Interplay of correlations & fluctuations at RHIC -- What do we learn?
Talk at the INT/RHIC Winter Workshop 2002 on First Two Years of RHIC: Theory versus Experiments, Seattle, WA, December 15 2002.

Mikhail Kopytine (Kent State University) for the STAR Collaboration

Argonne National Laboratory - USA, Brookhaven National Laboratory - USA, U. of Birmingham - UK, U. of California, Berkeley - USA, U. of California, Davis - USA, U. of California, Los Angeles - USA, Carnegie Mellon U. - USA, Creighton U. - USA, Laboratory for High Energy, JINR - Russia, Particle Physics Laboratory, JINR - Russia, U. of Frankfurt - Germany, Indiana U. - USA, Institute de Recherches Subatomiques - France, Kent State U. - USA, Lawrence Berkeley National Laboratory - USA, Max-Plank-Institute für Physik - Germany, Michigan State U. - USA, Moscow Engineering Physics Institute - Russia, City College of New York - USA, Ohio State U. - USA, Pennsylvania State U. - USA, Institute of High Energy Physics - Russia, Purdue U. - USA, Rice U. - USA, Universidade de Sao Paolo - Brazil, SUBATECH - France, Texas A & M - USA, U. of Texas - USA, Warsaw U. of Technology - Poland, U. of Washington - USA, Wayne State U. - USA, Institute of Particle Physics - China, and Yale U. - USA Correlations & fluctuations... how to learn anything?

• Discrete Wavelet Transform $\Rightarrow$ power spectra of local track density fluctuations

• `thermal' reference = mixed events
• How does the medium change with initial conditions ? In this language:
  • thermalization: reality $\rightarrow$ reference
  • correlation: reality $<$ reference
  • fluctuation: reality $>$ reference (e.g. jets)

$F^{\lambda}_{m,i,j}(\phi,\eta)$-Haar wavelet basis in 2D:

scale fineness ($m$), directional modes of sensitivity ($\lambda$), track density $\rho(\eta,\phi,p_T)$.

Basic observables:

Power of local fluctuations, mode $\lambda$:

$$P^\lambda(m) = \frac{1}{2^{2m}}\sum_{i,j}\langle \rho,F^\lambda_{m,i,j}\rangle^2 ,$$ (1)

Dynamic texture:

$$P^\lambda(m)_{true} - P^\lambda(m)_{mix}$$ (2)

``incoherently'' normalized :

$$(P^\lambda(m)_{true} - P^\lambda(m)_{mix})/P^\lambda(m)_{mix}$$ (3)

``coherently'' normalized :

$$(P^\lambda(m)_{true} - P^\lambda(m)_{mix})/P^\lambda(m)_{mix}/N,$$ (4)

where $N$ is (sub)event ($p_T$ bin) multiplicity

Scale is localized:

Event mixing scheme:

- no pixel is used twice

- not more than one pixel from any given true event per mixed event

- no mixing of ``different'' events: multiplicity, vertex

With $n$ pixels, need $\geq n^2$ events per event class.

Proper normalization $\Rightarrow$ results independent of bin size or subevent multiplicity.

Coherent: $(P^\lambda(m)_{true} - P^\lambda(m)_{mix})/P^\lambda(m)_{mix}/N$,

Incoherent: $(P^\lambda(m)_{true} - P^\lambda(m)_{mix})/P^\lambda(m)_{mix}$

HIJING - azimuthal back to back correlations (fineness=2 is enhanced!) $\bullet$ $\circ$- scale 1; $\bullet$ $\circ$ - scale 2.

$\bullet$ $\circ$- scale 1; $\bullet$ $\circ$ - scale 2. HIJING shows coherent scaling with $p_T$ bin width

$\sqrt{S_{NN}}=130$ GeV. Fineness scale=1 ($\delta \eta=1$); Charged hadrons: $\star$ - STAR; $\bullet$ - regular HIJING; $\circ$ - HIJING without jets. The HIJING texture is mostly jets. STAR data: a change of regime with centrality.

$\sqrt{S_{NN}}=130$ GeV. Fineness scale=1 ($\delta \eta=1$); $P_{true}<P_{mix} \Rightarrow$ long range correlation

What is the origin of the long range $\eta$ correlation = suppressed fluctuation ? Need common memory/communication over $\delta \eta \approx 1$. Different break-up points causally disjoint. Hadron rescattering can not increase order.

Fineness scale=1 ($\delta \eta=1$). Peripheral ($mult/n_0 <0.1$) events: $\star$ - STAR data for $\sqrt{S_{NN}}=200$ GeV. $\bullet$ - HIJING @ same energy.

Fineness scale=1 ($\delta \eta=1$). $\star$ - STAR $\sqrt{S_{NN}}=200$ GeV; $\bullet$ - regular HIJING; $\circ$ - HIJING+jet quenching (both 130 GeV). Central ( $0.65<mult/n_0<1$) events: Data more `thermal' at $p_T>0.6 GeV \rightarrow$ dissipation?

Bose-Einstein/Coulomb contribution at low $p_T$ needs to be quantified.

Conclusions:

- peripheral ($mult/n_0 <0.1$) data qualitatively agree with HIJING except for elliptic flow; details of $p_T$ behaviour differ

- long range correlation (suppressed fluctuation) in $\eta$ becomes visible in central events.

- $p_T$-dependence of $\eta$-texture: at soft $0.6<p_T<2$ GeV, jet texture is suppressed. At low $p_T$, need to understand the ``HBT'' contribution.

- more info: nucl-ex/0211015, nucl-ex/0211019