1. EHS/NA22 Collaboration Na Li Institute of Particle Physics
Boost Invariance and Multiplicity Dependence of the charge balance function in pi+p and K+p collisions at √sNN = 22 GeV
Phys. Lett. B 637(2006)
EHS/NA22 Collaboration
Na Li
Institute of Particle Physics
1. Introduction
● why BF ● current status ● motivation ● data
2. Main Results and Discussions
3. Summary

2. Introduction: ☞ Why Balance Function
old interest:
Charge compensation in hadronization in e+e- , l-h, h-h!
D. Drijard et al., Nucl. Phys. B155, 269(1979); B166, 233(1980);
H. Aihara etal., Phys. Rev. Lett. 53, 2199(1984);
P. D. Acton et al., Phys. Lett. B305, 415(1993).
is the conditional probability
BF measures how the conserved electric charges compensate in the phase space, i.e., how the surrounding net charges are rearranged if the charges of selected point change from negative to positive due to the charge conservation.

3. Clocking hadronization in A-A!
new interest :
Clocking hadronization in A-A!
S. A. Bass, P. Danielewicz, and S. Pratt, PRL 85, 2689(2000).
Relative rapidity
counting the pairs that satisfy the criteria in the rapidity window
If QGP is formed in the early stage of the collision, oppositely charged pairs are expected to be created later and correlate more tightly in momentum space, i.e., a significant narrowing of BF is expected in A-A.
Develpoing a quantitative understanding of the deconfining phase transition in hadronic matter and of QGP properties has proven to be a challenging task.

4. Introduction: ☞ Current status
Narrowing of the Balance Function with centrality in Au+Au Collisions at √sNN=130GeV
J. Adams et al., (STAR Coll.), PRL90, (2003);
Width of BF
Develpoing a quantitative understanding of the deconfining phase transition in hadronic matter and of QGP properties has proven to be a challenging task.

5. Introduction: ☞ Current status
System size and centrality dependence of the balance function in A+A Collisions at√sNN=17.2 GeV
C.Alt et al., (NA49 Coll.), PRC71, (2005);
Narrowing of BF with increasing system size and multiplicity
Develpoing a quantitative understanding of the deconfining phase transition in hadronic matter and of QGP properties has proven to be a challenging task.

6. Some Important Question
How BF behaves in h-h collision?
How the limited detector acceptance influences the width of BF?
Are the results form different heavy ion experiments comparable?
Introduction: ☞ Motivations ?
Central collision and heavy nuclear Narrowing of BF QGP
A useful formula
[S. Jeon and Scott Pratt, PRC (2002) ]
Boost invariance of BF?

7. Introduction: ☞ Data π+ p and + p Collisions at 22GeV
A total of NSD events GeV/c < pt < 10 GeV/c full 4π acceptance
M. Adamus, et al., (NA22 Coll.), Z. Phys. C32, (1986)475;
M. Adamus, et al., (NA22 Coll.), Eur. Phys. J. C21, (2001)271;

8. Results and discussion: ☞ A direct checking of boost invariance of
balance function in full phase space
☞ Boost invariance of BF is valid over the whole rapidity space, in contrast to the strong dependence of the particle density on rapidity;
☞ Charge correlation is essentially the same in any longitudinally-Lorentz-transformed frame!

9. ☞ BF becomes narrower with decreasing size of rapidity window
Results and discussion:
☞ BF for different widths of rapidity windows
☞ BF becomes narrower with decreasing size of rapidity window
☞ holds approximately, thus BF for whole phase space can be obtained, therefore, different experimental results are comparable.

10. Results and discussion:
☞ BF for different multiplicity intervals
in full phase space
☞ BF becomes narrower with increasing multiplicity in h-h collisions.
☞This multiplicity effect should be properly accounted if the narrowing of BF is used as a QGP signal.
☞ The hadronization scheme with string fragmentation implemented in PYTHIA qualitatively reproduces the multiplicity dependence of the data.

11. ☞ Limited acceptances will destroy the boost-invariance
Results and discussion: ☞ BF and charge fluctuations
S. Jeon and Scott Pratt, PRC65, (2002)
☞ D(Q) is independent of the position of the rapidity window , same as BF.
☞ Limited acceptances will destroy the boost-invariance

12. Summary
It is the first time to find that BF is invariant under a longitudinal boost over the whole rapidity region, in contrast to the strong dependence of the particle density on rapidity;
BF in a limited rapidity window is boost-invariantly related to that in the full rapidity range and the results from different collaborations are comparable;
BF becomes narrower for increasing multiplicity in h-h collision, therefore, this influence should be properly accounted for before using narrowing of BF as a QGP signal;
The charge fluctuations are boost invariant but depend on the size of the rapidity window.

13. Thank you!

14. Appendix I ● on the measure of charge balance function
Associated particle density:
the density of particles of charge Q at rapidity y under the condition that
a particle of charge Qs is detected at the rapidity ys.
Associated net charge density:
the net charge density at rapidity y under the condition that there exists
a particle of charge Qs at the rapidity ys.
Associated charge density balance:
Develpoing a quantitative understanding of the deconfining phase transition in hadronic matter and of QGP properties has proven to be a challenging task.
A measure of the change of the associated net charge density, when the
charge of the selected particle(s) is changed from negative to positive.
D. Drijard, et al., (ACCDHW Coll.) , Nucl. Phys. B166(1980) ;
D. Drijard, et al., (CCHK Coll.) , Nucl. Phys. B155(1979)269.

15. Monte Carlo: ☞ PYTHIA
☞ The hadronization scheme with string fragmentation implemented in PYTHIA qualitatively reproduces the trend of the data