substructure J. S. Moreland, J. E. Bernhard, W. Ke, S. A. Bass (Duke University) Quark Matter, Chicago, USA 8 February 2017 Funding provided by DOE NNSA Stewardship Science Graduate Fellowship Computing resources provided by the Open Science Grid, supported by the NSF and DOE Office of Science
functional form of initial entropy deposition (talk by J. Bernhard). Cannot modify the mapping without spoiling bulk A+A observables, but we can add fine structure to the inputs (thickness functions) Optical nucleus Nucleus w/ nucleons Historical analogue: nucleon position hot spots necessary for v3 J. Scott Moreland (Duke U.) 3 / 17
functional form of initial entropy deposition (talk by J. Bernhard). Cannot modify the mapping without spoiling bulk A+A observables, but we can add fine structure to the inputs (thickness functions) Optical proton Proton w/ partons Possibly similar picture for partons inside the nucleon? J. Scott Moreland (Duke U.) 3 / 17
width Number of partons Necessary constraints: Fit inelastic p+p cross section Preserve avg proton radial distribution Procedure 1 Sample parton radius v from deconvolved proton radius w rsample = √ w2 − v2 2 Given a nucleon pair, take all possible parton pairs. Parton pair collision prob given by: Pcoll = 1 − exp(−σppTpp) 3 Nucleon pair collides if one or more parton pairs collide. All partons in participant nucleon added to nucleon thickness function. 4 Partonic cross section parameter σpp is numerically tuned to fit σinel nn σinel nn = ∫ d2b 1 − i,j Pij miss J. Scott Moreland (Duke U.) 7 / 17
5 0 5 3 partons 20 partons width 0.2 fm 5 0 5 5 0 5 5 0 5 width 0.3 fm x [fm] y [fm] Parton number Proton 1 0 1 3 partons 20 partons width 0.2 fm 1 0 1 1 0 1 1 0 1 width 0.3 fm x [fm] y [fm] Parton number nucleon width fixed, w = 0.5 fm J. Scott Moreland (Duke U.) 8 / 17
parton width, etc Physics Model ▪ TRENTo initial conditions with partonic substructure ▪ iEBE VISHNU hybrid model CPC 199, 61-85 [1409.8164] Experimental Data ▪ ALICE p+Pb 5.02 TeV yields and correlations Gaussian Process Emulator ▪ nonparametric interpolation ▪ fast surrogate full model Markov chain Monte Carlo ▪ random walk through param space, weighted by posterior Bayes' Theorem ▪ posterior ∝ likelihood × prior Posterior Distribution ▪ prob distribution for true values of model parameters calc events on la�n hypercube a�er many steps, MCMC equilibriates to J. Scott Moreland (Duke U.) 9 / 17
nuclear thickness func’s Proton–lead collisions appear to prefer many partons (>10) No clear tension in A+A and p+A parameters using substructure Current estimates slightly overshoot gap between v2 and v3 To do Replace response function with e-by-e hydro+micro Calibrate to Pb+Pb and p+Pb simultaneously Increase max partons to ∼100 Add observables, e.g. mean pT , and additional collision systems J. Scott Moreland (Duke U.) 17 / 17
energy (entropy) deposition is local Sees only transverse nuclear densities TA,B Hence d2S dx2τ0 dη η=0 ≈ f(TA , TB) The mapping f : TA , TB → s(x, η) should be universal at a given beam energy! ...should not change across p+p, p+Pb, Pb+Pb systems at √ sNN = const. J. Scott Moreland (Duke U.) 1 / 6
mapping f which describes, ↓ Yields in large, then small systems ↓ Correlations in large systems ↓ Correlations in p+p, p+A? ∗hydrodynamic danger zone Prioritize observables logically simple to complex macroscopic to microscopic −3 −2 −1 0 1 2 3 Á 0.00 0.05 0.10 0.15 0.20 dN/dÁ −3 −2 −1 0 1 2 3 ΔÁ −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20 C(ΔÁ) J. Scott Moreland (Duke U.) 3 / 6
108, 252301 [1202.6646] EKRT Nucl. Phys. B 570, 379–389 [9909456] KLN PRC 74, 044905 [0605012] EPOS PRC 92, 034906 [1306.0121] Parametric models MC Glauber Ann. Rev. Nucl. Part. Sci. 57, 205–243 [0701025] TRENTo PRC 92, 011901 [1412.4708] All models effectively implement f : TA , TB → e(x, η) Can compare different model calculations though mapping f J. Scott Moreland (Duke U.) 6 / 6