14, 2012 *Special thanks to U. Heinz and S. Bass for their guidance and to the Krell Institute for funding my future graduate studies. - Adding quark and gluon degrees of freedom to Monte Carlo Color-Glass Condensate initial conditions
viscous hydrodynamics + Boltzmann cascade provide useful tool for extracting QGP shear viscosity η/s. 1. Initial conditions (IC) simulate transverse energy (entropy) density 2. Hydrodynamic transport equations evolve IC down to Tc (critical temperature) 3. Boltzmann cascade evolves hadron resonance gas from Tc to freeze-out 4. Particle interactions cease and particles free-stream J. Scott Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 2 / 17 vn ← anisotropic ﬂow η/s ↔ n ← spatial anisotropy viscosity η/s dampens conversion of spa- tial anisotropy into ﬂow anisotropy
for extracting η/s is uncertainty in initial conditions: MC-Glauber? DIPSY? AMPT? MC-KLN? MC-rcBK? NeXuS? UrQMD? IP-Sat? IP-Glasma?... It’s a zoo. Current models not yet converging, only discovering new sources of uncertainty Let’s concentrate on developments in ﬂuctuations Classic Example: Optical nucleus → Monte Carlo nucleus w/ﬁnite nucleons J. Scott Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 3 / 17
charged particle multiplicity Nch evidence for sub-nucleonic initial state ﬂuctuations K. Aamodt et al. (ALICE Collaboration) Eur.Phys.J. C68 (2010) 89-108 0 2 4 6 8 N ch /<N ch > 0.001 0.01 0.1 1 P(N ch ) ALICE INEL. pp 2.36 TeV ALICE NSD pp 2.36 TeV NBD(n=3.77; k=1.25) NBD(n=3.77; k=1.0) NBD(n=3.77; k=0.9) pp multiplicity ﬂuctuations cannot be explained using Glauber model for pp interaction where, P(b) = 1 − exp[−σgg Tpp(b)] Sub-nucleonic ﬂuctuations clearly exist in the initial state, but where to begin? J. Scott Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 4 / 17
in Color-Glass Condensate model M¨ uller-Sch¨ afer paper predicts structure of quantum ﬂuctuations! Paper calculates mean normalized covar. Cov[ (r)/ 0] = (∆ (r)/ 0)2 for collision of two inﬁnite sheets of nuclear matter Gaussian color distribution (color content contribution from each nucleon is independent). Correlation length proportional to 1/Qs ≈ 0.14 fm (relevant Qs at RHIC) Use M¨ uller-Sch¨ afer covariance of gluon-ﬁeld energy density ﬂuctuations to texture MC-KLN initial conditions J. Scott Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 5 / 17 B. M¨ uller, A. Sch¨ afer, Phys.Rev.D 85, 114030 (2012)
use GRF Turning Band SIMulator TBSIM developed by X. Emery and C. Lantu´ ejoul to generate a large 4000x4000 cell GRF w/ the M¨ uller-Sch¨ afer covariance X. Emery and C. Lantu´ ejoul, Computers and Geosciences 32, 1615 (2006) J. Scott Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 6 / 17 Fit to M¨ uller-Sch¨ afer covariance is nearly exact. One small problem: GRF allows for ﬂuctuations ∆ / 0 < −1, negative energy densities which are, of course, non-physical. fm fm −4 −2 0 2 4 −4 −2 0 2 4 −2 −1 0 1 2
Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 7 / 17 -1 0 1 2 3 Nch/<Nch> 0 0.1 0.2 0.3 0.4 0.5 P(Nch) 70 % Gaussian Dist. µ = 1, σ = 0.684 0 1 2 3 4 Nch/<Nch> 0 0.2 0.4 0.6 0.8 P(Nch) 70 % Negative Binomial Dist. µ = 1, σ = 0.684 7.2% chance Gaussian ﬂuctuations are negative (non-physical) Send Gaussian → Negative Binomial Distribution (NBD) motivated by p-p multiplicity ﬂuctuations NBD(¯ n, k; n) = Γ(k+n) Γ(k)Γ(n+1) ¯ nnkk (¯ n+k)n+k 2-parameter function on Z Generate single NBD with mean and standard deviation equal to Gaussian Equate random variables via their cumulative distribution functions (CDF’s) i.e. iﬀ x −∞ Gaussian(x)dx = y −∞ NBD(y)dy then x ↔ y
Imprinting Quantum Fluct. on Hydro IC August 14, 2012 8 / 17 Bulk of proﬁle is pulled down and hot spots are more sharply peaked Texture can be thought of as percent ﬂuctuation about mean gluon-ﬁeld energy density 0 0.2 0.4 0.6 0.8 r fm 0 0.1 0.2 0.3 0.4 Cov[ε(r)/ε 0 ] Mueller-Schaefer C(1+(r/a)2 )-b φ = 0 φ = π/8 φ = π/4 φ = 3π/8 φ = π/2 fm fm −4 −2 0 2 4 −4 −2 0 2 4 0 1 2 3 Nope. Almost indistinguishable from GRF ﬁt to M¨ uller-Sch¨ afer covariance
Nara “KNO scaling of ﬂuctuations in pp and pA, and eccentricities in heavy-ion collisions” Phys. Rev. C 85, 034907 (2012) [arXiv:1201.6382 [nucl-th]]. B. Schenke, P. Tribedy & R. Venugopalan “Fluctuating Glasma initial conditions and ﬂow in heavy ion collisions” arXiv:1202.6646 [nucl-th]. Strengths of the present analysis: Realistic covariance applicable in central (hot) regions of the ﬁreball Fluctuations can be turned on and oﬀ for comparison (factorized) and applied to any suitable Color-Glass Condensate model J. Scott Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 15 / 17
conditions with a uniform M¨ uller-Sch¨ afer covariance. We see a small increase in 2 − 5 in central collisions ≈ 5 − 10%. Increasing the correlation length to the width of a nucleon (as may happen for smaller Qs values) results in ≈ 20 − 25% increase of n in central collisions. Increases in 2 vanish for Npart < 300. Looking forward Reﬁne model to better account for ﬂuctuations in dilute regions, i.e. ﬁtting pp multiplicity ﬂuctuations Converge with parallel studies (B. Schenke, P. Tribedy, R. Venugopalan & A. Dumitru, Y. Nara) Run ﬂuctuated proﬁles through hydro J. Scott Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 16 / 17
Chun Shen and Jonah Bernhard for constructive advice and illuminating discussions. J. Scott Moreland (Duke) Imprinting Quantum Fluct. on Hydro IC August 14, 2012 17 / 17