Variable Energy Cyclotron Centre

1. Differential elliptic flow (v2(pT)) & number of constituent quark (NCQ) scaling at FAIR ParthaPratimBhaduri SubhasisChattopadhyay Variable Energy Cyclotron Centre Kolkata Submitted to Physical Review C

2. Introduction • Statistical QCD predicts that at high temperature and/or density, hadronic matter undergoes a phase transition to a new state , where strongly interacting matter shows partonic behavior. • In the laboratory, the only way to produce such a novel state of matter is to collide two heavy nuclei at relativistic energies. • Over past two decades, relativistic heavy-ion collision experiments are performed around the world with the ultimate aim to map the QCD phase diagram & to discover the new state of QCD matter the Quark Gluon Plasma (QGP). • The Compressed Baryonic Matter (CBM) experiment at FAIR is aiming at the exploration of the QCD phase diagram at high net baryon densities and moderate temperatures. Heavy-ions will be collided in the beam energy range between 10 – 40AGeV. • Main challenge is to predict unambiguous & experimentally viable probes to indicate the formation of dense partonic medium. • Collective flow of the produced particles in the transverse plane of the collision has been long predicted as a signature of the creation of a hot & dense medium in nuclear collisions. • Of particular interest is the elliptic flow parameter (v2) ; signals a strong evidence for the creation of a hot & dense system at a very early stage in the non-central collisions

3. Elliptic flow v2 Coordinate-Space Anisotropy Momentum-Space Anisotropy

4. Spatial asymmetry INPUT Initial spatial anisotropy Final momentum anisotropy High pressure OUTPUT Low pressure Momentum asymmetry

6. Motivation of our work: 1. To study the differential elliptic flow of identified hadrons in the FAIR energy regime. 2. To test the NCQ scaling of v2 of identified hadrons . • Models used for the study : • UrQMD (hadronic string transport model) • AMPT - string melting (partonic transport model) • AMPT- default (hadronic-string transport model) System : Au + Au Energy : EL = 25 AGeV & 40 AGeV Impact parameter : b = 5-9 fm.

7. Differential elliptic flow at top (40 AGeV)& intermediate (25 AGeV) FAIR energies Hydrodynamic mass ordering at low pT Baryon-Meson crossing at high pT

8. Elliptic Flow : comparison of different models Partonic scatterings enhances the flow

9. Comparison with existing data (NA49) AMPT with string-melting slightly over estimates the flow UrQMD & default AMPT under estimates the flow at high pT Large error bar in the data !! No conclusive picture

10. Constituent Quark Number Scaling No NCQ scaling in pT over the investigated pT range Ruling out of recombination picture ?

11. Transverse Kinetic Energy (KET = mT – m0) scaling Reasonable scaling behavior by UrQMD (hadronic) & AMPT with string melting (partonic) Validity of hydrodynamic mass scaling at FAIR

12. Observations • Observations are quite in-line with the elliptic flow measurements at RHIC. • At FAIR, v2 is an increasing function of pT. • Both the hadronic (UrQMD) and the partonic model (AMPT) shows mass ordering of v2(pT) compatible with hydrodynamic expansion of thermalized fluid. • Partonic scattering enhances the flow. • No, reasonable NCQ scaling is found in terms of transverse momentum pT , over the investigated pT range

13. Observations • However a remarkable scaling behavior is indeed found with respect to KET by both UrQMD & string melting version of AMPT. • This can be attributed to hydrodynamic mass scaling • The degree of scaling seems to be better for UrQMD than AMPT. • Observation of NCQ scaling w.r.t KET by both hadronic & partonic model makes this observable rather insensitive to indicate the formation of partonic matter at FAIR. • If at all, a universal scaling behavior of elliptic flow is observed at RHIC, whether it should be interpreted as a signature of color de-confinement is still a debated issue. • Relative values of v2 might serve as a better observable.

14. Thank you