 [nucl-th] .
- D. T. Son, Superconductivity by long range color magnetic interaction in high density quark matter, Phys. Rev. D59, 094019 (1999), arXiv:hep-ph/9812287 [hep-ph] .
- T. Schäfer and F. Wilczek, Superconductivity from perturbative one gluon exchange in high density quark matter, Phys. Rev. D60, 114033 (1999), arXiv:hep-ph/9906512 [hep-ph] .
- R. D. Pisarski and D. H. Rischke, Gaps and critical temperature for color superconductivity, Phys. Rev. D 61, 051501 (2000a), arXiv:nucl-th/9907041 .
- R. D. Pisarski and D. H. Rischke, Color superconductivity in weak coupling, Phys. Rev. D 61, 074017 (2000b), arXiv:nucl-th/9910056 .
- W. E. Brown, J. T. Liu, and H.-c. Ren, On the perturbative nature of color superconductivity, Phys. Rev. D61, 114012 (2000), arXiv:hep-ph/9908248 [hep-ph] .
- D. Nickel, J. Wambach, and R. Alkofer, Color-superconductivity in the strong-coupling regime of Landau gauge QCD, Phys. Rev. D 73, 114028 (2006), arXiv:hep-ph/0603163 .
- J. Braun, M. Leonhardt, and M. Pospiech, Fierz-complete NJL model study III: Emergence from quark-gluon dynamics, Phys. Rev. D101, 036004 (2020), arXiv:1909.06298 [hep-ph] .
- M. G. Alford, K. Rajagopal, and F. Wilczek, QCD at finite baryon density: Nucleon droplets and color superconductivity, Phys. Lett. B422, 247 (1998), arXiv:hep-ph/9711395 [hep-ph] .
- M. G. Alford, K. Rajagopal, and F. Wilczek, Color flavor locking and chiral symmetry breaking in high density QCD, Nucl. Phys. B 537, 443 (1999), arXiv:hep-ph/9804403 .
- M. Alford and K. Rajagopal, Absence of two flavor color superconductivity in compact stars, JHEP 06, 031, arXiv:hep-ph/0204001 .
- M. G. Alford, Color superconducting quark matter, Ann. Rev. Nucl. Part. Sci. 51, 131 (2001), arXiv:hep-ph/0102047 .
- D. H. Rischke, The Quark gluon plasma in equilibrium, Prog. Part. Nucl. Phys. 52, 197 (2004), arXiv:nucl-th/0305030 .
- M. Buballa, NJL model analysis of quark matter at large density, Phys. Rept. 407, 205 (2005), arXiv:hep-ph/0402234 [hep-ph] .
- I. A. Shovkovy, Two lectures on color superconductivity, Found. Phys. 35, 1309 (2005), arXiv:nucl-th/0410091 [nucl-th] .
- K. Fukushima and T. Hatsuda, The phase diagram of dense QCD, Rept. Prog. Phys. 74, 014001 (2011), arXiv:1005.4814 [hep-ph] .
- K. Rajagopal and F. Wilczek, The Condensed matter physics of QCD, in At the frontier of particle physics. Handbook of QCD. Vol. 1-3, edited by M. Shifman and B. Ioffe (2000) pp. 2061–2151, arXiv:hep-ph/0011333 .
- K. Rajagopal and F. Wilczek, Enforced electrical neutrality of the color flavor locked phase, Phys. Rev. Lett. 86, 3492 (2001), arXiv:hep-ph/0012039 .
- I. A. Shovkovy and P. J. Ellis, Thermal conductivity of dense quark matter and cooling of stars, Phys. Rev. C 66, 015802 (2002), arXiv:hep-ph/0204132 .
- B. B. Brandt, F. Cuteri, and G. Endrodi, Equation of state and speed of sound of isospin-asymmetric QCD on the lattice, JHEP 07, 055, arXiv:2212.14016 [hep-lat] .
- Y. Fujimoto, Enhanced contribution of pairing gap to the QCD equation of state at large isospin chemical potential, arXiv:2312.11443 [hep-ph] (2023).
- G. Baym and S. A. Chin, Landau Theory of Relativistic Fermi Liquids, Nucl. Phys. A 262, 527 (1976).
- G. Chapline, Jr. and M. Nauenberg, Phase Transition from Baryon to Quark Matter, Nature 264, 235 (1976).
- B. A. Freedman and L. D. McLerran, Fermions and Gauge Vector Mesons at Finite Temperature and Density. 1. Formal Techniques, Phys. Rev. D 16, 1130 (1977a).
- B. A. Freedman and L. D. McLerran, Fermions and Gauge Vector Mesons at Finite Temperature and Density. 3. The Ground State Energy of a Relativistic Quark Gas, Phys. Rev. D 16, 1169 (1977b).
- V. Baluni, Nonabelian Gauge Theories of Fermi Systems: Chromotheory of Highly Condensed Matter, Phys. Rev. D 17, 2092 (1978).
- T. Toimela, Perturbative QED and QCD at Finite Temperatures and Densities, Int. J. Theor. Phys. 24, 901 (1985), [Erratum: Int.J.Theor.Phys. 26, 1021 (1987)].
- D. H. Rischke and R. D. Pisarski, Color superconductivity in cold, dense quark matter, in 5th Workshop on QCD (QCD 2000) (2000) pp. 220–230, arXiv:nucl-th/0004016 .
- S. Bethke, The 2009 World Average of αssubscript𝛼𝑠\alpha_{s}italic_α start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT, Eur. Phys. J. C 64, 689 (2009), arXiv:0908.1135 [hep-ph] .
- P. Bedaque and A. W. Steiner, Sound velocity bound and neutron stars, Phys. Rev. Lett. 114, 031103 (2015), arXiv:1408.5116 [nucl-th] .
- S. Altiparmak, C. Ecker, and L. Rezzolla, On the Sound Speed in Neutron Stars, Astrophys. J. Lett. 939, L34 (2022), arXiv:2203.14974 [astro-ph.HE] .
- A. Kurkela, K. Rajagopal, and R. Steinhorst, Astrophysical Equation-of-State Constraints on the Color-Superconducting Gap, arXiv:2401.16253 [astro-ph.HE] (2024).
- A. W. Steiner, S. Reddy, and M. Prakash, Color neutral superconducting quark matter, Phys. Rev. D 66, 094007 (2002), arXiv:hep-ph/0205201 .
- D. F. Litim and J. M. Pawlowski, On gauge invariant Wilsonian flows, in Workshop on the Exact Renormalization Group (1998) pp. 168–185, arXiv:hep-th/9901063 .
- J. Braun, Fermion Interactions and Universal Behavior in Strongly Interacting Theories, J. Phys. G 39, 033001 (2012), arXiv:1108.4449 [hep-ph] .
- H. Gies and C. Wetterich, Renormalization flow of bound states, Phys. Rev. D 65, 065001 (2002), arXiv:hep-th/0107221 .
- H. Gies and C. Wetterich, Universality of spontaneous chiral symmetry breaking in gauge theories, Phys. Rev. D 69, 025001 (2004), arXiv:hep-th/0209183 .
- J. M. Pawlowski, Aspects of the functional renormalisation group, Annals Phys. 322, 2831 (2007), arXiv:hep-th/0512261 .
- H. Gies, Introduction to the functional RG and applications to gauge theories, Lect. Notes Phys. 852, 287 (2012), arXiv:hep-ph/0611146 [hep-ph] .
- S. Floerchinger and C. Wetterich, Exact flow equation for composite operators, Phys. Lett. B680, 371 (2009), arXiv:0905.0915 [hep-th] .
- W.-j. Fu, J. M. Pawlowski, and F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D 101, 054032 (2020), arXiv:1909.02991 [hep-ph] .
- K. Fukushima, J. M. Pawlowski, and N. Strodthoff, Emergent hadrons and diquarks, Annals Phys. 446, 169106 (2022), arXiv:2103.01129 [hep-ph] .
- F. Englert and R. Brout, Broken Symmetry and the Mass of Gauge Vector Mesons, Phys. Rev. Lett. 13, 321 (1964).
- P. W. Higgs, Broken symmetries, massless particles and gauge fields, Phys. Lett. 12, 132 (1964a).
- P. W. Higgs, Broken Symmetries and the Masses of Gauge Bosons, Phys. Rev. Lett. 13, 508 (1964b).
- G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Global Conservation Laws and Massless Particles, Phys. Rev. Lett. 13, 585 (1964).
- C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301, 90 (1993), arXiv:1710.05815 [hep-th] .
- J. Braun, M. Leonhardt, and J. M. Pawlowski, Renormalization group consistency and low-energy effective theories, SciPost Phys. 6, 056 (2019), arXiv:1806.04432 [hep-ph] .
- T. Papenbrock and C. Wetterich, Two loop results from one loop computations and nonperturbative solutions of exact evolution equations, Z. Phys. C 65, 519 (1995), arXiv:hep-th/9403164 .
- D. F. Litim and J. M. Pawlowski, Perturbation theory and renormalization group equations, Phys. Rev. D 65, 081701 (2002), arXiv:hep-th/0111191 .
- J. Braun, H. Gies, and J. M. Pawlowski, Quark Confinement from Color Confinement, Phys. Lett. B 684, 262 (2010a), arXiv:0708.2413 [hep-th] .
- D. H. Rischke, Debye screening and Meissner effect in a two flavor color superconductor, Phys. Rev. D 62, 034007 (2000), arXiv:nucl-th/0001040 .
- G. W. Carter and D. Diakonov, The Nonperturbative color Meissner effect in a two flavor color superconductor, Nucl. Phys. B 582, 571 (2000), arXiv:hep-ph/0001318 .
- D. H. Rischke, Gluon self-energy in a two-flavor color superconductor, Phys. Rev. D 64, 094003 (2001), arXiv:nucl-th/0103050 .
- D. H. Rischke and I. A. Shovkovy, Longitudinal gluons and Nambu-Goldstone bosons in a two flavor color superconductor, Phys. Rev. D 66, 054019 (2002), arXiv:nucl-th/0205080 .
- T. Schäfer and F. Wilczek, High density quark matter and the renormalization group in QCD with two and three flavors, Phys. Lett. B 450, 325 (1999), arXiv:hep-ph/9810509 .
- J. Berges and K. Rajagopal, Color superconductivity and chiral symmetry restoration at nonzero baryon density and temperature, Nucl. Phys. B 538, 215 (1999), arXiv:hep-ph/9804233 .
- A. Gerhold and A. Rebhan, Gauge dependence identities for color superconducting QCD, Phys. Rev. D 68, 011502 (2003), arXiv:hep-ph/0305108 .
- J. Braun and B. Schallmo, Zero-temperature thermodynamics of dense asymmetric strong-interaction matter, Phys. Rev. D 106, 076010 (2022b), arXiv:2204.00358 [nucl-th] .
- O. Ivanytskyi and D. Blaschke, Density functional approach to quark matter with confinement and color superconductivity, Phys. Rev. D 105, 114042 (2022), arXiv:2204.03611 [nucl-th] .
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.