Three-dimensional Levy HBT in Au+Au collisionsat PHENIX

Balint Kurgyis

Eotvos University, Budapest

International School of Subnuclear Physics 56th CourseErice 14-23 June 2018

”SUPPORTED BY UNKP-17-1 NEW NATIONAL EXCELLENCE PROGRAMME GRANT”

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

What are we looking for?

Big bang in the laboratory - heavy-ion collisions

Timeline of the Universe

GalaxiesAtomsNucleiElementary particles

How should we investigate?

Reproduce in the laboratory!

Create “little bangs”

→ Heavy-ion collisions

Detect the created particles

→ Study the sQGP

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 2 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

What are we looking for?

The PHENIX experiment

Different collision energies

7.7-200 GeV in√s

NN

20-400 MeV in µB

Different collision systems

p+p, p+A, A+A

This analysis: 200 GeV Au+Au

particle emitting sourcespace-time evolution of sQGP

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 3 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

What are we looking for?

The HBT effect and the Bose-Einstein correlations

R. Hanbury Brown, R. Q. Twiss - radio telescopes

Intensity correlations as function of detector distance→ Measuring the size of the source (Sirius)

Goldhaber et al. - application in high energy physics

Bose-Einstein correlations - momentum correlationsRelated to the source function

C (q) ∼= 1 + |∫S(r)e iqrdr|2, where q = p2 − p1

Measuring momentum correlations → femtoscopic space-time geometry

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 4 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

What are we looking for?

Levy distribution and the shape of the correlation functionExpanding medium → increasing mean free path→ Anomalous diffusion

Levy-stable distribution (generalized cent. lim. theor.)

L(r ;α,R) =1

(2π)3

∫d3qe iqre−

12|qR|α

Power-law tail: ∝ r−1−α

Levy exponent: α (Gaussian: α = 2, Cauchy: α = 1)

Lévy-HBT correlations 4 / 15

Two component source:

Core: thermalized medium, expanding sourceHalo: long lived resonances (τ > 10 fm/c)→ experimentally unresolvable

True q→ 0 limit: C (q = 0) = 2; Experimentally: C (q→ 0) = 1 + λ

Correlation strength: λ =(

NCoreNCore+NHalo

)2

Corr. func.: C (q;R, α, λ) = 1 + λe−|qR|α

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 5 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

What are we looking for?

The connection of Levy-index and the critical point

Looking for critical behavior with critical exponents

Critical spatial correlation: ∼ r−(d−2−η)

Levy source: ∼ r−(1+α) → η ⇐⇒ α ?Csorgo et al. Eur. Phys. J. C36 67 (2004)

QCD universality class ⇐⇒ 3D IsingHalasz et al., Phys. Rev. D58 096007 (1998)Stephanov et al., Phys. Rev. Let. 81 4816 (1998)

Critical point:

Random field 3D Ising: η = 0.50± 0.05Rieger, Phys. Rev. B52 6659 (1995)

3D Ising: η = 0.03631(3)El-Showk et al., J. Stat. Phys. 157 (4-5):869

Motivation for precise Levy HBT!

Finite size, non-equilibrium effects

What does the power-law tail mean?

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 6 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

The results of this work

Three-dimensional correlation functionBertsch-Pratt coordinates (LCMS): q = (qout, qside, qlong)

Identified same charged pion pairs

Measured in 31 different transverse-mass (mT) bins

Charged pions → Coulomb interaction → (approx.) Coulomb correction

0-30% Centrality

Example corr. func.

1D projections

out side long

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 7 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

The results of this work

The size of the sourceLevy-scale parameter vs. mT describes the size of the sourceComparison with 1D Levy results

A. Adare et al. (PHENIX), Phys. Rev. C 97, 064911 arXiv:1709.05649

Source is not sphericalHydro scaling: R ∝ 1/

√mT

out side long

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 8 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

The results of this work

The strength of the correlation

]2 [GeV/cTm0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

λ

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

3D-π-π 3D+π+π 1D (arXiv:1709.05649)-π-π 1D (arXiv:1709.05649)+π+π

PHENIX 0-30% Centrality = 200 GeVNNsAu+Au

PH ENIXpreliminary

Correlation strength vs. mT

Ratio of resonance pions from Core-Halo model:√λ = NCore

NCore+NHalo

Agreement with previous 1D Levy results

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 9 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

The results of this work

The shape of the correlation

]2 [GeV/cTm0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

α

0.8

1

1.2

1.4

1.6

1.8

3D-π-π 3D+π+π 1D (arXiv:1709.05649)-π-π 1D (arXiv:1709.05649)+π+π

PHENIX 0-30% Centrality = 200 GeVNNsAu+Au

PH ENIXpreliminary

Levy exponent vs. mT describes the shape of correlation function

Far from Gaussian (α = 2) or Cauchy (α = 1)

Also far from 3D Ising value at CEP (α ≤ 0.5)

Agreement with previous 1D Levy results

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 10 / 12

Introduction Three-dimensional Levy analysis Levy HBT at the PHENIX experiment Summary

Status of Levy analyses

Open questions

Centrality and collision energy dependence? → PHENIX Preliminary

Do we see any non-monotonicity?

What is the reason for the appearing Levy distributin?

Checking different hadrons (kaons)Smaller tot. cross-section → heavier tail ?

Correlation strength only affected by Core-Halo effects?

Three particle correlations may show if coherence plays a role

Balint Kurgyis Eotvos University, Budapest

Three-dimensional Levy HBT 11 / 12

Summary

The results of this work:

Acceptable fits assuming Levy source in 3D

These results are consistent with the 1D Levy results

α Levy exponent: non-Gaussian, anomalous diffusion?

Scale parameter: hydro like scaling: R ∝ 1/√mT

The source is not spherical

]2 [GeV/cTm0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

λ

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

3D-π-π 3D+π+π 1D (arXiv:1709.05649)-π-π 1D (arXiv:1709.05649)+π+π

PHENIX 0-30% Centrality = 200 GeVNNsAu+Au

PH ENIXpreliminary

out side long

]2 [GeV/cTm0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

α

0.8

1

1.2

1.4

1.6

1.8

3D-π-π 3D+π+π 1D (arXiv:1709.05649)-π-π 1D (arXiv:1709.05649)+π+π

PHENIX 0-30% Centrality = 200 GeVNNsAu+Au

PH ENIXpreliminary

Thank you for your attention!