Elliptic flow. p y. Non-central collision of spherical nuclei or central collision of deformed nuclei. Overlapping zone is of almond shape

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3 Non-central collision of spherical nuclei or central collision of deformed nuclei Overlapping zone is of almond shape Co ordinate space anisotropy is converted into momentum space anisotropy via the action of azimuthally asymmetric pressure gradient. Elliptic flow It is sensitive to the early phase and does not depend on the freeze out dynamics of the system. Coordinate space y Momentum space p y ` x Elliptic Flow: self quenching P. Kolb & U. Heinz, in Quark Gluon Plasma, nucl-th/ The driving force of elliptic flow dominates at early times. Elliptic flow acts against its own cause, it shuts itself off after some time as pressure gradient vanishes.

4 At mid rapidity (y=0) and for collision of same type of nuclei, p T dn(b) dp dy df T dn(b) 2p p dp T T [1 dy + 2v 2 p,b cos(2f ) + 2v p,b cos(4f) +... ] T 4 T Systems evolution is mirror symmetric with respect to the reaction plane. Thus observable under investigation respect the symmetry f(f)=f(-f), no sin term in the above equation. Also, f(f)=f(p+f) only even terms (v 2,v 4,....) survive in the above series. v 2 (p T,b) = d cos(2 ) d dn(b) p T dp T dyd dn(b) p T dp T dyd

5 Direct photons e -p t/t t d 3 N/dyd 2 p T Jet-matter qgp phase hadronic phase 1/p t n pre-equilibrium phase mixed phase z ~3 GeV ~5 GeV p t Mean free path of photons is larger than system size. Once produced, photons leave the system without any re-scattering. As a result photons carry undistorted information from the production point to the detector. Prompt photons: emitted from the initial state of the collision. Jet-matter interaction: test matter density. Thermal photons: temperature and equation of state of the hot and dense matter.

6 Experimental challenges Inclusive photon spectrum contains a huge background. More than 90% of the produced photons are from 2-g decay of p 0 and h mesons. from p o from from h from h Need to subtract the huge background in order to get direct photons. Different techniques are there (such as mixed event analysis) to subtract decay contribution from inclusive photon spectrum. Direct photon measurement by the subtraction method: WA98 PRL 85 (2000) 3595, PHENIX PRL 94 (2005)

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8 The thermal photon emission from the QGP and the hadronic phases are obtained by integrating the rates of emission over the space time history of the fireball. E dng/d 3 p= [{ } exp (p m.u m /T )] d 4 x p m =( p T coshy, p x, p y, p T sinhy ) =>4-momentum of the photons u m =g T (cosh h, v x (x,y), v y (x,y), sinh h ) =>4 velocity of the flow field d 4 x=t dt dx dy dh =>4-volume element, Y= rapidity (=0 in mid rapidity) t= [t 2 - z 2 ] 1/2 =>proper time, h= tanh -1 (z/t) => space time rapidity g T =1/[1 - v T2 ] 1/2 => Lorentz factor, v T = [v x2 + v y2 ] 1/2 =>radial flow velocity and p T = [p x2 + p y2 ] 1/2 =>transverse momentum

9 Hydrodynamic description of v 2 PRL 91, 2003 (PHENIX) Hydrodynamics by Huovinen et al. Elliptic flow of identified particles and mass ordering is well described by ideal hydrodynamics.

10 Thermal photons from QGP & hadronic matter Relative contributions from different channels in the hadronic phase At small p T values, photons from hadronic matter dominate the spectrum. r p p g & p p r g are the dominant photon producing channels upto p T ~ 0.4 GeV. Above that p T range, p r p g becomes significant. Radiations from QGP phase outshine those from hadronic phase for p T beyond 1 GeV.

11 Elliptic flow of thermal photons as function of transverse momentum RC, E. Frodermann, U. Heinz, D. K. Srivastava. PRL 96, (2006) v 2 is not simple addition of v 2 (QM) and v 2 (HM). v2(qm)*dn(qm) + v (HM) *dn(hm) dn(qm) + dn(hm) 2 v2 Sum v 2 tracks v 2 (QM) at high p T, reflects anisotropies of the partonic phase at early times. Interesting structure at p T 0.4 GeV. v 2 (p) & v 2 r) are plotted to compare with v 2 (HM). v 2 (QM) is small at high p T and rises with smaller values of p T, peaks around GeV & then drops. v 2 (HM) rises monotonically with higher values of p T.

12 RC, E. Frodermann, U. Heinz, & D. Srivastava. PRL 96, (2006) v 2 (p T ) increases with rise in impact parameter b. With rise in b, relative contributions of QM & HM in the total v 2 changes. HM contribution increases compared to QM at larger b values. p T integrated v 2 (b) rises with b. For b 2R A, ( R A is the nuclear radius) v 2 (b) drops as system size itself becomes very small. RC, D. K. Srivastava, & U. Heinz; arxiv:

13 Time evolution of spectra and flow from Quark Matter & Hadronic Matter

14 Time evolution of spectra and elliptic flow at b=7 fm For p T > 2.0 GeV most of the photons are from QGP phase and within a time period of 4 fm. For very low p T, radiation from HM is significant. v 2 (t) as function of t from different phases are shown separately. v 2 (QM) saturates within a time period of 4-5 fm. v 2 (HM) continuously grows upto a larger time period.

15 direct photons v 2 from PHENIX 15

16 Photon v 2 from hydrodynamics and PHENIX data Plot shown by Kentaro Direct photon v 2, Turbide et al. Phys.Rev.C77:024909,2008

17 Elliptic flow of thermal photons considering ideal 3D hydrodynamic expansion of the matter. Fu-Ming Liu, Hirano, Werner, Zhu. Phys.Rev.C80:034905,2009.

18 Results for p & r mesons for 200A GeV Au+Au collisions at impact parameter b = 6 fm. t 0 is changed from 0.2 to 1.0 fm/c in steps of 0.2 fm/c keeping total entropy fixed. p and r spectra as a function of p T do not change significantly with changing t 0. Similar results are obtained for other hadrons. RC & D. K. Srivastava, PRC 79, (R) (2009).

19 Elliptic flow parameter as a function of p T is almost independent of the value of t 0 for hadrons. Early start of flow drives the freezeout to happen earlier. As hadrons are emitted only from the surface of freezeout, their flow is not affected much with changing t 0. Any conclusion about t 0 from v 2 of hadrons is difficult. RC & D. K. Srivastava, PRC 79, (R) (2009).

20 Effect of changing the freeze-out energy density on spectra and v 2 p T distribution and v 2 (p T ) for p and r mesons at energy densities of & GeV/fm 3, which correspond to freeze-out temperatures of about 100 and 140 MeV respectively. The p T distributions continue to evolve as the system cools from 140 to 100 MeV, owing to the radial flow. The elliptic flow is seen to have essentially acquired its final value when the temperature is still large.

21 Photons from HM are affected only marginally at low p T with changing t 0. QM contribution increases significantly with smaller values of t 0 and at high p T. PHENIX data along with results from NLO pqcd calculation and ideal hydrodynamics are shown.

22 v 2 for thermal photons reveals a large sensitivity to the initial time t 0 for p T greater than about 1.5 GeV/c. With smaller t 0 QM contribution increases, however v 2 (QM) decreases. v 2 (HM) increases with smaller t 0 and the overall v 2 decreases. RC & D. K. Srivastava, PRC 79, (R) (2009).

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24 Direct photon production in 158 A GeV Pb+Pb collisions at CERN SPS First observation of single photons in relativistic heavy ion collisions by WA98. Important milestone in our search for the quark-hadron phase transition. Photon invariant yield or upper limit as a function of p T in the interval 0.5 < p T < 4.0 GeV/c presented. Srivastava & Sinha, PRC 64, (2001). M. M. Aggarwal et al., WA98 Collaboration, PRL 85, 3595 (2000). Alam et al., PRC 63, (2001) Huovinen et al., PLB 535, 109 (2002). Turbide et al., PRC 69, (2004).

25 Prompt photons using NLO pqcd and comparison with experimental data Effect of parton shadowing and iso-spin on prompt photon production Shadowing and iso-spin corrected prompt photons using NLO pqcd at s NN = 17.3 GeV, which corresponds to the nucleon nucleon centre of mass energy for the WA98 experiment.

26 Central collision. t from 0.2 to 1.0 fm/c. Flow patterns Results differ marginally beyond 1 fm/c. Time evolution of temperature Total entropy & net baryon fixed for all t 0. Energy density Time evolution of average effective temperature Radial flow velocity dx dy f ( x, y) ( x, y, t ) f dx dy ( x, y, t ) Effective temperature : T eff T v v T T

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28 t 0 = 0.2 fm/c t 0 = 1.0 fm/c Single photon, SPS 0-10% most central. WA98 Centrality dependent Hydrodynamics with well tested EOS. Quantitative explanation of the data by multiplying prompt yield with a K factor (Cronin effect?) t 0 (fm) K

29 t 0 = 0.4 fm/c t 0 = 0.6 fm/c t 0 = 0.8 fm/c

30 Spectra & elliptic flow for pions at different t 0. Spectra and elliptic flow parameter v 2 for pions from Pb+Pb collisions having b = 7 CERN SPS for different initial times keeping entropy fixed. p spectra are flatter for smaller t 0. For p T 1 GeV, spectra are indifferent to change in t 0. Elliptic flow of p is insensitive to the initial thermalization time. similar results are observed for other hadrons.

31 p T dependent elliptic flow at different t 0 Thermal photon v 2 for different t 0. Results for photons from hadronic matter are also given. v 2 for single photons. Results for p T < 2.15 GeV are obtained by arbitrarily using the normalizing factor at p T = 2.15 GeV.

32 Enhanced production of direct photons in Au+Au collisions at sqrt(s_nn)=200 GeV and implications for the initial temperature. PHENIX Collaboration Phys.Rev.Lett.104:132301,2010. e-print: arxiv: [nucl-ex]

33 20-40 % 0-20 %

34 Elliptic flow of electromagnetic radiation has a great potential to explore the properties and early time dynamics of Quark Gluon Plasma. Photon flow at large p T reflects the anisotropies of the initial partonic phase. Temporal contours of elliptic flow and spectra show the gradual build up of flow and the relative contribution of quark matter and hadronic matter in the total flow with changing time. The spectra and v 2 for thermal photons are seen to be strongly affected by the formation time as the relative contribution from QM and HM changes. The differential elliptic flow for hadrons is seen to be only marginally affected by the variation in t 0. Photon v 2 can be used to estimate the value of t 0 with help of experimental result. Single photon data from relativistic collisions of Pb CERN SPS (measured by WA98) have been re-analyzed. The data can be explained well at different t 0 using varying k factors for prompt photons.

35 Collaborators Dinesh K. Srivastava Ulrich Heinz Evan Frodermann Sangyong Jeon

36 Thank you