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Gluon Condensate in Dense Quark Matter

Gluon Condensate in Dense Quark Matter. Yin Jiang (Tsinghua University) In collaboration with Lianyi He(Tsinghua University) Pengfei Zhuang(Tsinghua University). Outline. 1. Motivation. 2. Scale symmetry and Gluon condensate 3. Numerical results in Nambu-Jona-Lasinio model. 4. Summary.

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Gluon Condensate in Dense Quark Matter

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  1. Gluon Condensate in Dense Quark Matter Yin Jiang (Tsinghua University) In collaboration with Lianyi He(Tsinghua University) Pengfei Zhuang(Tsinghua University)

  2. Outline 1.Motivation. 2.Scale symmetry and Gluon condensate 3. Numerical results in Nambu-Jona-Lasinio model. 4.Summary

  3. Motivation • Gluon condensate indicates QCD non- perturbative properties. • Unlike quark condensates, gluon condensate can not be calculated directly via low energy effective models . • Gluon condensate can be evaluated through thermodynamics in strongly coupled baryon and isospin matter.

  4. Gluon condensate and scale symmetry • Gauge field action is • Trace anomaly relation is expressed as Scale symmetry preserved Obviously scale symmetry broken Noether theorem Derivation of the Noether current of scale transformation From obviously scale symmetry broken (Classical ) From running coupling constant (Quantum Effect)

  5. Gluon condensate and thermodynamics • The trace of equals to that of energy- momentum tensor • For QCD, the gauge field part is gluon condensate Energy density Pressure Gluon condensate Quark condensate

  6. Gluon condensate and thermodynamics Gluon condensate can be calculated through thermodynamics in effective models. He Jiang and Zhuang Phys. Rev. C 79, 045205 (2009) Max A. Metlitski and Ariel R. Zhitnitsky got the similar result in Physics Letters B 633 (2006) 721–728. NJL Why? LHY

  7. Gluon condensate in dense quark matter Calculating gluon condensate in strong coupled isospin matter by Mean field NJL model (a good model for condensed matter) “ Trace anomaly” relation At mean field level there is no anomaly term in the effective model. Obviously broken scale symmetry

  8. Gluon condensate in dense quark matter • Taking thermodynamics in NJL model The scale symmetry is spontaneously broken by quark condensates . A reliable model Chiral condensate Pion condensate

  9. Results in NJL model • Chiral restoration at finite temperature • Gluon and chiral condensate behave qualitatively the same.

  10. Results in NJL model • Pion superfluidity Gluon condensate controlled by competition of chiral and pion condensate.

  11. Results in NJL model • Color supercondctivity Gluon condensate controlled by competition of chiral and diquark condensate.

  12. Comparison with PQCD • Extension of PQCD calculation at extremely high density

  13. Summary • We calculated gluon condensate in dense quark matter through thermodynamics of the system. • Gluon condensate’s behavior is controlled by competition of quark condensates at finite density. • Scale symmetry is spontaneously broken in condensed matter. • This work has been extended to including quantum fluctuations.

  14. Thank you！

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