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Mass and running effects in the pressure for cold and dense matter

Mass and running effects in the pressure for cold and dense matter. Letícia F. Palhares Eduardo S. Fraga. Outline. Quark mass and RG corrections in in-medium QCD The Linear Sigma Model (LSM) at finite density Renormalization of the LSM at finite density Properties of the RG running

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Mass and running effects in the pressure for cold and dense matter

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  1. Mass and running effects in the pressure for cold and dense matter Letícia F. Palhares Eduardo S. Fraga

  2. Outline • Quark mass and RG corrections in in-medium QCD • The Linear Sigma Model (LSM) at finite density • Renormalization of the LSM at finite density • Properties of the RG running • Conclusions and perspectives 2nd Rio-Saclay: QCD under extreme conditions

  3. Phase diagram of QCD with massive quarks • Finite quark masses can bring qualitative and quantitative modifications of the phase diagram: • Expected behavior of the critical point with quark mass • [Stephanov (2006)] 2nd Rio-Saclay: QCD under extreme conditions

  4. Lattice calculations including massive quarks show sensible corrections in the chiral condensate [Bernard et al – MILC collab. (2003)] Within effective models quark mass effects are also relevant for the chiral transition: [Dumitru, Röder & Ruppert (2004)] What about the axis? ? 2nd Rio-Saclay: QCD under extreme conditions

  5. In-medium QCD with massive quarks • Inperturbative QCD: • 2-loop pressure in QCD at finite mu: Quark mass and RG corrections up to ~25% [Fraga & Romatschke (2005)] • Consequences on the nature and intensity of the chiral transition • astrophysical implications: new class of stars for a strongly 1st order chiral transition. [Fraga, Pisarski & Schaffner-Bielich (2001/2002)] • Complementary study: Low energy effective models at finite density (e.g. Linear Sigma Model) 2nd Rio-Saclay: QCD under extreme conditions

  6. Explicit SB The Linear Sigma Model at finite density Quark-meson coupling: Yukawa type • QCD: approximate chiral symmetry • Spontaneous Symmetry Breaking: • Parameters are fixed to reproduce measured vacuum properties • Renormalizable However: Truncation of the perturbative series introduces a renormalization scale [even for mean-field!] . implementation of RG running 2nd Rio-Saclay: QCD under extreme conditions

  7. Beyond mean-field for ( resummation needed! ): . • ZPT + 2-loop + MSC Resummation [Caldas, Mota & Nemes (2001)] • CJT + Hartree approx. [Röder, Ruppert & Rischke (2003)] • ZPT+ Averaged sigma fluctuations [Mócsy, Mishustin & Ellis (2004)] • ... • Mean-field calculation of the effective potential at finite T and (no loops, no RG running, zero point (ZPT) logs neglected) • Previous results in the LSM: [Scavenius et al (2001)] 2nd Rio-Saclay: QCD under extreme conditions

  8. Effects on the position of • Consequences on the nature of the chiral PT  astro implications • Proposal: Beyond mean-field at finite density and zero T (no resummation needed) • Study the sigma direction • Other condensates don’t affect much the chiral one • [Röder, Ruppert & Rischke (2003)] • ZPT and renormalization in the scheme • Implementation of RG running 2nd Rio-Saclay: QCD under extreme conditions

  9. Mean-field Exchange contribution with both fields massive:  more involved than QCD Effective Potential • Using a standard procedure [Jackiw], one obtains the loop expansion for the effective potential, neglecting terms of : 2nd Rio-Saclay: QCD under extreme conditions

  10. Results Zero-PoinT terms Vacuum (ZPT) • Exchange where… • Free Terms (quarks [Mean-field] and sigma) 2nd Rio-Saclay: QCD under extreme conditions

  11. exact analytical results (for all values of parameters: ): allows full implementation of RG running 2nd Rio-Saclay: QCD under extreme conditions

  12. Renormalized results ( scheme) R R R • Free Terms (quarks [Mean-field] and sigma) R R 2nd Rio-Saclay: QCD under extreme conditions

  13. Renormalized results ( scheme) R R R R R Vacuum • Exchange 2nd Rio-Saclay: QCD under extreme conditions

  14. RG running & NF (Yukawa coupling) • : mass scale • larger NF more perturbative • m0 = 0.1 (chosen) • large NF flattens running 2nd Rio-Saclay: QCD under extreme conditions

  15. Conclusion and Perspectives • Finite mass effects do play an important role in the phase structure of QCD • We have computed the exchange correction in the LSM at finite mu for arbitrary masses (up to finite barMS corrections) • Next steps: • , , nature of the chiral PT... • Corrections to and • Implementation of RG running • On the lattice, calculations with realistic quark masses and finite mu (also for effective theories!) [Hands, (2007)] are under way  comparison possible 2nd Rio-Saclay: QCD under extreme conditions

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