1. Effect of thermal fluctuation of baryons on vector mesons and low mass dileptons ρ ω Sanyasachi Ghosh (VECC, Kolkata, India)

2. Mass term  0 remain invariant under global symmetry & associated conserved Noether currents Parity doublet Vector current Axial vector current Real world Spontaneous Breaking of Chiral Symmetry (SBCS) Spontaneous Breaking of Chiral Symmetry (SBCS)

3. Broken Chiral SymmetryRestored Chiral Symmetry Vacuum Strongly interacting matter The spectral properties of vector mesons and axial Vector mesons in strongly-interacting matter may indicate about Chiral Symmetry Restoration (CSR). The spectral properties of vector mesons and axial Vector mesons in strongly-interacting matter may indicate about Chiral Symmetry Restoration (CSR). Spectral function of ρ and a_1 are measured via hadronic decays of τ lepton at LEP by ALEPH and OPAL experimental data from heavy ion collision seems to prefer melting scenario experimental data from heavy ion collision seems to prefer melting scenario Rapp et.al. arXiv:0901.3289

4. Vector mesons are very special to study its in-medium property. Because they are directly couple with electromagnetic (e.m.) channels. Low mass enhancement due to in-medium modification of light vector mesons (specially ρ ). Low mass enhancement due to in-medium modification of light vector mesons (specially ρ ). Being motivated by this in-medium signature, we have evaluated spectral functions of light Vector mesons (ρ and ω) in hot and dense hadronic matter using Real-time formalism of Thermal Field theory (RTF).

5. Fourier transform Probabilistic amplitude of Unstable particle time space (t) energy space 5 QFT definition of spectral function Propagator

6. = + + + ……………∞ =+ + + ………….( an infinite g.p. series ) = = where  is called self energy term Vacuum interacting propagator Vacuum free propagator  Im = m

7. Mass shift Spectral function = Im [propagator]

8. -∞-∞+∞+∞ t-axis - i b 0 -∞ (+∞,-i b /2) +∞ t -plane Time evolution operator ~ density matrix Essence of RTF Field Theory of vacuum Field Theory at finite temperature thermal propagator Thermal self-energy Diagonalization Thermal averagedVacuum expectation

9. Self Energy of ρ for mesonic loops : (k) (q) (p=q – k) Landau cutsUnitary cuts

10. ρ pp ρ Mesonic collision rate ρ ρ k k p p Bose enhancement of decay rate

11. + o Unitary cut Self Energy of ρ for baryonic loops : ρ ρ Pauli blocking of decay rate Landau cut ρ ρ Baryonic collision rate

12. 12 o Unitary cutLandau cut N*(1520) N*(1650) N*(1720)

13. ---------------------------- vacuum part of loop (unitary cut ) ------------------------- thermal part of loops (unitary cut) ---------------------------- loops (Landau cut ) ---------------------------- loops (Landau cut)

14. Effect of baryonic chemical potential on ρ spectral function in low mass region:

15. Effect of temperature on ρ spectral function in low mass region:

16. Effect of momentum of ρ in off mass shell on its spectral function in low mass region:

17. S. Sarkar & S. Ghosh arXiv:1204.0893 S. Sarkar & S. Ghosh arXiv:1204.0893

18. ρ meson spectral function ω meson spectral function S. Ghosh and S. Sarkar arXiv:1207.2251 [nucl-th] S. Ghosh and S. Sarkar arXiv:1207.2251 [nucl-th]

19. Strong interacting current Leptonic current Final phase spaceThermal average Dilepton multiplicity Formalism of dilepton :

20. HM QM 2

21. Contribution of ω is down by a factor ~ 10

22. Effect of mesonic as well as baryonic medium modification of ρ on dilepton rate in low mass region :

23. 23 Dilepton production in invariant mass after Space time evolution : Invariant mass spectra Fluid element

24. Low mass enhancement at SPS : S. Sarkar & S. Ghosh arXiv:1204.0893 S. Sarkar & S. Ghosh arXiv:1204.0893 Meson (S.Ghosh, S.Mallik. S.Sarkar Eur. Phys. C 70, (2010) 251) + Bayon (S.Ghosh, S.Sarkar Nucl. Phys. A 870, (2011) 94) -loop self-energies Meson loop self-energies (S.Ghosh, S.Mallik. S.Sarkar Eur. Phys. C 70, (2010) 251) + Baryon part from Eltesky et. al. (Phys. Rev. C 64, (2001) 035202)

25. S. Sarkar & S. Ghosh arXiv:1204.0893 S. Sarkar & S. Ghosh arXiv:1204.0893

26. Analytic structure of ρ meson propagator at finite temperature Eur. Phys. J. C 70, 251 (2010). S.Ghosh, Sourav Sarkar, (VECC), S. Mallik, (SINP) ρ self-energy at finite temperature and density in the real-time formalism Nucl. Phys. A 870, 94 (2011) S. Ghosh, Sourav Sarkar, (VECC) Observing many-body effects on lepton pair production from low mass enhancement and flow at RHIC and LHC energies Eur. Phys. J. C 71, 1760 (2011). S. Ghosh, Sourav Sarkar, Jan-e Alam, (VECC) The $\rho$ meson in hot hadron matter and low mass dilepton spectra. Nucl. Phys. A 862, 294 (2011) S. Ghosh, Sourav Sarkar, Jan-e Alam, (VECC) In-medium vector mesons and low mass lepton pairs from heavy ion Collisions arXiv:1204.0893 [nucl-th] Sourav Sarkar, S. GhoshSourav Sarkar Elliptic flow of thermal dileptons as a probe of QCD matter Phys.Rev. C (R) 85 (2012) 031903 Payal MohantyPayal Mohanty, Victor Roy, S. Ghosh, Santosh K. Das, Bedangadas Mohanty, Victor Roy Santosh K. Das Bedangadas Mohanty Sourav SarkarSourav Sarkar, Jane Alam, Asis K. Chaudhuri, (VECC) Jane Alam Asis K. Chaudhuri Analytic structure of ρ meson propagator at finite temperature Eur. Phys. J. C 70, 251 (2010). S.Ghosh, Sourav Sarkar, (VECC), S. Mallik, (SINP) ρ self-energy at finite temperature and density in the real-time formalism Nucl. Phys. A 870, 94 (2011) S. Ghosh, Sourav Sarkar, (VECC) Observing many-body effects on lepton pair production from low mass enhancement and flow at RHIC and LHC energies Eur. Phys. J. C 71, 1760 (2011). S. Ghosh, Sourav Sarkar, Jan-e Alam, (VECC) The $\rho$ meson in hot hadron matter and low mass dilepton spectra. Nucl. Phys. A 862, 294 (2011) S. Ghosh, Sourav Sarkar, Jan-e Alam, (VECC) In-medium vector mesons and low mass lepton pairs from heavy ion Collisions arXiv:1204.0893 [nucl-th] Sourav Sarkar, S. GhoshSourav Sarkar Elliptic flow of thermal dileptons as a probe of QCD matter Phys.Rev. C (R) 85 (2012) 031903 Payal MohantyPayal Mohanty, Victor Roy, S. Ghosh, Santosh K. Das, Bedangadas Mohanty, Victor Roy Santosh K. Das Bedangadas Mohanty Sourav SarkarSourav Sarkar, Jane Alam, Asis K. Chaudhuri, (VECC) Jane Alam Asis K. Chaudhuri Theoretical work on dilepton by VECC group (India)

27. Understanding low mass enhancement of SPS data in the language of Thermal Field Theory : Mesonic collision rate Baryonic collision rate Bose enhancement of decay rate Vacuum decay rate + + + Hdronic Matter Quark Matter Total +

28. (with Feynman boundary condition) (with K.M.S. boundary condition) Temporal Fourier transform spatial Fourier transform Free scalar propagator in vacuum satisfies Free scalar propagator in medium satisfies

29. Extra slides

30. Real part of self-energy Baryonic loops Mesonic loops