LevyfemtoscopywithPHENIXatRHIC QM2019 - XXVIIIth International Conference on Ultra-relativistic Nucleus-Nucleus Collisions Brett Fadem for the PHENIX Collaboration The PHENIX experiment at RHIC West Beam View PHENIX Detector 2010 East MPC RxNP HBD PbSc PbSc PbSc PbSc PbSc PbGl PbSc PbGl TOF-E PC1 PC1 PC3 PC2 Central Magnet TEC PC3 BB RICH RICH DC DC Aerogel TOF-W 7.9 m = 26 ft • Collisions of various nuclei, 7.7 −200 GeV/nucleon • Charged pion ID from ∼0.2 to 2 GeV/c • Pair reconstruction (in q = p1 −p2) from ∼10 MeV/c Bose-Einstein correlations map out the femtometer source • N1(p), N2(p1, p2), N3(p1, p2, p3), . . . - invariant momentum distributions, the deﬁnition of the correlation function: Cn(p1, . . . , pn) = Nn(p1, . . . , pn) N1(p1) · · · N1(pn), where Nn(p1, . . . , pn) = Z S(x1, p1) · · · S(xn, pn)|Ψsymm n (x1, . . . , xn)|2d4x1 · · · d4xn • S(x, p) source function (usually assumed to be Gaussian - Levy if more general, c.f. anomalous diﬀusion) • Ψ2 two-particle wave function - interaction free case: |Ψ2|2 = 1 + cos(qx) • Leads to eS, the Fourier-transformed of S; if S normalized: C2(q, K) ≃1 + eS(q, K) 2 , eS(q, K) = Z S(x, K)eiqxd4x, q = k1 −k2, K = (k1 + k2)/2, q ≪K Final state interactions, resonances to take into account • Identical charged pions: Coulomb interaction distort the simple picture • Diﬀerent methods of handling, e.g. Coulomb-correction factor: CB-E(q) = K(q) · Cmeas.(q) • Two-component pion source: S = Score + Shalo – Primordial pions: Core ≲10 fm – Resonance pions - from very far regions: Halo – Observed Cn(q →0) = 1 + λn ̸= 2 – Measure: √λ2 = fc = core/(core+halo) – Resonances reduce corr. func. [1, 2] – Cross-check: √λ3 = 3f 2 c + 2f 3 c [3] – Introduce κ3 = 0.5(λ3 −3λ2)/√λ2 3 ≡1 – If partial coherence: possible deviations, κ3 ̸= 1? 1 2 1+ core core+halo unresolvable region C(q) The Levy-distribution as source function • Expanding hadron resonance gas, increasing mean free path →Levy-ﬂight • Anomalous diﬀusion, generalized central limit theorem →Levy-distribution L(α, R, r) = (2π)−3 Z d3qeiqre−1 2 |qR|α, α = 1 : Cauchy, α = 2 : Gauss • Shape of the correlation function [4]: C2(|q|) = 1 + λ · e−(R|q|)α with |k| = |q|/2 • Critical behaviour is described by critical exponents • Spatial correlation ∝r−(d−2+η) →deﬁnes η exponent • Symmetric stable distributions (Levy) lead to source ∝r−1−α  α ≡critical exponent η • QCD universality class ↔3D Ising [5, 6] nη(CEP) = 0.03631(3) (3D Ising) [7] η(CEP) = 0.5 ± 0.05 (random ﬁeld 3D Ising) [8] Levy exponent α vs. mT • Levy source: statistically valid description in 1D & 3D • Far from Gaussian (α = 2) and expo. (α = 1) • Far from rfd.3D Ising value at CEP (α = 0.5) • See more details in Ref. [9, 10] Levy exponent α vs. centrality • Clear decrease of α for central collisions • All far from Gauss (α = 2) and CEP (α = 0.5) • See more details in Ref. [11] Correlation strength λ vs. mT { • Core-Halo model: √ λ = core/(core + halo) • Small mT -decrease: in-medium η′ mass reduction? • See more details in Ref. [9] Levy exponent α vs. √sNN [GeV] NN s 10 2 10  1 1.1 1.2 1.3 1.4 1.5 [GeV]: NN s ]: 2 [MeV/c T m ∆ 14.6 300 19.6 300 27 200 39 150 62.4 50 200 12 +  +  + - - , 2 = 0.420 GeV/c 〉 T m 〈 PHENIX 0-30% Au+Au, PH ENIX preliminary • No clear collision energy dependence • All far from Gauss (α = 2) and CEP (α = 0.5) • See more details in Ref. [12] Chaoticity analysis via κ3 • If pure core-halo model: κ3 ≡1 • Deviations: coherence or other phenomena [3] • If partially coherent production: ⇒κ3 < 1 • Results so far compatible with chaotic π production • See more details in Ref. [13] Summary • Levy femtoscopy at √sNN = 200 GeV – Statistically acceptable description, far from Gaussian – 1D and 3D ﬁts yield similar results – α far from CEP value – 3π analysis: chaoticity & core-halo assumptions valid – Decrease of λ at small mT : resonance eﬀects – In-medium η′ mass modiﬁcation? • Centrality and collision energy dependence – Clear centrality dependence of α – No stro