Cold Quark Matter (0912.1856v2)

Abstract: We perform an O(alpha_s^2) perturbative calculation of the equation of state of cold but dense QCD matter with two massless and one massive quark flavor, finding that perturbation theory converges reasonably well for quark chemical potentials above 1 GeV. Using a running coupling constant and strange quark mass, and allowing for further non-perturbative effects, our results point to a narrow range where absolutely stable strange quark matter may exist. Absent stable strange quark matter, our findings suggest that quark matter in compact star cores becomes confined to hadrons only slightly above the density of atomic nuclei. Finally, we show that equations of state including quark matter lead to hybrid star masses up to M~2M_solar, in agreement with current observations. For strange stars, we find maximal masses of M~2.75M_solar and conclude that confirmed observations of compact stars with M>2M_solar would strongly favor the existence of stable strange quark matter.

• The paper presents a perturbative calculation of the QCD pressure for cold quark matter using order αs² corrections, incorporating running coupling and realistic strange quark mass effects.
• It methodically separates contributions from massless and massive quarks along with vacuum-matter effects to refine the traditional bag model approach.
• The results imply that hybrid stars could reach masses up to 2M☉, supporting the possibility of stable strange quark matter in compact astrophysical objects.

Overview of Perturbative Calculation of Cold Quark Matter in QCD

The paper "Cold Quark Matter" undertakes an intricate perturbative analysis of the quantum chromodynamics (QCD) equation of state (EoS) at zero temperature but high density, considering a system with two massless quark flavors and one massive quark flavor. The paper is intriguing as it explores scenarios where quark chemical potentials exceed 1 GeV, a regime where perturbation theory can reasonably converge.

Methodology and Key Contributions

The authors utilize a methodical approach, building upon the seminal work of Freedman, McLerran, and Baluni by calculating the QCD pressure to ${\mathcal O}(\alpha_s^2)$. This order captures important interactions beyond the leading-order contributions, providing better insights into the EoS for cold quark matter.

1. Running Coupling and Strange Quark Mass: The research incorporates a running coupling constant and a realistic treatment of the strange quark mass. The authors acknowledge the limitations of perturbation theory near the masses of strange quarks and incorporate non-perturbative effects, extending traditional models by suggesting a refined bag model approach with a perturbative EoS.
2. Peturbative Expansion: The paper meticulously separates contributions to the grand potential, considering massless quark contributions, massive quark loop corrections, and complex vacuum-matter effects comprehensively.
3. Hybrid Star Predictions: The implications of the perturbative calculations suggest that compact star masses, including quark matter in their cores, can reach values consistent with current astronomical observations. Specifically, the maximal mass for hybrid stars with a quark matter core can reach up to $2M_\odot$ and potentially higher for pure strange stars at $M\sim2.75M_\odot$.
4. Stability of Strange Quark Matter: Interestingly, the researchers suggest that if future observations confirm compact stars with $M>2M_\odot$, it would strongly support the existence of stable strange quark matter. This conclusion challenges more classical models based on the MIT bag model and invites re-thinking of the phase structure of dense nuclear matter.

Implications and Future Directions

This work has numerous implications both in theoretical and astrophysical research domains. It offers a more intricate view of the quark matter EoS that could significantly impact the paper of neutron stars and compact star cores. The inclusion of running coupling and massive quark corrections creates a more physically realizable model of denser phases of hadronic matter.

1. Transition Dynamics and Stability Analysis: The results contribute to a deeper understanding of the deconfinement transition and the potential stability of different phases of dense matter. They provide a framework to assess QCD phase transitions in neutron star interiors and could potentially guide the development of future quantum field and string-theoretical models of high-energy matter.
2. Toward Higher-Order Corrections: Given the current renormalization scale uncertainties, future work could focus on higher-order corrections to further refine the calculation, addressing the remaining challenges observed at lower chemical potential regimes.
3. Link with Lattice QCD: Although finite-density lattice QCD remains significantly challenging due to the sign problem, comparisons or attempts to link perturbative results with lattice calculations in overlapping domains could validate and enhance predictive models of quark matter EoS.

In conclusion, this paper adds substantial depth to the field by offering a refined perturbative framework for understanding cold quark matter, informing both theoretical investigations and observational astrophysics.