particle production from ee to aa and search for the qcd ... · particle production from ee to aa...

Particle production from ee to AAand search for the QCD Critical Point with PHENIX

Mate Csanad (Eotvos University, Budapest)for the PHENIX Collaboration

and for Roy L. et al (the authors of arXiv:1601.06001)

54th International School of Subnuclear Physics, Erice, Sicily, 2016

June 19, 2016

Mate Csanad (Eotvos University) 54th ISSP, Erice, 2016 1 / 15

Particle production from ee to AA

Particle production mechanisms from ee to AA

A+A(B) collisions: frequently described with thermo/hydrodynamics

Model ingredients: macroscopic variables (temperature, entropy)see e.g. W. Kittel and E. A. DeWolf, Soft Multihadron Dynamics, (World Scientic, 2005)

or recent PHENIX, PHOBOS, STAR, ALICE, CMS and ATLAS papers

Microscopic phenomenology used in e− + e+, e± + p, p(p)+p or p+A

Perturbative gluon exchange, gauge fields, strings, partonssee e.g. Kharzeev et al., NPA747; Armesto et al., PRL94, Dusling et al., PRD87

and other references in arXiv:1601.06001

Similarity in particle production ⇔ available Eeff for part. productionFeinberg Phys Rept. 5, Albini et al. Nuovo Cim A32, Basile et al. PLB92&Nuovo Cim A67, Nyiri, IJMP A18

Sarkisyan and Sakharov, hep-ph/0410324

κ1

√see ≈ κ2

√spp ≈ κ3

√sep with κ1 ≡ 1 (1)

Role of quark participant pairs in pp, pA and AA describing initial stage

What do the measurements tell us?



〈Nch〉 vs.√s scaling in e− + e+, p(p)+p and e± + p


Entropy ansatz: S ∼ (TR)3,dNch/dη and 〈Nch〉 ∼ S

Initial stage variable Npp number ofparticipant pairs (Npp = 1 here)

Global assumption: N1/3pp ∝ R

Simple result:[〈Nch〉/Npp]1/3 ∼ T ∼ 〈pT 〉Scaling versus κn

√s

Fit result:〈Nch〉 =

[b〈Nch〉 + m〈Nch〉 log(κn

√s)]3

b〈Nch〉 = 1.22± 0.01m〈Nch〉 = 0.775± 0.006See details and references

in Lacey et al., arXiv:1601.06001


Quark participant scaling from pp through pA to AA


Initial stage size measure: Npp

Use quark participant pairs Nqpp

Recall [(dNch/dη)/Nqpp]1/3 ∼ T

Flat size (Nqpp) dependence

Strikingly similar√sNN trends for

p+p and A+A(B) collisions

Common production mechanism?

Small deviation for . 2 TeV

Smooth trend over full range

Details in Lacey et al.,

arXiv:1601.06001

When does QGP production start?

Phases of QCD?

Emergent QCD phenomena

Exploring the QCD phase diagram

QCD: fundamental theory mostly understood

Emergent phenomena (phases, nucleons, etc): hard to handle

Important part of the phase diagram: RHIC energies!



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

CentralMagnet TEC

PC3

BB

RICH RICH

DC DC

Aerogel

TOF-W 7.9 m =

26 ft

RHIC collisions: versatile in energy, 5-500 GeV/nucleon

Versatile in colliding nuclei: p, d, Cu, Au, Al, He, U

Tracking via Drift Chambers & Pad Chambers

PID via time of flight from TOF & EMCal

Momentum resolution: δp/p ≈ 1.3%⊕ 1.2%× p GeV/c

Charged pion ID from p ≈ 0.18 to 2 GeV/c



The RHIC Beam Energy Scan


Bose-Einstein correlations

Introduction to Bose-Einstein correlations

In case of free bosons, momentum correlation function:

C2(q) ' 1 +

∣∣∣∣∣ S(q)

S(0)

∣∣∣∣∣2

, S(q) =

∫S(x)e iqxd4x , q = p1 − p2 (2)

Final state interactions distort the simple Bose-Einstein picture

Coulomb interaction important, handled via two-particle wave function

Resonance pions: Halo around primordial Core

Halo part unresolvable

J.

Bolz et al, Phys.Rev. D47 (1993) 3860-3870


Bose-Einstein correlations

Levy shaped source and the Critical Point

Levy distributed source and resulting correlation function:

S(r)α,R =1

(2π)3

∫d3qe iqre−

12|qR|α ⇒ C2(q) = 1 + λ · e−(R|q|)α (3)

Parameters: λ,R, α, may depend on average pair momentumRelated to anomalous diffusion or generalized random walkMetzler, Klafter, Physics Reports 339 (2000) 1-77

α = 2: Gauss, α = 1: Cauchy; power-law tail for α < 2

Levy index α identified with critical exponent ηSpatial correlation function ∝ r−(d−2+η) → critical η exponentSymmetric stable distributions (Levy) → spatial corr. ∝ r−1−α

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

3D Ising: η = 0.03631(3), Random field 3D Ising: η = 0.50± 0.05Rieger, Phys.Rev.B52 (1995) 6659, El-Showk et al., J.Stat.Phys.157 (4-5): 869

Change in α↔ proximity of CEP

Motivation for precise Levy HBT


PHENIX Levy HBT analysis results

Example correlation function measurement result

Measured in 31 m2T = m2 + p2

T bins for π+π+ and π−π− pairs

Physical parameters: R, λ, α; measured versus pair mTMate Csanad (Eotvos University) 54th ISSP, Erice, 2016 10 / 15


Levy scale parameter R versus pair mT

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

R [f

m]

3

4

5

6

7

8

9

10

freeα

= 200 GeVNNsMinBias Au+Au @

freeα

-π-π+π+π

PH ENIXpreliminary

Similar decreasing trend as usual Gaussian HBT radii

Hydro behaviour: 1/R2 ∼ mT , not incompatible

Interesting, since simple hydro would mean α = 2



Correlation strength λ versus pair mT

]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

freeα


freeα

-π-π+π+π

PH ENIXpreliminary

From the Core-Halo model: λ = (NC/(NC + NH))2

Large and correlated systematic uncertainties

Observed decrease at small mT → increase of halo fractionMay be interesting phyics in λ, strange speculations:

Resonance effects, chiral symmetry restoration?Partially coherent pion production?Aharanov-Bohm effect?



Levy exponent α versus pair mT

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

α

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5 = 200 GeVNNsMinBias Au+Au @

0.003± = 1.134 0α

/ndf = 159/612χ

-π-π+π+π

PH ENIXpreliminary

Far from Gaussian (α = 2) and Cauchy/exponential (α = 1)

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

More or less constant (at least within systematic errors)

Although the constant fit is statistically not acceptable

Motivation to do fits with fixed α = 1.134



Newly discovered scaling parameter R

]2 [GeV/cTm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

[1/fm

]R

1/

0

0.1

0.2

0.3

0.4

0.5

0.6

freeα


freeα

)α(1+⋅λR = R

-π-π+π+π

PH ENIXpreliminary

Empirically found scaling parameter

Linear in mT

Physical interpretation → open question


Summary

Scaling of Nch from ee to AA data from GeV to TeV√s regions

Effective energy notation successfulQuark participants emergingSpecial signatures at special energies?

Seach for the QCD critical point at RHIC

New measurement method of Levy sources developed with PHENIX

Levy exponent α at√sNN = 200 GeV far from Gaussian or critical values

Correlation strength λ hints at interesting physicsNew empirically found scaling parameter R


Thank you for your attention!

Let me invite You to the 16th Zimanyi Winter School on Heavy Ion PhysicsBudapest, Hungary, Dec. 5 – 9, 2016

http://zimanyischool.kfki.hu/16/




Similarities from p+p through p+A to A+A(B)

Similar charged particle multiplicities (Nch)

Similar pseudorapidity densities (dNch/dη)

Azimuthal long range (|∆η| ≥ 4) angular correlations, “ridge”

Collective anisotropic flow in A+A collisions

Also in p+p, p+Pb, d+Au and He+AuALICE PLB719, ATLAS PRL110, CMS PLB718, PHENIX PRL114, PHENIX PRL115

Qualitative consistency achieved with hydroSee e.g. Bozek, PRC85, the Buda-Lund model from Csorgo et al., NPA661, JPhysG30, EPJA38, . . .

Common underlying particle production mechanism dominating?


Our framework to capture underlying physics

Macroscopic entropy (S) ansatz

S ∼ (TR)3 ∼ const. (4)

dNch/dη and 〈Nch〉 ∼ S (5)

Initial stage variable Npp number of participant pairsNpp = 1 for e− + e+, e± + p and p(p)+pNucleon or quark participant pairs (Nnpp, Nqpp) in p+A, A+A(B)

Further assumption: N1/3pp ∝ R ⇒ [(dNch/dη)/Npp]1/3 ∼ T ∼ 〈pT 〉

Monte Carlo Glauber calculations performed to obtain Nnpp and Nqpp.Lacey et al. PRC83, Eremin et al. PRC67, Bialas et al. PLB649, Nouicer EPJC49, PHENIX PRC89

Subset of initial particles become participants by an initial inelasticN+N or q+q interaction.

Nnp = 2Nnpp or Nqp = 2Nqpp

N+N (q+q) cross sections taken from literature Fagunders et al, J. Phys. G40


Nucleon participant scaling in A+A(B) collisions


All systems:[dNch/dη||η|=0.5

Nnpp

]1/3∼ T

(a): ∝ log(dNch/dη) ∼ log S ,

(b): ∝ N1/3npp ∼ R

Logarithmic S-dependenceLinear size dependence(at a given

√sNN)

〈pT 〉 increases with√sNN and log(dNch/dη)

Pseudorapidity density factorizes

into contributions depending on√sNN and N

1/3npp

Slope increaseses with beam energy

Lack of sensitivity to system type (Cu+Cu, Cu+Au,Au+Au, U+U), for fixed

√sNN.

PHENIX Levy HBT analysis

Dataset:√sNN = 200 GeV Au+Au, min. bias, ∼7 billion events

Goal: detailed shape analysis of two-pion correlation functions

Correlation functions measured in fine pair mT =√m2 + p2

T binsLevy source instead of Gaussian → better agreement with dataPrecision measurement of source parameters versus pair mT

Result: λLevy (mT ), αLevy (mT ),RLevy (mT )

Tracking: DCH & PC1, 2σ matching cuts in TOF & EMCal

Particle identification:

time-of-flight data from EMCal & TOF, momentum, flight length2σ cuts on m2 distribution

Pair-cuts:

Exclude particles hitting the same tower/slat/stripCustomary shaped cuts in ∆ϕ−∆z plane for TOF, EMCal, DCH


Example correlation functions

|k| [GeV/c]0 0.05 0.1 0.15 0.2 0.25 0.3

2C

1

1.1

1.2

1.3

1.4

1.5

1.6

Raw corr. function

Coulomb factor×Raw corr.

Coulomb factor

|k|)ε N(1+×;|k|) α,R,λ(LevyCoulC

|k|)ε N(1+×;|k|) α,R,λ(Levy0C

|k|)εN(1+

= 0.48-0.5 GeV/cT

, p-π-π = 200 GeV, NNsMinBias Au+Au @

0.06± = 1.14 λ 0.28 fm±R = 6.90 fm

0.03± = 1.09 α 0.001± = -0.025 ε 0.0001±N = 1.0015

/NDF = 295/2512χconf. level = 0.0293

|k|)ε N(1+×)) α |k|)⋅ R⋅ exp(-(2⋅λ=(1+Levy0C

|k| [GeV/c]0 0.05 0.1 0.15 0.2 0.25 0.3

(dat

a-fit

)/er

ror

-4-3-2-101234

PH ENIXpreliminary


Example correlation functions

|k| [GeV/c]0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

2C

1

1.1

1.2

1.3

1.4

1.5

1.6

Raw corr. function

Coulomb factor×Raw corr.

Coulomb factor

|k|)ε N(1+×;|k|) α,R,λ(LevyCoulC

|k|)ε N(1+×;|k|) α,R,λ(Levy0C

|k|)εN(1+

= 0.72-0.74 GeV/cT

, p+π+π = 200 GeV, NNsMinBias Au+Au @

0.09± = 1.05 λ 0.30 fm±R = 4.84 fm

0.05± = 1.20 α 0.000± = -0.038 ε 0.0002±N = 1.0007

/NDF = 413/3802χconf. level = 0.1180

|k|)ε N(1+×)) α |k|)⋅ R⋅ exp(-(2⋅λ=(1+Levy0C

|k| [GeV/c]0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

(dat

a-fit

)/er

ror

-4-3-2-101234

PH ENIXpreliminary


Levy scale parameter R versus pair mT

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

R [f

m]

3

4

5

6

7

8

9

10

freeα


freeα

-π-π+π+π

PH ENIXpreliminary

]2 [GeV/cTm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

]2 [1

/fm2

1/R

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

freeα


freeα

-π-π+π+π

PH ENIXpreliminary

Similar decreasing trend as usual Gaussian HBT radii

Hydro behaviour: 1/R2 ∼ mT , not incompatible

Hard to say whether the 1/R2 scaling is linear or not


Correlation strength λ versus pair mT

]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

freeα


freeα

-π-π+π+π

PH ENIXpreliminary

From the Core-Halo model: λ = (NC/(NC + NH))2

Large and correlated systematic uncertainties

Observed decrease at small mT → increase of halo fractionDifferent effects can cause change in λ, strange speculations

Resonance effects, partial chiral symmetry restoration?Partially coherent pion production?Aharanov-Bohm effect?


Levy exponent α versus pair mT

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

α

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5 = 200 GeVNNsMinBias Au+Au @

0.003± = 1.134 0α

/ndf = 159/612χ

-π-π+π+π

PH ENIXpreliminary

Far from Gaussian (α = 2) and Cauchy/exponential (α = 1)

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

More or less constant (at least within systematic errors)

Although the constant fit is statistically not acceptable

Motivation to do fits with fixed α = 1.134


Levy scale parameter R with fixed α = 1.134

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

R [f

m]

3

4

5

6

7

8

9

10

= 1.134α


= 1.134α

-π-π+π+π

PH ENIXpreliminary

]2 [GeV/cTm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

]2 [1

/fm2

1/R

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

= 1.134α


= 1.134α

-π-π+π+π

PH ENIXpreliminary

More smooth trend

Hydro behaviour seems to be more valid

The linearity of 1/R2 holds


Correlation strength λ with fixed α = 1.134

]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

= 1.134α


= 1.134α

-π-π+π+π

PH ENIXpreliminary

More smooth trend

Smaller systematic errors


Newly discovered scaling parameter R

α = 1.134 fixed

]2 [GeV/cTm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

[1/fm

]R

1/

0

0.1

0.2

0.3

0.4

0.5

0.6

= 1.134α


= 1.134α

)α(1+⋅λR = R

-π-π+π+π

PH ENIXpreliminary

Empirically found scaling parameter

Linear in mT

Physical interpretation → open question


Beam energy & system size dependence of HBT radii

Corr. func. in 3D, Gaussian fit (details: arXiv:1410.2559)

π+π+, π−π− data combined

Linear 1/√mT scaling of HBT radii

Interpolation to common mT , PHENIX and STAR consistent


Beam energy & system size dependence of HBT radii

quantities related to emissionduration and expansionvelocity

non-monotonic patterns

indication of CEP?

More precise mapping and further detailed studies required

Is there any other way to find the critical point?

Maybe Levy exponent α!


Generalized random walks

Random walk, step size with infinite varianceRandom Walk Generalized random walk


(Speculative) connection between λ(mT ) and UA(1)

Partial chiral UA(1) restoration ⇒ reduction of the η′ mass

Reduced η′ mass ⇒ larger abundance of η′

Decay: η′ → ηπ+π−, η → π+π−π0 (some probability)

In summary: UA(1) restoration ⇒ larger number of decay pions

Larger number of decay pions ⇒ larger halo, i.e. reduced λ

These decay pions have small momentum, as η′ has no availableenergy to give them momentum

λ reduces only at small momentum!

Hole in λ(mt) distribution!


(Speculative) connection: λ(mT ) and Aharanov-Bohm

Mixing of a→ A, b → B and a→ B, b → A

Correlation strength: 〈|Ψ2|2 − 1〉, with|Ψ2|2 = 1 + cos(∆x∆k) and∆x = x1 − x2, ∆k = k1 − k2

Average on local production probability and random phases at emission(c.f. incoherent production); if no random phases, no correlation!

Observation: closed loop in the above figure

Particles go through an expanding, fluctuating medium

Pairs picking up additional random phases φ,|Ψ2|2 = 1 + cos(∆x∆k + φ)

Assume φ distribution of exp[−φ2/(2σ2), average on possible φ values

〈|Ψ2|2 − 1〉φ = exp[−σ2/2] cos(∆x∆k)

Correlation strength λ reduced by exp[−σ2/2]

Suppose σ2 ∼ 1/m2T ⇒ “hole” in λ(mT )

Idea from Antal Jakovac (Eotvos University)


particle production from ee to aa and search for the qcd ... · particle production from ee to aa...

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