light from cascading partons in relativistic heavy-ion collisions
DESCRIPTION
Light from Cascading Partons in Relativistic Heavy-Ion Collisions. Steffen A. Bass. Duke University & RIKEN BNL Research Center. Motivation The PCM: Fundamentals & Implementation Photon production in the PCM Medium Effects: Jet-Photon Conversion (FMS Photons). Part #1: - PowerPoint PPT PresentationTRANSCRIPT
Steffen A. Bass Light from Cascading Partons #1
Steffen A. Bass
Duke University &RIKEN BNL Research Center
• 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
Steffen A. Bass Light from Cascading Partons #2
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, nucl-th/0505059
Steffen A. Bass Light from Cascading Partons #3
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
Steffen A. Bass Light from Cascading Partons #4
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
Steffen A. Bass Light from Cascading Partons #5
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
Steffen A. Bass Light from Cascading Partons #6
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
Steffen A. Bass Light from Cascading Partons #7
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
Steffen A. Bass Light from Cascading Partons #8
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
Steffen A. Bass Light from Cascading Partons #9
Photons: pre-equilibrium vs. thermal
Photons: pre-equilibrium vs. thermal
•short emission time in the PCM, 90% of photons before 0.3 fm/chydrodynamic calculation with τ0=0.3 fm/c allows for a smooth continuation of emission rate
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
Steffen A. Bass Light from Cascading Partons #10
• 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
Steffen A. Bass Light from Cascading Partons #11
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
Steffen A. Bass Light from Cascading Partons #12
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 it’s 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
Steffen A. Bass Light from Cascading Partons #13
LPM: Reaction Dynamics
LPM: Reaction Dynamics
• high pt: harder slope, enhanced particle production
• low pt: suppression of particle production
gluon pt distribution
Steffen A. Bass Light from Cascading Partons #14
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
• good agreement with data
Steffen A. Bass Light from Cascading Partons #15
Part #2:Photons via Jet-Plasma
Interactions
R.J. Fries, B. Mueller & D.K. Srivastava, PRL 90, 132301 (2003)
Steffen A. Bass Light from Cascading Partons #16
Photon sourcesPhoton sources
• Hard direct photons
• EM bremsstrahlung
• Thermal photons from hot medium
• Jet-photon conversion
Turbide, Gale & Rapp, PRC 69 014903 (2004)
Steffen A. Bass Light from Cascading Partons #17
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?
Steffen A. Bass Light from Cascading Partons #18
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
Steffen A. Bass Light from Cascading Partons #19
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 Cd p m
( )
4 3 61
23 ( )
16
2(2 )
( 4 )(
(
)[1 ( )] ( ) ( )2
)f
q
NA
q
Agq
EdNEd 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
EdNEd xd p
s md
f
p f p f p s q qE E
p
Steffen A. Bass Light from Cascading Partons #20
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, ms in preparation)
Steffen A. Bass Light from Cascading Partons #21
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. Bass Light from Cascading Partons #22
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
Steffen A. Bass Light from Cascading Partons #23
SummarySummary
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 short emission duration in pre-equilibrium phase: small radii at high pt
larger source at later times due to emission of thermal photons
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