Rho mesons in strongly interacting matter

1. Rho mesons in strongly interacting matter Sabyasachi Ghosh (S.R.F.) V.E.C.C.

2. Outline of talk • Motivation • Field theoretical framework • Results of ρ propagation • Effect on dilepton spectra • summary

3. Hadronic particle zoo Strongly interacting matter nucleus nucleus

4. Motivation Propagation of ρ mesons through a medium is strongly affected by interaction significant modification in spectral properties . Because of this ρ meson plays the most significant role in the theoretical analysis of low mass dilepton spectra obtained in heavy ion collision .[e.g CERES,NA60] The issue of mass reduction / width enhancement of the ρ (modification of pion cloud ,scattering etc.) studied using various approaches is still a matter of debate. Here we have carried out a unified description of different physical processes occurring in the medium using the framework of thermal field theory with interactions from Chiral perturbation theory which is the low energy effective theory of QCD.

5. Perturbative form of interacting propagator + = + + ……………∞ Propagation Unstable particle In vacuum Propagation of unstable particle In thermal medium Quantum field theory in vacuum or at T=0 Thermal field theory or QFT at T ≠ 0 At q=M (physical mass of unstable particle) theoretically calculated quantity self energy ( ∑ ) relates with experimentally observed quantity decay width ( Γ ) Example:- for Chanel ,

6. Analytic structure of self energy function : S.G. ,S.Sarkar and S.Mallik Eur.Phys.J.C. [in press] arxiv:0911.3504 (nucl.th) D(k) (q) (q) D(q - k)

7. Branch Cut structure of ∑ in vacuum : We take Im [ ] = q [ ] H H The branch cut region of ‘∑’ give the region where ‘Im∑’ has nonzero value o Unitary cut

8. Branch Cut structure of ∑ in medium : [1st term] Im [ ] = q [{ } - { } ] H H H o Unitary cut

9. [ 2nd term ] H Im [ ] = q [ { } - { } ] H H o Landau cut Unitary cut

10. Tensor structure experimentally observed scalar quantity Interpretation of the quantity ‘Γ’ in medium : Rate at which the unstable particle (here ρ) equilibrates through all possible forward and inverse decay as well as scattering processes

11. Lagrangian coming from Chiral Perturbation theory :

12. Result :

13. Imaginary and Real part of self energy for various loops :

14. Spectral function of ρ in hot hadronic matter T [GeV] M [GeV]

15. Application of ρ-spectral function in dilepton spectra: Hadronic tensor (~current-current Correlation function) Field current identity Spectral function of neutral vector mesons (in general neutral vector boson)

16. Low mass enhancement in static rate of dilepton:

17. Space time evolution : S.G , S.Sarkar and J. Alam arXiv:1009.1260 [nucl-th]

21. Summary and conclusion: We have calculated ρ spectral function in medium with the help of thermal field theory in real time formulism, which give a unifying description of propagation of particle through thermalized medium. Landau cut and unitary contribution both are coming from the calculation . So anyone of them should not be ignored , as done in literature Using the spectral function of ρ we have construct dilepton spectra in low invariant mass-space which shows a reasonable low mass enhancement due Landau cut contribution of higher masses loops

22. Thank you

24. Real part of self energy

25. Rate from QGP (qqbar results for massless quarks) :