steffen a. basslight from cascading partons #1 steffen a. bass duke university motivation the pcm:...

Steffen A. Bass Light from Cascading Partons #1

Steffen A. Bass

Duke University

• Motivation• The PCM: Fundamentals & Implementation• Photon production in the PCM• Medium Effects: Jet-Photon Conversion (FMS Photons)

Light from Cascading Partons in Relativistic Heavy-Ion

Collisions

Light from Cascading Partons in Relativistic Heavy-Ion

Collisions


A brief history of the PCM

A brief history of the PCM

• concept developed by Klaus Kinder-Geiger and Berndt Mueller in 1991 (Nucl.Phys.B369:600-654,1992 )

• original implementation VNI by KKG was not further maintained after his untimely death in the crash of Swissair 111

• newly revised and improved implementation VNI/BMS by SAB, B. Mueller and D.K. Srivastava

• various (simplified) implementations from other groups available as well: MPC, ZPC, gromit…


Basic Principles of the PCM

Basic Principles of the PCM

• degrees of freedom: quarks and gluons• classical trajectories in phase space (with relativistic kinematics)• initial state constructed from experimentally measured nucleon structure functions and elastic form factors• an interaction takes place if at the time of closest approach dmin of two partons

• system evolves through a sequence of binary (22) elastic and inelastic scatterings of partons and initial and final state radiations within a leading-logarithmic approximation (2N)• binary cross sections are calculated in leading order pQCD with either a momentum cut-off or Debye screening to regularize IR behavior • guiding scales: initialization scale Q0, pT cut-off p0 / Debye-mass μD

3 4

1 2 3 4

min,

ˆ; , , ,ˆ with

ˆtot

totp p

d s p p p pdt

dtd

Goal: provide a microscopic space-time description of relativistic heavy-ion collisions based on perturbative QCD


Initial State: Parton Momenta

Initial State: Parton Momenta

• virtualities are determined by:

• flavour and x are sampled from PDFs at an initial scale Q0 and low x cut-off xmin

• initial kt is sampled from a Gaussian of width Q0 in case of no initial state radiation

2 2 2 2

2N

i i i ix y z

i i i iME p p p

1with and i i N i iz z N zp x P E p


Parton-Parton Scattering Cross-Sections

Parton-Parton Scattering Cross-Sections

g g g g q q’ q q’

q g q gq qbar q’ qbar’

g g q qbar q g q γ

q q q q q qbar g γ

q qbar q qbar

q qbar γ γ

q qbar g g

2 2 2

93

2

tu su st

s t u

2 2

2

4

9

s u

t

2 2

2

4

9

t u

s

2

3qe u s

s u

28

9 q

u te

t u

42

3 q

u te

t u

2 2

2

4

9

s u s u

u s t

2 2

2

1 3

6 8

t u t u

u t s

2 2

2

32 8

27 3

t u t u

u t s

2 2 2 2 2

2 2

4 8

9 27

s u s t s

t u tu

2 2 2 2 2

2 2

4 8

9 27

s u u t u

t s st

• a common factor of παs2(Q2)/s2 etc.

• further decomposition according to color flow


Initial and final state radiation

Initial and final state radiation

space-like branchings:

time-like branchings:

max

max

,, , exp

2 ,

ts a a a

a aa a a at

a ae

t x f x tS x t t dt dz

x f tP z

x

Probability for a branching is given in terms of the Sudakov form factors:

max

max, , exp2

t

d dat

d d es P zt

T x t t dt dz

• Altarelli-Parisi splitting functions included: Pqqg , Pggg , Pgqqbar & Pqqγ


Parton Fusion (21) Processes

Parton Fusion (21) Processes

wor

k in

pro

gres

s• qg q*• gg g*

•in order to account for detailed balance and study equilibration, one needs to account for the reverse processes of parton splittings:

• explicit treatment of 32 processes (D. Molnar, C. Greiner)• glue fusion:


HadronizationHadronization

•requires modeling & parameters beyond the PCM pQCD framework•microscopic theory of hadronization needs yet to be established•phenomenological recombination + fragmentation approach may provide insight into hadronization dynamics•avoid hadronization by focusing on:

net-baryons direct photons


Testing the PCM Kernel: Collisions

Testing the PCM Kernel: Collisions

• in leading order pQCD, the hard cross section σQCD is given by:

min min

1 12 2 2 min 2

1 2 1 2,

ˆˆ( ) ( , ) ( , ) θ ( )

ˆij

QCD i j Ti j x x

ds dx dx dt f x Q f x Q Q p

dt

• number of hard collisions Nhard (b) is related to σQCD by:

2

23

3

( ) ( )

( ) ' ' ( ')

1 K ;

96

har QCDdN b A b

A b d b h b b h b

b b

• equivalence to PCM implies: keeping factorization scale Q2 = Q0

2 with αs evaluated at Q2

restricting PCM to eikonal mode


Testing the PCM Kernel: pt distribution

Testing the PCM Kernel: pt distribution

,2 21 2 1 22

,1 2

ˆ( , ) ( , ) 1 2 1

ˆ 2jet ij i j

i ji jt

d dx x f x Q f x Q

dp dy dy dt

• the minijet cross section is given by:

• equivalence to PCM implies:

keeping the factorization scale Q2 = Q0

2 with αs evaluated at Q2

restricting PCM to eikonal mode, without initial & final state radiation

• results shown are for b=0 fm


Parton Cascade in a Box

Parton Cascade in a Box

• run PCM in a box with periodic boundary conditions:

kinetic and chemical equilibration

relaxation times Equation of State

• box mode with 2-2 scattering:

proper thermal and chemical equilibrium obtained

chemical equilibration time ~2500 fm/c!!

T. Renk


Parton Rescattering: cut-off Dependence

Parton Rescattering: cut-off Dependence

• duration of perturbative (re)scattering phase: approx. 2-3 fm/c

• decrease in pt cut-off strongly enhances parton rescattering


Collision Rates & Numbers

Collision Rates & Numbers

•lifetime of interacting phase: ~ 3 fm/c•partonic multiplication due to the initial & final state radiation increases the collision rate by a factor of 4-10 are time-scales and collision rates sufficient for thermalization?

b=0 fm

# of collisions

lo full

q + q 70.6 274

q + qbar 1.3 38.52

q + g 428.32422.6

g + g 514.44025.6


SPS vs. RHIC: a study in contrast

SPS vs. RHIC: a study in contrast

SPS RHIC

cut-off ptmin (GeV) 0.7 1.0

# of hard collisions

255.03618.

0

# of fragmentations

17.02229.

0

av. Q2 (GeV2) 0.8 1.7

av. (GeV) 2.6 4.7•perturbative processes at SPS are negligible for overall reaction dynamics•sizable contribution at RHIC, factor 14 increase compared to SPS


Part #1: Photon Production in the PCM

•Light from cascading partons in relativistic heavy-ion collisions- S.A. Bass, B. Mueller and D.K. Srivastava, Phys. Rev. Lett. 90 (2003) 082301

•Intensity interferometry of direct photons in Au+Au collisions- S.A. Bass, B. Mueller and D.K. Srivastava, Phys. Rev. Lett. 93 (2004) 162301

•Dynamics of the LPM effect in Au+Au Collisions at 200 AGeV- T. Renk, S.A. Bass and D.K. Srivastava, Phys. Lett. B632 (2006) 632


Photon Production in the PCM

Photon Production in the PCM

relevant processes:•Compton: q g q γ

•annihilation: q qbar g γ

•bremsstrahlung: q* q γ

photon yield very sensitive to parton-parton rescattering


What can we learn from photons?

What can we learn from photons?

•photon yield directly proportional to the # of hard collisions photon yield scales with Npart

4/3

•primary-primary collision contribution to yield is < 10%•emission duration of pre-equilibrium phase: ~ 0.5 fm/c


Photons: pre-equilibrium vs. thermal

Photons: pre-equilibrium vs. thermal

• short emission time in the PCM, 90% of photons before 0.3 fm/c hydrodynamic calculation with τ0=0.3 fm/c allows for a smooth continuation of emission rate caveat: medium not equilibrated at τ0

pre-equilibrium contributions are easier identified at large pt:

•window of opportunity above pt=2 GeV

•at 1 GeV, need to take thermal contributions into account


• Correlation between two photons with momenta k1 and k2 is given by:

with S(x,k) the photon source function for a chaotic source

use Wigner function scheme (Hansa code by Sollfrank & Heinz)• emission vertices of a semiclassical transport are not valid Wigner fnct. need to smear out emission vertices xi by ħ/pi

results are given in terms of outward, sideward & longitudinal correlators

HBT Interferometry: formalism

HBT Interferometry: formalism

24

1 2 1 24 41 2

( , )1( , ) 1 with and ( ) / 2

2 ( , ) ( , )

ixqd x S x K eC q K q k k K k k

d x S x k d x S x k

1 2 1 1 2 2sinh sinh

/

/

long z z T T

out T T T

side T out T T

q k k k y k y

q q K K

q q q K K


Photons: HBT InterferometryPhotons: HBT Interferometry

•pt=2 GeV: pre-thermal photons dominate, small radii

•pt=1 GeV: superposition of pre- & thermal photons: increase in radii


Landau-Pomeranchuk-Migdal Suppression

Landau-Pomeranchuk-Migdal Suppression

a

b

cd

ef

kt

form 2 2 2 2

1

1a a

d e t a

z z E E

z q z q k q

• the radiated parton e is assigned a formation time:

• if the radiating parton d suffers a collision before τform has elapsed, then the radiation of parton e and its daughters does not take place• likewise for parton f with respect to e …

• the LPM effect accounts for the suppression of radiation due to coherence effects in multiple scattering


LPM: Reaction Dynamics

LPM: Reaction Dynamics

• high pt: harder slope, enhanced particle production

• low pt: suppression of particle production

gluon pt distribution


Photon Production: LPM & comparison to data

Photon Production: LPM & comparison to data

PCM without LPM:• overprediction of

photon yield

PCM with LPM:• photon yield for pt < 6

GeV strongly reduced

• strong pt dependence of LPM suppression

• decent agreement with data


Part #2:Photons via Jet-Plasma

Interactions

R.J. Fries, B. Mueller & D.K. Srivastava, PRL 90, 132301 (2003)R.J. Fries, B. Mueller & D.K. Srivastava, PRC 72, 041902 (2005)


Photon sourcesPhoton sources

• Hard direct photons

• EM bremsstrahlung

• Thermal photons from hot medium

• Jet-photon conversion

Turbide, Gale & Rapp, PRC 69 014903 (2004)


Jet-Plasma interactionsJet-Plasma

interactionsplasma mediates a jet-photon conversion: jet passing through the medium:

•large energy loss: jet quenching•electromagnetic radiation (real and virtual photons) from jet-medium interactions

•suppressed by αEM; negligible as a source of additional jet quenching

• can escape without rescatteringuse as probe of energy loss?

visible among other sources of electromagnetic signals?


QGP-Induced EM Radiation

QGP-Induced EM Radiation

• annihilation and Compton processes peak in forward and backward directions:

• one parton from hard scattering, one parton from the thermal medium; cutoff p,min > 1 GeV/c.

photon carries momentum of the hard parton Jet-Photon Conversion

u

t

t

u

dt

d~

t

s

s

t

dt

d~

q

q

pp

pp


Jet-Photon Conversion: RatesJet-Photon Conversion: Rates

• annihilation and compton rates:

• thermal medium:

4 23 2 2

42( ) ( ) ln

8 3s

q q

dN E TE d x f p f p T C

d p m

( )

4 3 61

23 ( )

16

2(2 )

( 4 )(

(

)[1 ( )] ( ) ( )2

)f

q

NA

q

Agq

EdNE

d xd p

s s md p

f p

f p f p s q qE E

( )

4 3 61

23 ( )

16

2(2 )

( )[1 ( )] ( ) ( )2

( )f

q

NC

q

Cg q

EdNE

d xd p

s md

f

p f p f p s q qE E

p


FMS Results: Comparison to Data

FMS Results: Comparison to Data

calibrate pQCD calculation of direct and Bremsstrahlung photons via p+p data:

for pt<6 GeV, FMS photons give significant contribution to photon spectrum: 50% @ 4 GeV

Fries, Mueller & Srivastava, PRC 72 (2005) 041902


Application: Monitoring Jet Quenching

Application: Monitoring Jet Quenching

full jet reconstruction not possible at RHIC:Measure suppression of single inclusive

hadron spectra (compare to p+p baseline)

better: photon-tagged jets (Wang & Sarcevic) • q+g q+: recoil photon knows the initial energy of

the jetmeasure energy loss of quark as a function of quark

energy Ephotons from jet-photon conversion provide a

third, independent measurement. (FMS)better handle on the L dependence of energy loss jet-photon conversion is background for photon

tagged jets


SummarySummary

Parton Cascade Model:• promising tool to study the dynamics of hard probes• pQCD processes cannot create sQGP medium

Photon Production in the PCM:• Photon yield very sensitive to parton rescattering LPM effect needed for proper description of reaction dynamics• HBT experimentally challenging, but feasible with high statistics data sets calculable in the framework of PCM and hydro

Photon Production via Jet-Medium Interactions: • jet-photon conversion may contribute up to 50% @ 4 GeV to photon yield

• results compatible with PHENIX data (centrality dependence, RAA)

• analogous process for virtual photons: contribution to dilepton production


FMS: Centrality Dependence and Jet-

Quenching

FMS: Centrality Dependence and Jet-

Quenching

• centrality dependence well described

• effect of energy-loss on jets before conversion ~ 20%(Turbide, Gale, Jeon & Moore: hep-ph/0502248)

steffen a. basslight from cascading partons #1 steffen a. bass duke university motivation the pcm:...

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