Femtoscopic signatures of collective behavior as a probe of the thermal nature of relativistic heavy ion collisions Thomas J. Humanic, Ohio State University Adam Kisiel, CERN

Outline Motivation: testing the necessity for strong assumptions of hydrodynamics Simple rescattering model Quantifying collectivity Probing collectivity via femtoscopy Emission asymmetries for non-identical particles Realistic rescattering model Cross-checks of the simple model Realistic simulation for RHIC conditions

Does femotscopy probe collectivity? Hydrodynamics is effective in describing spectra and elliptic flow, what about femtoscopy? Requires strong assumptions (zero mean free path, local thermalization, “large” system) Relaxing assumptions seems not to affect femtoscopy – is it really probing the collectivity (and hence thermalization) of the system? Gombeaud C., Lappi T., Ollitrault J., Phys.Rev.C79:054914,2009. arXiv:0901.4908 [nucl-th]

Simple rescattering model A. Kisiel, T.J. Humanic; arXiv:0908.3830 Event consists of 1000 “pions” and 100 “kaons”, initial distribution of: , temperature distribution: and Hubble-like flow in z direction: Two temperature scenarios: “uniform” - Tmax = Tbase = 300 MeV and “gradient” Tmax = 500 MeV, Tbase= 100 MeV 𝑑𝑁 𝑑𝑥𝑑𝑦𝑑𝑧 ≈exp − 𝑥 2 + 𝑦 2 2R 2 Θ 𝑧 𝑚𝑎𝑥 −𝑧 Θ 𝑧 𝑚𝑎𝑥 +𝑧 𝑇 𝑥,𝑦 = 𝑇 𝑚𝑎𝑥 − 𝑇 𝑏𝑎𝑠𝑒 exp − 𝑥 2 + 𝑦 2 2R 𝑇 2 + 𝑇 𝑏𝑎𝑠𝑒 𝑣 𝑧 =𝑎∗𝑧+𝑏

Rescattering simulation Controlling parameter: interaction distance d. We perform calculations for d=0.1, 1.0, 2.0, 5.0, 10.0 fm For each time slice (0.1 fm/c) we check all pairs. Scattering occurs if the distance of closest approach is less than d, is within time slice, and Scatterings are elastic and relativistic. Scatterings in the same time slice are carried out simultaneously. Procedure continues until no scattering remain. Position of last scattering is the “emission point” which is saved, together with final momentum. 𝑟 1 − 𝑟 2 𝑣 1 − 𝑣 2 <0 d [fm] 0.1 1.0 2.0 5.0 10.0 <Nc> 0.15 2.2 4.7 9.2 12.9 Initial K=λ/R ~2.2 ~1.7 ~0.95 ~0.46 ~0.22

Quantifying collectivity Chojnacki M., Florkowski W. nucl-th/0603065, Phys. Rev. C74: 034905 (2006) Hydrodynamics produces collective flow: common velocity of all particles We test if rescattering alone can produce similar effects Small cross-section gives no common velocity, large cross- section resembles hydro 𝑣 𝑜𝑢𝑡 = 𝑣 𝑇 𝑟 𝑇 | 𝑟 𝑇 | 𝑣 𝑠𝑖𝑑𝑒 = 𝑣 𝑇 × 𝑟 𝑇 | 𝑟 𝑇 |

Single particle spectra We see the spectra in the “gradient” case No rescattering produces spectra with non-thermal shapes Increasing d results in evolution towards a known picture: thermal spectra modified by collective velocity Pions: concave Kaons: curving downwards Closed: pions Open: kaons d 0.1 fm 1.0 fm 2.0 fm 5.0 fm 10.0 fm

Source shape – “gradient” no interactions We inspect emission patterns vs. velocity direction For the gradient case expected effect is seen: high pT particles are emitted from a smaller region (a “hot” core). But no apparent shift of average emission position is seen, also as expected. 𝑥 𝑠𝑖𝑑𝑒 = 𝑟 × 𝑣 𝑇 | 𝑣 𝑇 | 𝑥 𝑜𝑢𝑡 = 𝑟 𝑣 𝑇 | 𝑣 𝑇 | pions faster pions same velocity kaons

Source shape with interactions When d is increased, one still sees the size decrease with particles pT. But is it still due to temperature gradients or is it flow? An additional effect is seen: Average emission points of particles are shifted to the positive “out” direction

mT scaling = collectivity? pions kaons Therminator prediction Phys.Rev.C73:064902,2006. nucl-th/0602039 “Gradient” case with no interactions shows mT dependence – scenario alternative to collectivity? Simulations with interactions also show mT dependence, but now kaons follow the same trend as pions open: uniform closed: gradient kaons kaons pions Two competing scenarios to explain the “mT scaling”: temperature gradients with little interactions or collectivity from many interactions

Isotropization via interactions As d increases – the differences between “gradient” and “unfiorm” radii disapear: interactions make the system more isotropic With many interactions the mT scaling of radii is coming only from collectivity, original temperature gradients are forgotten

Asymmetries from collectivity Emission asymmetry between pions and kaons increases linearly with number of collisions per particle – clean and unambigous signature of collectivity Initial temperature gradients do not matter – asymmetry depends only on collectivity μ 𝑜𝑢𝑡 π𝐾 = 𝑥 𝑜𝑢𝑡 π − 𝑥 𝑜𝑢𝑡 𝐾

Lessons from a simple model Interactions produce collective effects. Even a purely microscopic rescattering calculation gives “hydro-like” features for reasonable values of “interactions per particle” Initial temperature gradients may explain some of the “mT dependence” but fail to explain scaling for all masses and do not produce asymmetries Emission asymmetries a clean probe of collectivity No collectivity = no assymmetry Asymmetry depends linearly on Nc Insensitive to initial temperature gradients

Superposition-rescattering model for A+A collision Initial p+p “thin disk” of radius r = 1 fm i-th particle j-th pp collision A A * Superimpose f*A PYTHIA pp events, where f=overlap fraction for impact param. * Assume all particles have the same proper time for hadronization, , so that the hadronization space-time for each particle is given by “geometry+causality”, i.e. ti = Ei/mi ; xi = xoi +  pxi/mi ; yi = yoi +  pyi/mi ; zi =  pzi/mi * Perform hadronic rescattering using a “full” Monte Carlo rescattering calculation

Time evolution of hadronic rescattering Rescattering hadron Frozen-out hadron t ~ 1 fm/c All hadrons are rescattering t ~ 10 fm/c Some hadrons have stopped rescattering, i.e. “frozen out” t ~ 30 fm/c Most hadrons have stopped rescattering --> “freezeout”

Other details of the model…. Use PYTHIA v.6409 to generate hadrons for 200 GeV (and 5.5 TeV) p+p “minimum bias” (non-elastic and non-diffractive) events “final” hadrons from PYTHIA to use:  K, N, , K* ’ Use mult > 20 cut on p+p events --> cuts out ~ 20-25% of events and helps dn/dagree better with PHOBOS 200 GeV/n Au+Au Monte Carlo hadronic rescattering calculation: Let hadrons undergo strong binary collisions (elastic and inelastic) until the system gets so dilute that all collisions cease. Use 0.5 fm/c timesteps to 200 (400) fm/c. --> isospin-averaged (i,j) from Prakash, etc.. Record the time, mass, position, and momentum of each hadron when it no longer scatters.  freezout condition Take  = 0.1 fm/c for all calculations --> found to agree with Tevatron HBT data (T. Humanic, Phys.Rev.C76, 025205 (2007)) Au+Au Model calculations found to describe observables from RHIC experiments reasonably well (T. Humanic., Phys.Rev.C79, 044902 (2009)).

for minimum bias sqrt(sNN)=200 GeVAu+Au collisions. Time evolution up to 50 fm/c of the particle density calculated at mid-rapidity ( −1 < y < 1) and the number of rescatterings per time step from the model for minimum bias sqrt(sNN)=200 GeVAu+Au collisions. { Big assumption: binary collisions of hadrons or hadron-like particles here, too!! 200 fm/c

Spectra: Model vs PHOBOS, PHENIX, and STAR Model describes the trends of the spectra data reasonably well. Absolute normalizations used

v2/nq vs. pT/nq for Model vs. PHENIX For pions, kaons, and protons. Model v2 shows scaling with quark number like exp.

Azimuthal  HBT: Model vs. STAR Model describes and multiplicity dependences of HBT reasonably well.

Repeating simple model calculations The simple model calculations have been repeated with the more realistic rescattering The “uniform” and “gradient” initial conditions have been used as a cross-check with realistic rescatterings (both elastic and inelastic) In addition a “realistic” scenario described before was used as well, to test if the purely hadronic model will give the same signatures

Calculating system size All particles are grouped in pairs and the separation distribution is calculated Fitting with a gaussian around the peak of the rescattering model dN/Δxout distribution for pions to extract the xout widths for two mTave ranges. Similar procedure for the asymmetries

Size trends for realistic model Both gradient and “pp superposition” produce mT dependence, uniform does not With realistic cross- sections kaons sizes are close to pions (universal) Differences biggest for “gradient” scenario

Asymmetry in realistic model Realistic cross-section gives large asymmetry Uniform and gradient case give different asymmetries in contrast to the simple model Superposition model gives largest asymmetry, comparable to the uniform

Comparing emission points Difference between gradient and uniform: much larger pion shift: With higher temperature larger rate of inelastic rescattering via rho – larger shift for pions Uniform case more similar to the superposition The “realistic” simulation favors the uniform case

Summary Simple rescattering model: complementary approach to studies on relaxing hydrodynamic assumptions Collective “hydro-like” effects develop with sufficient amount of interactions Dependence of femtoscopic radii on mT not unambiguous signature of collectivity. Must utilize mass dependence: “universal” scaling for pions and kaons Emission asymmetries most sensitive to rescatterings: unambiguous probe of collectivity “Realistic” rescattering model gives similar results, favors the “unfiorm temperature” initial condition