Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #1
Steffen A. Bass, Berndt Mueller, Dinesh K.
SrivastavaDuke UniversityRIKEN BNL Research Center
VECC Calcutta
• Motivation• The PCM: Fundamentals & Implementation• Tests: comparison to pQCD minijet calculations• Application: Reaction Dynamics & Stopping @ RHIC• Outlook & Plans for the Future
Net baryon density in Au+Au collisions at the Relativistic Heavy
Ion Collider
Net baryon density in Au+Au collisions at the Relativistic Heavy
Ion Collider
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #2
Why is stopping important?
Why is stopping important?
• the amount of stopping / baryon-transport is a direct measure of the violence of the collision
• Thermodynamics: net-baryon density relates to μB
• validation of simplified scenarios: e.g. Bjorken scenario• tests the validity of novel physics concepts: e.g. Baryon Junctions
Initial theoretical expectations:• TDHF and mean field calculations: complete transparency• 1F Hydrodynamics: complete stopping• String models: incomplete (weak) stopping• Microscopic transport with rescattering: incomplete (strong) stopping
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #3
Complication: pair production of B & B
Complication: pair production of B & B
STAR preliminary
0.8pbar pair
p pair Tr
Y Y
Y Y Y
4pair
Tr
Y
Y
(ISR)
at RHIC, pair production dominates over baryon transport!
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #4
BRAHMS: Net protons vs Rapidity!
BRAHMS: Net protons vs Rapidity!
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #5
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 behaviour
• guiding scales: initialization scale Q0, pT cut-off p0 / Debye-mass μD, intrinsic kT, virtuality > μ0
3 4
1 2 3 4
min,
ˆ; , , ,ˆ with
ˆtot
totp p
d s p p p pdt
dtd
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #6
Initial State: Parton Momenta
Initial State: Parton Momenta
• virtualities are determined by:
• flavor 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
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #7
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
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #8
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
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #9
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:direct photonsnet-baryons
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #10
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
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #11
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
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #12
Debye Screening in the PCM
Debye Screening in the PCM
2 32 0
3 1lim
6g q qs
D pqq
pd p F p F p F pq
q p
•the Debye screening mass μD can be calculated in the one-loop approximation [Biro, Mueller & Wang: PLB 283 (1992) 171]:
•PCM input are the (time-dependent) parton phase-space distributions F(p)
•Note: ideally a local and time-dependent μD should be used to self-consistently calculate the parton scattering cross sectionscurrently beyond the scope of the numerical implementation of the PCM
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #13
Choice of pTmin: Screening Mass as Indicator
Choice of pTmin: Screening Mass as Indicator
•screening mass μD is calculated in one-loop approximation
•time-evolution of μD reflects dynamics of collision: varies by factor of 2!
•model self-consistency demands pTmin> μD :
lower boundary for pTmin : approx. 0.8 GeV
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #14
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
• are time-scales and collision rates sufficient for thermalization?
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #15
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
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #16
Stopping at RHIC: Initial or Final State
Effect?
Stopping at RHIC: Initial or Final State
Effect?
•net-baryon contribution from initial state (structure functions) is non-zero, even at mid-rapidity!initial state alone accounts for dNnet-baryon/dy5
•is the PCM capable of filling up mid-rapidity region?•is the baryon number transported or released at similar x?
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #17
Stopping at RHIC: PCM Results
Stopping at RHIC: PCM Results
•primary-primary scattering releases baryon-number at corresponding y•multiple rescattering & fragmentation fill up mid-rapidity domaininitial state & parton cascading can fully account for data!
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #18
Stopping: Dynamics & Parameters
Stopping: Dynamics & Parameters
•net-baryon density at mid-rapidity depends on initialization scale and cut-off Q0
•collision numbers peak strongly at mid-rapidity
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #19
pt dependence of net-quark dynamics
pt dependence of net-quark dynamics
•slope of net-quark pt distribution shows rapidity dependence
•qbar/q ratio sensitive to rescattering
•forward/backward rapidities sensitive to different physics than yCM
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #20
Time evolution of net-quark dynamics
Time evolution of net-quark dynamics
•net-quark distributions freeze out earlier in the fragmentation regions than at yCM
larger sensitivity to initial state?
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #21
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
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #22
Limitations of the PCM Approach
Limitations of the PCM Approach
Fundamental Limitations:• lack of coherence of initial state• range of validity of the Boltzmann Equation• interference effects are included only schematically• hadronization has to be modeled in an ad-hoc fashion• restriction to perturbative physics!
Limitations of present implementation (as of Oct 2003)• lack of detailed balance: (no N 2 processes)• lack of selfconsistent medium corrections (screening)• heavy quarks?
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #23
PCM: status and the next steps …
PCM: status and the next steps …
results of the last year:•Parton Rescattering and Screening in Au+Au at RHIC - Phys. Lett. B551 (2003) 277•Light from cascading partons in relativistic heavy-ion collisions - Phys. Rev. Lett. 90 (2003) 082301•Semi-hard scattering of partons at SPS and RHIC : a study in contrast - Phys. Rev. C66 (2002) 061902 Rapid Communication• Net baryon density in Au+Au collisions at the Relativistic Heavy Ion Collider- Phys. Rev. Lett. 91 (2003) 052302• Transverse momentum distribution of net baryon number at RHIC- Journal of Physics G29 (2003) L51-L58the next steps: • inclusion of gluon-fusion processes: analysis of thermalization
• investigation of the microscopic dynamics of jet-quenching• heavy quark production: predictions for charm and bottom• hadronization: develop concepts and implementation
Bass, Mueller, Srivastava RHIC Physics with the Parton Cascade Model #24
stay tuned for a lot more!
stay tuned for a lot more!