Dense Matter Breaks Fundamental Physics Law Governing Sound Speed

Scientists are increasingly focused on understanding the behaviour of matter at extreme densities, particularly concerning potential violations of the conformal limit observed in quantum chromodynamics (QCD). Francisco X. Azeredo, Arthur E. B. Pasqualotto, and Bruno S. Lopes, all from the Departamento de Física at Universidade Federal de Santa Maria, with contributions from Dyana C. Duarte, Ricardo L. S. Farias and et al., present new research applying the medium separation scheme to investigate this phenomenon in diverse scenarios including finite isospin density QCD, two-colour QCD, and two-flavour colour superconductivity. This work is significant because it demonstrates how effectively regularised effective models, such as the Nambu, Jona-Lasinio model, can consistently describe non-perturbative features of dense QCD matter and provide complementary insights when compared with lattice QCD results.

Furthermore, the analysis extends beyond isospin-rich matter, demonstrating that the violation of the conformal limit is a broader phenomenon within dense QCD.

By employing the Cornwall, Jackiw, Tomboulis formalism, the team achieved a unified description of diquark superfluids, pion superfluids, and two-flavor color superconducting phases, identifying enhancements and negative values for the normalized trace anomaly. The 3D cutoff directly modifies the upper integration limit of momentum integrals from infinity to a finite value, Λ3D, introducing this value as a new model parameter alongside the current quark mass and scalar coupling.
Alternatively, Pauli, Villars regularization replaces the integrand with a linear combination of fictitious mass terms, carefully chosen to cancel ultraviolet divergences, utilising coefficients and regulator values defined as c1 = 1, α1 = 0, c2 = −2, α2 = 1, c3 = 1, α3 = 2, with a regulator ΛPV. The partition function, Z(T, μB, μI), is calculated through a functional integral over quark fields, incorporating a chemical potential matrix μ relating isospin and baryon chemical potentials via μu= μB 3 + μI 2 and μd= μB 3 −μI 2.

Working with a basis of charged pion combinations (τ+, τ−, τ3), the Lagrangian is rewritten to explicitly break isospin symmetry, allowing for the condensation of charged pions while suppressing neutral pion condensation. Mean-field approximations introduce scalar and pion condensates, σ and Δπ, respectively, leading to an effective Lagrangian and a thermodynamic potential, Ω, dependent on these condensates and the isospin chemical potential.

This potential includes integrals over three-momentum, which are again subject to regularization using both the 3D cutoff and the medium separation scheme, as detailed previously, to obtain physically meaningful results and minimise the effective potential through gap equations ∂Ω ∂σ= ∂Ω ∂Δπ = 0. The research highlights that exceeding the conformal limit correlates strongly with supporting massive neutron stars exceeding 2M⊙. Investigations focused on the equation of state of QCD matter, particularly in systems with finite isospin density, which are characteristic of compact stellar objects like neutron stars. The study builds upon previous work employing chiral perturbation theory at low density and perturbative QCD techniques at high densities.

Vacuum regularisation and its impact on dense matter thermodynamics

Recent analyses utilising the medium separation scheme demonstrate a consistent description of dense quantum chromodynamics across various regimes. Investigations into scenarios including quantum chromodynamics at finite isospin density, two-color quantum chromodynamics, and two-flavor color superconductivity reveal how effective models, when appropriately regularized, can accurately capture essential non-perturbative features of dense matter.

These calculations offer complementary insights to those obtained through lattice quantum chromodynamics. The observed peak structure in the speed of sound across these scenarios arises from proper vacuum regularization of the theory and its effect on bosonic condensates and the thermodynamics of strongly interacting matter.

Improper regularization, such as uniform application to both vacuum and medium terms, systematically suppresses physical effects and introduces unphysical artifacts. The medium separation scheme enforces physically motivated regularization, allowing condensates to persist at high densities and softening equations of state at moderate-to-high densities.

This approach supports a picture of strongly interacting phases with enhanced stiffness at intermediate densities, while still converging towards conformality at very high densities. Limitations acknowledged by the authors include the use of effective models which, while providing valuable insights, are approximations of the full theory. Future research may focus on refining the regularization procedure and extending these analyses to incorporate additional complexities of dense quantum chromodynamics, such as more realistic equations of state or the inclusion of additional particle species.