Net baryon density in Au+Au collisions at the Relativistic Heavy Ion Collider

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


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


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!


BRAHMS: Net protons vs Rapidity!

BRAHMS: Net protons vs Rapidity!


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


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


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


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


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


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


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


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?


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


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?


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!


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


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


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?


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


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?


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


stay tuned for a lot more!

stay tuned for a lot more!

Documents

Net baryon density in Au+Au collisions at the Relativistic Heavy Ion Collider