Electromagnetic Probes

Different processes: different characteristic spectra

A jet passing through QGP

Penetrating probes are emitted at all stages then survive unscathed (e <<s). “Historians” of the heavy ion collision: encode all sub-processes at all times

Photons are result of convolutions of the emissions from the entire history of the nuclear collision, so we need rates & a model for evolution.

• Hydrodynamics.• Cascades.• Fire-balls.• Cascade+Hydro.

E

Rate

Hadron Gas Thermal Tf

QGP Thermal Ti

“Pre-Equilibrium”?

Jet Re-interaction √(Tix√s)

pQCD Prompt x√s

“New”

Upper Limit of Single Photons, WA80

Ruled out hadronic gas with limited hadrons: Srivastava and Sinha, PRL 73 (1994) 2421;

Dumitru et al., PRC 51 (1995) 2166.

Sollfrank et al., Lee & Brown, Arbex et al., .

Cleymans, Redlich, & Srivastava, PRC 55 (1997) 1431.However, nhad >> 2-3 /fm3 ! For No Phase Transition.

Pb+Pb@SPS

Srivastava & Sinha, PRC 64, 034902 (2001).

Alam et al., PRC 63, 021901 (2001)Huovinen et al., PLB 535, 109 (2002).Turbide et al., PRC 69, 014903 (2004).

Prompt photons using NLO pQCD and comparison with experimental data

Iso-spin corrected prompt photons at different collider energies as function of xT.

Iso-spin as well as shadowingcorrected prompt photons at different energies.

Shadowing and iso-spin corrected prompt photons using NLO pQCD at sNN = 17.3 GeV, which corr-esponds to the nucleon nucleon centre of mass energy for the WA98 experiment.

),,(),,(),(

yxdxdyyxyxdxdyf

f

Flow patterns

T

Teff

vvT

11

Effective temperature :

Results differ marginally

beyond 1 fm/c.

Central collision. from 0.2 to 1.0 fm/c.

Time evolution of temperature

Energy density

Radial flow velocityTime evolution of average effective temperature

Total entropy & net baryon fixed for all 0.

Sources: Electromagnetic radiation from QCD

First approaches:

McLerran, Toimela (1986); Kajantie, Kapusta, McLerran, Mekjian (1986)Baier, Pire, Schiff (1988); Altherr, Ruuskanen (1992)

Rates diverge: 2~ ln( / 0)s T q

HTLresummation

Going to two loops: Aurenche, Kobes, Gelis, Petitgirard (1996)

Aurenche, Gelis, Kobes, Zaraket (1998)

Co-linear singularities:2

22

~s sth

T

m

AMY, Arnold, Moore, and Yaffe, JHEP 12, 009 (2001); JHEP 11, 057 (2001): incorporates LPM; photon rates complete to leading order in αs

Can be expressed in terms of the solution to a linear integral equation

Hadrons from the confined sector: a similar treatment

Single

photon,

Pb+Pb@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 ?)

0 (fm) K

0.2 2.7

0.4 4.8

0.6 5.4

0.8 5.7

1.0 5.9

0 = 1.0 fm/c0 = 0.2 fm/c

0 = 0.8 fm/c0 = 0.6 fm/c0 = 0.4 fm/c

Spectra and elliptic flow parameter v2 for pions from Pb+Pb collisions having b = 7 fm @ CERN SPS for different initial times keeping entropy fixed.

spectra are flatter for smaller 0. For pT 1 GeV, spectra are indifferent to change in 0.

Elliptic flow of is insensitive to the initial thermalization time. similar results are observed for other hadrons.

Thermal photon

v2 for different 0.

Results for

photons from

hadronic matter

are also given.

v2 for single

photons. Results for pT

< 2.15 GeV

are obtained by

arbitrarily using the

normalizing factor

at pT = 2.15 GeV.

pT dependent elliptic flow at different 0

Summary & conclusions Single photon data from relativistic collisions of Pb

nuclei @ CERN SPS (measured by WA98) have been re-analyzed.

Iso-spin and shadowing corrected NLO pQCD treatment is used for prompt photon production along with an optimized scale for factorization, renormalization, and fragmentation.

For thermal part centrality dependent hydrodynamic model with a well tested EOS has been used considering a set of initial thermalization times.

The data can be explained well at different 0 using varying multiplicative factors for prompt photons.

Photon v2 is sensitive to initial thermalization time and can be used to estimate the value of 0.

Thank you