S. PrattNSCLMSU

1
Hadronization When and How
Scott Pratt, Michigan State University

• Is hadronization delayed beyond 1 fm/c timescale?
• What is the pre-hadronic state? (QGP? quark
  soup? gluonic slush?)
• Is strangeness produced at hadronization?
• Are anti-baryons produced at hadronization?

2
Charge is Created at Hadronization

• Gluonic modes carry entropy, but no charge
• Coalescence of quarks at sameT should have
  ? quark number doubles
• Coherent sources (chiral fields, bag energy) can
  produce new charge.

Over half of electric charge, strangeness and
antibaryons should be created at hadronization!
3
Suppose one could identify balancing Charges
Early hadronization ? large dh Delayed
hadronization ? small dh
4
Balance Functions How They Work
For each charge Q, there is one extra balancing
charge Q.
Charges electric, strangeness, baryon number
5
Balance Function Properties
In general, B(P2P1) is 6-d object
P2 can refer to any function of pa and
pb. Simple Example P1 ? anywhere in the
detector P2 ? relative rapidity
6
Balance Function Properties
If chance of finding balancing charge 100,
? normalizes to unity True even when
?Q? ? 0.

• Normalization reduced for
• Imperfect Acceptance
• Loss of Charge through other channels, e.g.,
  p balanced by K-.

7
Balance Function Properties
Relation between Balance Function and Q
Fluctuations S.Jeon and S.P., hep-th (2001).

• Similar relation between C(y) and F2(D). Wieand
  et al., PLB (89)
• B(y) more physically transparent.
• Each pair contributes ONCE and ONLY ONCE.
• Easier to analyze errors.

8
Balance Function Properties
Statistical Errors

• Error independent of multiplicity
• KK, pp, pp have same error
• number events determined by
• chance of observing balancing charge.

9
Thermal Model

• Assume Q Q produced at same point.?Dy?
  determined only by T and m.
• Proton balance functionnarrower that pions.
• Thermal model always narrower than string model.

10
Thermal Model HBT

• HBT Weight
• Use parameters to getweight T190 MeV, l.7,
  Rinv7 fm
• Dip at small Dy
• Applied to non-partners
• Proportional to dn/dy
• Does not change norm.
• No significant changein ??y?
• Dip similar to that seenby STAR

S.Jeon and S.P., hep-th (2001)
No HBT HBT Coulomb
11
Thermal Model Radial Flow

• Inclusion of flow requires lower temperature
  but not lower transverse mass
• Result Narrower B(Dy)
• Would make more sense to plot as function of Qinv

12
Thermal Model Resonances

• Resonances may be less important for AA
• May affect normalization (loss of charge to
  other channels)
• Can be crudely accounted for by using lower T
• For more complete treatment, see talk of Sen
  Cheng

13
Thermal Model Diffusion

• Procedure
• Generate a pair thermally at h0, tt0.
• Perform Ncoll collisions randomly in ln t.
• Between collisions, move particles with
  straight-line trajectories.
• Rethermalize to local T flow velocity.T(t01
  fm/c) 225 MeVT(tf15 fm/c) 120 MeV
• For Annihlations, convolute pairs.

Collisions Annihilations magnify difference
between early vs. late creation !
14
Balance Functions Quantitative Expectations
Hadronic Model pp Balance functions 10
BROADER for AA than for pp due to diffusion.
Proton-antiproton balance functions become
broader due to annihilation.
RQMD, provided by Q.H.Zhang.

• Delayed Hadronization
• Width determined by Breakup T.
• pp Balance functions 25 NARROWER for Central
  AA than for pp.

15
What if Balance functions are observed to be
NARROWER for AA than they are for pp?
RQMD-type descriptions are qualitatively
wrong AND
EITHER

• Late-stage production of charge
• Anomalously short mean free paths

• Change in degrees of freedom
• QGP least exotic explanation

OR

• would be contrary to common wisdom

16
What if AA balance functions are BROADER?
RQMD, provided by Q.H.Zhang.

• Gluonic modes did not contribute to entropy
• No dramatic change in degrees of freedom.
• Usual strangeness enhancement arguments are
  wrong.
• J/Y Jet-quenching phenomenology are misguided.

17
Preliminary STAR Results
M. Tonjes, ParkCity, 2001
Identified Pions
More Central Collisions ? Narrower Balance
Functions !!!
18
STAR Summary
QUANTITATIVELY consistent with HIJING ?
Thermal Production in Late Stage
19
STAR, width vs. centrality
All Charges
Identified Pions
As b? 0, data are consistent with 100
delayedproduction with T 110 MeV, v? 0.75
20
Can We Convict the QGP?

• Analyze pp collisions.
• Analyze KK- and pp balance functions.
• Decipher pt dependence.
• Study as functions of Qbeam, Qout, Qside, Qinv.
• Quantitatively understand normalization.(Loss of
  partners to other channels, e.g., p balancing
  partner could be K-.)

• Much can be accomplished with STARs 200 GeV data
  
• PHENIX may be able to measure pp balance function