Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Neutrino absorption in two-flavor color-superconducting quark matter

M. G. Alford1,*, L. Brodie1,†, M. Buballa2,3,‡, H. Gholami2,§, A. Haber1,4,∥, and M. Hofmann1,2,¶

  • *Contact author: alford@physics.wustl.edu
  • †Contact author: b.liam@wustl.edu
  • ‡Contact author: michael.buballa@tu-darmstadt.de
  • §Contact author: mohammadhossein.gholami@tu-darmstadt.de
  • ∥Contact author: a.haber@soton.ac.uk
  • Contact author: marco.hofmann.physics@protonmail.com

Phys. Rev. C 114, 055801 – Published 2 November, 2026

DOI: https://doi.org/10.1103/dg6d-6cv3

Abstract

We calculate the absorption mean free paths of electron and muon neutrinos in two-flavor color-superconducting (2SC) quark matter in the density and temperature range that is relevant to binary neutron star mergers. We model the strong interaction between quarks using a Nambu–Jona-Lasinio model, performing calculations self-consistently in the mean-field approximation. Since the 2SC gap is large we restrict our analysis to the contribution of unpaired quarks. We find that at low temperatures absorption by a down quark ν+d→u+e−/μ− is kinematically not allowed, so absorption by a strange quark, ν+s→u+e−/μ−, dominates the mean free path. As temperature or neutrino energy rises, the d quark absorption channel becomes active, and the mean free path shrinks. We find that in equilibrated 2SC matter with an electron lepton fraction YLe=0.1, the neutrinos form a degenerate gas with a mean free path of meters or less, independently of the temperature.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (71)

  1. A. Perego, S. Bernuzzi, and D. Radice, Thermodynamics conditions of matter in neutron star mergers, Eur. Phys. J. A 55, 124 (2019).
  2. P. L. Espino, P. Hammond, D. Radice, S. Bernuzzi, R. Gamba, F. Zappa, L. F. L. Micchi, and A. Perego, Neutrino trapping and out-of-equilibrium effects in binary neutron-star merger remnants, Phys. Rev. Lett. 132, 211001 (2024).
  3. M. A. Pajkos and E. R. Most, Influence of muons, pions, and trapped neutrinos on neutron star mergers, Phys. Rev. D 111, 043013 (2025).
  4. H. H.-Y. Ng, C. Musolino, S. D. Tootle, and L. Rezzolla, Accurate muonic interactions in neutron star mergers and impact on heavy-element nucleosynthesis, Astrophys. J. Lett. 985, L36 (2025).
  5. E. R. Most, A. Haber, S. P. Harris, Z. Zhang, M. G. Alford, and J. Noronha, Emergence of microphysical bulk viscosity in binary neutron star postmerger dynamics, Astrophys. J. Lett. 967, L14 (2024).
  6. M. G. Alford, A. Haber, and Z. Zhang, Isospin equilibration in neutron star mergers, Phys. Rev. C 109, 055803 (2024).
  7. M. G. Alford, L. Brodie, F. Foucart, and A. Haber, Thermalization of neutrinos in a neutron star merger simulation, Phys. Rev. D 114, 043033 (2026).
  8. A. Schmitt and P. Shternin, Reaction rates and transport in neutron stars, in The Physics and Astrophysics of Neutron Stars, Astrophysics and Space Science Library, edited by L. Rezzolla, P. Pizzochero, D. Jones, N. Rea, and I. Vidaña (Springer, Cham, 2018), Vol. 457, pp. 455–574.
  9. F. Foucart, Neutrino transport in general relativistic neutron star merger simulations, Living. Rev. Comput. Astrophys. 9, 1 (2022).
  10. M. G. Alford, J. Berges, and K. Rajagopal, Unlocking color and flavor in superconducting strange quark matter, Nucl. Phys. B 558, 219 (1999).
  11. J. Braun and B. Schallmo, From quarks and gluons to color superconductivity at supranuclear densities, Phys. Rev. D 105, 036003 (2022).
  12. J. Braun, A. Geißel, and B. Schallmo, Speed of sound in dense strong-interaction matter, SciPost Phys. Core 7, 015 (2024).
  13. A. Geißel, T. Gorda, and J. Braun, Pressure and speed of sound in two-flavor color-superconducting quark matter at next-to-leading order, Phys. Rev. D 110, 014034 (2024).
  14. A. W. Steiner, M. Prakash, and J. M. Lattimer, Diffusion of neutrinos in proto-neutron star matter with quarks, Phys. Lett. B 509, 10 (2001).
  15. N. Iwamoto, Neutrino emissivities and mean free paths of degenerate quark matter, Ann. Phys. 141, 1 (1982).
  16. V. K. Gupta, Neutrino emissivity of quark matter at finite temperatures, Pramana 45, 195 (1995).
  17. G. C. Colvero and G. Lugones, Neutrino diffusive transport in hot quark matter: A detailed analysis, Phys. Rev. C 89, 055803 (2014).
  18. Q. Wang, Z.-g. Wang, and J. Wu, Phase space and quark mass effects in neutrino emissions in a color superconductor, Phys. Rev. D 74, 014021 (2006).
  19. G. Baym and S. A. Chin, Landau theory of relativistic Fermi liquids, Nucl. Phys. A 262, 527 (1976).
  20. K. Pal and A. K. Dutt-Mazumder, Non-Fermi liquid corrections to the neutrino mean free path in dense quark matter, Phys. Rev. D 84, 034004 (2011).
  21. S. P. Adhya, P. K. Roy, and A. K. Dutt-Mazumder, Next-to-leading order non-Fermi-liquid corrections to the neutrino emissivity and cooling of the neutron star, Phys. Rev. D 86, 034012 (2012).
  22. D. Blaschke, T. Klähn, and D. N. Voskresensky, Diquark condensates and compact star cooling, Astrophys. J. 533, 406 (2000).
  23. P. Jaikumar and M. Prakash, Neutrino pair emission from Cooper pair breaking and recombination in superfluid quark matter, Phys. Lett. B 516, 345 (2001).
  24. P. Jaikumar, M. Prakash, and T. Schäfer, Neutrino emission from Goldstone modes in dense quark matter, Phys. Rev. D 66, 063003 (2002).
  25. M. Alford, P. Jotwani, C. Kouvaris, J. Kundu, and K. Rajagopal, Astrophysical implications of gapless color-flavor locked quark matter: A hot water bottle for aging neutron stars, Phys. Rev. D 71, 114011 (2005).
  26. H. Grigorian, D. Blaschke, and D. Voskresensky, Cooling of neutron stars with color superconducting quark cores, Phys. Rev. C 71, 045801 (2005).
  27. P. Jaikumar, C. D. Roberts, and A. Sedrakian, Direct Urca neutrino rate in color superconducting quark matter, Phys. Rev. C 73, 042801 (2006).
  28. A. Schmitt, I. A. Shovkovy, and Q. Wang, Neutrino emission and cooling rates of spin-one color superconductors, Phys. Rev. D 73, 034012 (2006).
  29. R. Anglani, G. Nardulli, M. Ruggieri, and M. Mannarelli, Neutrino emission from compact stars and inhomogeneous color superconductivity, Phys. Rev. D 74, 074005 (2006).
  30. R. Negreiros, V. A. Dexheimer, and S. Schramm, Quark core impact on hybrid star cooling, Phys. Rev. C 85, 035805 (2012).
  31. J. Berdermann, D. Blaschke, T. Fischer, and A. Kachanovich, Neutrino emissivities and bulk viscosity in neutral two-flavor quark matter, Phys. Rev. D 94, 123010 (2016).
  32. M. G. Alford and A. Schmitt, Bulk viscosity in 2SC quark matter, J. Phys. G: Nucl. Part. Phys. 34, 67 (2007).
  33. X. Wang and I. A. Shovkovy, Bulk viscosity of spin-one color superconducting strange quark matter, Phys. Rev. D 82, 085007 (2010).
  34. M. Alford, A. Harutyunyan, A. Sedrakian, and S. Tsiopelas, Bulk viscosity of two-color superconducting quark matter in neutron star mergers, Phys. Rev. D 110, L061303 (2024).
  35. M. Alford, A. Harutyunyan, A. Sedrakian, and S. Tsiopelas, Bulk viscosity of two-flavor color superconducting quark matter in neutron star mergers, Front. Astron. Space Sci. 12, 1648066 (2025).
  36. G. W. Carter and S. Reddy, Neutrino propagation in color superconducting quark matter, Phys. Rev. D 62, 103002 (2000).
  37. S. Reddy, M. Sadzikowski, and M. Tachibana, Neutrino rates in color flavor locked quark matter, Nucl. Phys. A 714, 337 (2003).
  38. J. Kundu and S. Reddy, Neutrino scattering off pair-breaking and collective excitations in superfluid neutron matter and in color-flavor-locked quark matter, Phys. Rev. C 70, 055803 (2004).
  39. P. Rehberg, S. P. Klevansky, and J. Hufner, Hadronization in the SU(3) Nambu–Jona-Lasinio model, Phys. Rev. C 53, 410 (1996).
  40. F. Gastineau, R. Nebauer, and J. Aichelin, Thermodynamics of the three-flavor Nambu–Jona-Lasinio model: Chiral symmetry breaking and color superconductivity, Phys. Rev. C 65, 045204 (2002).
  41. T. Klähn, D. Blaschke, F. Sandin, C. Fuchs, A. Faessler, H. Grigorian, G. Ropke, and J. Trumper, Modern compact star observations and the quark matter equation of state, Phys. Lett. B 654, 170 (2007).
  42. M. Kobayashi and T. Maskawa, Chiral symmetry and η−X mixing, Prog. Theor. Phys. 44, 1422 (1970).
  43. G. 't Hooft, Symmetry breaking through Bell-Jackiw anomalies, Phys. Rev. Lett. 37, 8 (1976).
  44. H. Gholami, M. Hofmann, and M. Buballa, Renormalization-group consistent treatment of color superconductivity in the NJL model, Phys. Rev. D 111, 014006 (2025).
  45. J. Braun, M. Leonhardt, and J. M. Pawlowski, Renormalization group consistency and low-energy effective theories, SciPost Phys. 6, 056 (2019).
  46. H. Gholami, L. Kurth, U. Mire, M. Buballa, and B.-J. Schaefer, Renormalizing the quark-meson-diquark model, Phys. Rev. D 113, 114020 (2026).
  47. H. Gholami, I. A. Rather, M. Hofmann, M. Buballa, and J. Schaffner-Bielich, Astrophysical constraints on color-superconducting phases in compact stars within the RG-consistent NJL model, Phys. Rev. D 111, 103034 (2025).
  48. J.-E. Christian, I. A. Rather, H. Gholami, and M. Hofmann, Comprehensive analysis of constructing hybrid stars with a renormalization group-consistent Nambu-Jona-Lasino model, Astron. Astrophys. 701, A145 (2025).
  49. M. Buballa, NJL-model analysis of dense quark matter, Phys. Rep. 407, 205 (2005).
  50. F. Foucart, P. C.-K. Cheong, M. D. Duez, L. E. Kidder, H. P. Pfeiffer, and M. A. Scheel, Robustness of neutron star merger simulations to changes in neutrino transport and neutrino-matter interactions, Phys. Rev. D 110, 083028 (2024).
  51. H. H.-Y. Ng, P. C.-K. Cheong, A. T.-L. Lam, and T. G. F. Li, General-relativistic radiation transport scheme in Gmunu. II. Implementation of novel microphysical library for neutrino radiation—Weakhub, Astrophys. J. Suppl. Series 272, 9 (2024).
  52. L. Chiesa, M. Bhattacharyya, F. Mazzini, F. M. Guercilena, A. Perego, and D. Radice, Open-source library for performance-portable neutrino reaction rates: Application to neutron star mergers, Phys. Rev. D 111, 063053 (2025).
  53. P.-C. Chu, B. Wang, H.-Y. Ma, Y.-M. Dong, S.-L. Chang, C.-H. Zheng, J.-T. Liu, and X.-M. Zhang, Quark matter in an SU(3) Nambu–Jona-Lasinio model with two types of vector interactions, Phys. Rev. D 93, 094032 (2016).
  54. P.-C. Chu, B. Wang, Y.-Y. Jia, Y.-M. Dong, S.-M. Wang, X.-H. Li, L. Zhang, X.-M. Zhang, and H.-Y. Ma, Quark magnetar in three-flavor Nambu–Jona-Lasinio model under strong magnetic fields with two types of vector interactions, Phys. Rev. D 94, 123014 (2016).
  55. H. Liu, J. Xu, and C. M. Ko, Properties of strange quark stars with isovector interactions, Phys. Lett. B 803, 135343 (2020).
  56. H. Liu, X.-M. Zhang, and P.-C. Chu, Properties of quark-matter cores in massive hybrid stars, Phys. Rev. D 107, 094032 (2023).
  57. E. Loffredo, A. Perego, D. Logoteta, and M. Branchesi, Muons in the aftermath of neutron star mergers and their impact on trapped neutrinos, Astron. Astrophys. 672, A124 (2023).
  58. H. Gieg, F. Schianchi, M. Ujevic, and T. Dietrich, Role of muons in binary neutron star mergers: First simulations, Phys. Rev. D 112, 023036 (2025).
  59. J. Knoll and D. N. Voskresensky, Classical and quantum many-body description of bremsstrahlung in dense matter, Ann. Phys. 249, 532 (1996).
  60. G. Raffelt and G. Sigl, Numerical toy-model calculation of the nucleon spin autocorrelation function in a supernova core, Phys. Rev. D 60, 023001 (1999).
  61. D. N. Voskresensky, Neutrino cooling of neutron stars: Medium effects, in Physics of Neutron Star Interiors, Lecture Notes in Physics, edited by D. Blaschke, A. Sedrakian, and N. K. Glendenning (Springer, Berlin, 2001), Vol. 578, p. 467.
  62. E. N. E. van Dalen, A. E. L. Dieperink, and J. A. Tjon, Neutrino emission in neutron stars, Phys. Rev. C 67, 065807 (2003).
  63. M. G. Alford, A. Haber, and Z. Zhang, Beyond modified Urca: The nucleon width approximation for flavor-changing processes in dense matter, Phys. Rev. C 110, L052801 (2024).
  64. E. R. Most, L. J. Papenfort, V. Dexheimer, M. Hanauske, S. Schramm, H. Stöcker, and L. Rezzolla, Signatures of quark-hadron phase transitions in general-relativistic neutron-star mergers, Phys. Rev. Lett. 122, 061101 (2019).
  65. A. Bauswein, N.-U. F. Bastian, D. B. Blaschke, K. Chatziioannou, J. A. Clark, T. Fischer, and M. Oertel, Identifying a first-order phase transition in neutron-star mergers through gravitational waves, Phys. Rev. Lett. 122, 061102 (2019).
  66. E. O'Connor, An open-source neutrino radiation hydrodynamics code for core-collapse supernovae, Astrophys. J. Suppl. Series 219, 24 (2015).
  67. E. O'Connor, nulib: Neutrino interaction library, GitHub, 2025, https://github.com/evanoconnor/NuLib.
  68. A. Perego, D. Radice, F. M. Guercilena, L. Chiesa, and M. Bhattacharyya, bns_nurates, GitHub, 2025, https://github.com/RelNucAs/bns_nurates.
  69. https://arxiv.org/src/2509.04240v2/anc.
  70. M. Hofmann, H. Gholami, M. Pelicer, and Y. Yang, Nambu–Jona-Lasinio equation of state module, Zenodo, 2026, https://doi.org/10.5281/zenodo.18249032.
  71. J. Jahan et al., Studying the QCD matter produced in heavy-ion collisions using the MUSES calculation engine, arXiv:2606.26326.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation