Boost Invariance and Multiplicity Dependence of the Charge

Boost Invariance and Multiplicity Dependence of the Charge Balance Function in π+ p and K + p Collisions at Ge. V The NA 22 Collaboration Presented by Na Li Institution of Particle Physics ISMD Aug. 11 2005

Outline Ø Introduction • Why balance function • Experimental results • Motivations • Data Ø Results • BF for different positions of rapidity windows • BF for different widths of rapidity windows • BF for different multiplicity intervals • BF and charge fluctuations Ø Summary ISMD 2020/9/15 Na Li IOPP

Definition: Relative rapidity All the particles are within the rapidity window counting the pairs that satisfy the criteria in the rapidity window ISMD 2020/9/15 Na Li IOPP

Why balance function? Clocking Hadronization Charge-anticharge pairs are created at the same location in space-time, and are correlated in rapidity due to the strong collective expansion inherent to a relativistic heavy-ion collision. Pairs created earlier can separate further in rapidity due to the higher initial temperature and due to the diffusive interactions with other particles. [Steffen A. Bass, Pawel Danielewicz, and Scott Pratt, PRL (2000) ]. QGP Signal The balance function is expected to be narrower for a scenario with delayed hadronization , and is therefore sensitive to the conjecture that a quark-gluon plasma may be produced. [J. Adams et al. (STAR Collaboration), PRL (2003) ]. ISMD 2020/9/15 Na Li IOPP

Late Hadronization Early Hadronization With QGP Late hadronization Charge pairs separate nearer Narrowing of balance function ISMD 2020/9/15 Na Li IOPP

Some experimental results STAR Au+Au Ge. V ISMD 2020/9/15 Na Li IOPP

NA 49 Ge. V Width of Balance Function is the bin number of the BF histogram ISMD 2020/9/15 Na Li IOPP

QGP? Wider BF Peripheral collision Lighter nuclei ISMD 2020/9/15 Narrower BF Central collision Heavier nuclei Na Li IOPP

Motivations Some Important Questions u Multiplicity is increasing accompanying with narrowing of BF ØTrivial multiplicity dependence? u Acceptances of current heavy ion experiments are limited ØAcceptance dependence? A useful formula [S. Jeon and Scott Pratt, PRC (2002) ] ØBoost-invariance? ISMD 2020/9/15 Na Li IOPP

Data π+ p and + p Collisions at 22 Ge. V A total of 44 524 NSD events 0. 001 Ge. V/c < pt < 10 Ge. V/c full 4π acceptance ISMD 2020/9/15 Na Li IOPP

Results BF for different positions of rapidity windows u. Boost invariance of BF is valid over the whole rapidity space! ISMD 2020/9/15 Na Li IOPP

BF for different widths of rapidity windows u. BF becomes narrower with decreasing u holds approximately u. Validity of this formula depends only on the BI of charge correlation u. BF for the whole rapidity can be obtained! obtained ISMD 2020/9/15 Na Li IOPP

BF for different multiplicity intervals u. BF becomes narrower with increasing multiplicity u. This trivial multiplicity effect should be properly accounted for! ISMD 2020/9/15 Na Li IOPP

BF and charge fluctuations [S. Jeon and Scott Pratt, PRC (2002) ] u is independent of the position of the rapidity window but sensitive to the size of the observed window u. In agreement with the properties of BF! u. Limited acceptances will destroy the boost-invariance! ISMD 2020/9/15 Na Li IOPP

Summary Ø In contrast to the strong dependence of the particle density on rapidity, the BF is invariant under a longitudinal boost over the whole rapidity region. This property allows to determine the BF in full rapidity from a measurement with limited rapidity acceptance; Ø BF becomes narrower with decreasing size of the window. Therefore, only the full-rapidity BF can be used in comparing data from different experiments; Ø BF becomes narrower for increasing multiplicity, an effect also observed in heavy ion interactions when the centrality of the collision increase; Ø The charge fluctuations are boost invariant but depend on the size of the rapidity window. ISMD 2020/9/15 Na Li IOPP

ISMD 2020/9/15 Na Li IOPP

Definition: charge balance function (BF) is the conditional probability of observing a particle b in bin given the existence of a particle a in bin y 1 1 y counting the number of pairs that satisfy the criteria from each event, and the resulting values are summed over all events ISMD 2020/9/15 Na Li IOPP