phenix results on the lévy analysis of bose-einstein ...balaton workshop 2017 { tihany m at e csan...

PHENIX BEC Lévy HBT PHENIX results√sNN & centrality dep. Summary

PHENIX results on the Lévy analysis of

Bose-Einstein correlation functionsBalaton Workshop 2017 – Tihany

Máté Csanád for the PHENIX Collaboration

Eötvös University, Budapest, Hungary

M. Csanád for PHENIX Balaton Workshop 2017 1 / 30


Outline

1 The PHENIX experiment

2 Bose-Einstein correlations

3 Lévy-type HBT and the critical point

4 PHENIX Lévy HBT results:√sNN = 200 GeV, MinBias

5 PHENIX Lévy HBT results:√sNN & centrality dependence

6 Summary



The PHENIX Experiment

I Versatile detector, operating until 2016

I Tracking via Drift Chambers and Pad Chambers

I Charged pion ID with TOF, from ∼ 0.2 to 2 GeV/cI This analysis: PID also with EMCal



PHENIX runs at a glance



Outline






6 Summary



Bose-Einstein correlations in heavy ion physics

I Quantum statistics connects spatial and momentum space distributions

I Spatial source S(x) versus momentum correlation function C2(q):

C2(q) ' 1 +∣∣∣S̃(q)/S̃(0)∣∣∣2 , S̃(q) = ∫ S(x)e iqxd4x , q = p1 − p2

I Final state interactions distort the simple Bose-Einstein picture

I Coulomb interaction important, handled via two-particle wave function

I Resonance pions: Halo around primordial Core

Bolz et al, Phys.Rev. D47 (1993) 3860-3870; Csörgő, Lörstad, Zimányi, Z.Phys. C71 (1996) 491-497



The out-side-long system, HBT radiiI C (q) usually measured in the Bertsch-Pratt pair coordinate-system

I out: direction of the average transverse momentum (Kt)I long: beam directionI side: orthogonal to the latter two

I Rout ,Rside ,Rlong : HBT radii

I Out-side difference → ∆τ emission durationI From a simple hydro calculation:

R2out =R2

1 + u2TmT/T0+ β2T∆τ

2

R2side =R2

1 + u2TmT/T0

I RHIC: ratio is near one → no strong 1st order phase transitionI Plus lots of other details (pre-eq flow, initial state, EoS, ...)

S. Chapman, P. Scotto, U. Heinz, Phys.Rev.Lett. 74 (1995) 4400T. Csörgő and B. Lörstad, Phys.Rev. C54 (1996) 1390S. Pratt, Nucl.Phys. A830 (2009) 51C



Example: recent PHENIX HBT measurements

I Corr. func. in BP system, radii from Gaussian fit

I Linear 1/√mT scaling of HBT radii for all systems and energies

I Interpolation to common mT , PHENIX and STAR consistent

PHENIX Collaboration, arXiv:1410.2559



HBT radii and the search for the critical endpoint

I Signals of QCD CEP: softestpoint, long emission

I R2o − R2s : related toemission duration

I (Rs −√

2 · R)/Rl : related toexpansion velocity

I Non-monotonic patterns

I Indication of the CEP?

I Further detailed studies doneRoy Lacey, arXiv:1606.08071 &

arXiv:1411.7931 (PRL114)

I Maybe Levy exponent αgives further insight?

PHENIX Collaboration, arXiv:1410.2559



Outline






6 Summary



Lévy distributions in heavy ion physics

I Expanding medium, increasing mean free path: anomalous diffusion

Metzler, Klafter, Physics Reports 339 (2000) 1-77, Csanád, Csörgő, Nagy, Braz.J.Phys. 37 (2007) 1002

I Lévy-stable distribution: L(α,R, r) = 1(2π)3

∫d3qe iqre−

12|qR|α

I Generalized Gaussian from generalized central limit theoremI α = 2 Gaussian, α = 1 Cauchy

I Shape of the correlation functions with Levy source:

C2(q) = 1 + λ · e−(Rq)α α = 2 : Gaussian

α = 1 : Exponential

I Critical behaviour → described by critical exponentsI Spatial corr. ∝ r−(d−2+η) → defines η exponentI Symmetric stable distributions (Levy) → spatial corr. ∝ r−1−αI α identical to critical exponent η

Csörgő, Hegyi, Zajc, Eur.Phys.J. C36 (2004) 67, nucl-th/0310042



A possible way of finding the critical point

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

I At the critical point:I random field 3D Ising: η = 0.50± 0.05

Rieger, Phys.Rev.B52 (1995) 6659

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

I Modulo finite size effects

I Distance from the critical point?

I Motivation for precise Levy HBT!

I Change in αLevy ↔ proximity of CEP?I Non-static system, finite size effects...



Outline






6 Summary



PHENIX Lévy HBT analysis

I Dataset used for the analysis:I Run-10, Au+Au,

√sNN = 200 GeV, 7.3·109 events

I Minimum bias results so far

I Additional offline requirements:I Collision vertex position less than ±30 cm

I Particle identification:I time-of-flight data from PbSc e/w, TOF e/w, momentum, flight lengthI 2 σ cuts on m2 distribution

I Single track cuts:I 2σ matching cuts in TOF & PbSc for pions

I Pair-cuts:I A random member of pairs assoc. with hits on same tower were removedI customary shaped cuts on ∆ϕ− ∆z plane for PbSc e/w, TOF e/w

I 1D corr. func. as a function of |k |LCMS in various mT binsI Levy fits for 31 mT bins with Coulomb effect incorporated



Example C (|k |LCMS) measurement resultMeasured in 31 m2T = m

2 + p2T bins for π+π+ and π−π− pairs

Physical parameters: R, λ, α; measured versus pair mTM. Csanád for PHENIX Balaton Workshop 2017 15 / 30


Levy scale parameter R

]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

]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

I Similar decreasing trend as Gaussian HBT radii

I Hydro behaviour not invalid

I The linear scaling of 1/R2, breaks for high mT



Levy scale parameter R

]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

I Similar decreasing trend as Gaussian HBT radii

I Hydro behaviour not invalid

I The linear scaling of 1/R2, breaks for high mT



Correlation strength λ

]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

I From the Core-Halo model: λ =(

NCNC+NH

)2I Observed decrease (“hole”) at small mT → increase of halo fractionI Different effects can cause change in λ

I Resonance effects, partially coherent pion production

I λ/λmax with smaller systematic uncertaintiesI Precise measurement may help extract physics info



A possible (?) interpretation of λ(mT )

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

max

λ/λ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PRL105:182301(2010),

PRC83:054903(2011)

2(0.5-0.7) GeV/c〉λ〈 = maxλ=958 MeV'ηm=900 MeV'ηm=700 MeV'ηm=500 MeV'ηm=250 MeV'ηm= 50 MeV'ηm

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

max

λ/λ

0

0.2

0.4

0.6

0.8

1

1.2

1.4 = 200 GeVNNsMinBias Au+Au @

〉λ〈 = maxλ

-π-π+π+π

'η(0.5-0.7) GeV/c2

'η

freeα

PH ENIXpreliminary

I λ(mT ) measures core/(core+halo) fractionI May be connected to mass modifications (c.f. chiral restoration)

I Decreased η′ mass → η′ enhancement → halo enhancementI Kinematics: η′ decay pions will have low mT → decreased λ at small mT

I Incompatibility with unmodified in-medium η′ mass?Kapusta, Kharzeev, McLerran, Phys.Rev. D53 (1996) 5028, hep-ph/9507343Vance, Csörgő, Kharzeev, Phys.Rev.Lett. 81 (1998) 2205, nucl-th/9802074

Csörgő, Vértesi, Sziklai, Phys.Rev.Lett. 105 (2010) 182301, arXiv:0912.5526



A possible (?) interpretation of λ(mT )

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

max

λ/λ

0

0.2

0.4

0.6

0.8

1

1.2


PRL105:182301(2010),

PRC83:054903(2011)

2(0.5-0.7) GeV/c〉λ〈 = maxλ

-π-π+π+π

=958 MeV'ηm=900 MeV'ηm=700 MeV'ηm=500 MeV'ηm=250 MeV'ηm= 50 MeV'ηm

freeα

PH ENIXpreliminary(data only)

I λ(mT ) measures core/(core+halo) fractionI May be connected to mass modifications (c.f. chiral restoration)

I Decreased η′ mass → η′ enhancement → halo enhancementI Kinematics: η′ decay pions will have low mT → decreased λ at small mT

I Incompatibility with unmodified in-medium η′ mass?Kapusta, Kharzeev, McLerran, Phys.Rev. D53 (1996) 5028, hep-ph/9507343Vance, Csörgő, Kharzeev, Phys.Rev.Lett. 81 (1998) 2205, nucl-th/9802074

Csörgő, Vértesi, Sziklai, Phys.Rev.Lett. 105 (2010) 182301, arXiv:0912.5526



Levy exponent α

]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


0.003± = 1.134 0α

/ndf = 159/612χ

-π-π+π+π

PH ENIXpreliminary

I The measured value is far from Gaussian (α = 2) and expo. (α = 1)

I Also far from the rfd.3D Ising value at CEP (α = 0.5)

I More or less constant (at least within systematic errors)

I Motivation to do fits with fixed α = 1.134

I Note: α(mT ) = constant fit statistically not acceptable



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

I More smooth trend

I Remarkable linearity of 1/R2

I Hydro behavior valid, despite α < 2



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

________

________

________

________

__

I More smooth trend

I Remarkable linearity of 1/R2

I Hydro behavior valid, despite α < 2



Newly discovered scaling parameter R̂




]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

I Empirically found scaling parameter

I Linear in mTI Physical interpretation → open question




I 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

I Empirically found scaling parameter

I Linear in mTI Physical interpretation → open question



Outline






6 Summary



Lévy exponent α at 200 GeV

I Slightly non-monotonic behavior as a function of mTI Average 〈α〉 non-monotonic behavior versus NpartI α = 〈α〉 constant fits were performed

]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

2

2.2 = 200 GeVNNsPHENIX Au+Au

+π+π+-π-π

= 200 GeVNNsPHENIX Au+Au

+π+π+-π-π


+π+π+-π-π


+π+π+-π-π


+π+π+-π-π

> = 1.096α0-10% , <> = 1.247α10-20% , <> = 1.373α20-30% , <> = 1.422α30-40% , <> = 1.403α40-50% , <> = 1.348α50-60% , <

PH ENIXpreliminary

partN0 50 100 150 200 250 300 350

>α<

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

= 200 GeVNNsPHENIX Au+Au +π+π+-π-π

PH ENIXpreliminary



Lévy exponent α at 62 and 39 GeV

I Lévy exponent α: no significant change vs√sNN at 39-62-200 GeV

I Usual values between 1 and 1.5

I Non-monotonicity in mT

α

1

1.2

1.4

1.6

1.8

2

0-10%10-20%20-30%30-40%

+π+π+-π-π = 62 GeV, NNsPHENIX Au+Au 0-10%10-20%20-30%30-40%



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

α/α δ -0.1

00.1 rel. syst. uncertaintiesrel. syst. uncertaintiesrel. syst. uncertaintiesrel. syst. uncertainties

PH ENIXpreliminary

α

1

1.2

1.4

1.6

1.8

2

0-20%

20-40%

+π+π+-π-π = 39 GeV, NNsPHENIX Au+Au

0-20%

20-40%

]2 [GeV/cTm0.3 0.4 0.5 0.6 0.7

α/α δ -0.1

00.1 rel. syst. uncertaintiesrel. syst. uncertainties

PH ENIXpreliminary



Lévy scale R : similar trends for all√sNN and cent.

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

]2[1

/fm 2

/ R 1

0

0.05

0.1

0.15

0.2

0.25


+π+π+-π-π

freeα

linear fit


+π+π+-π-π

freeα

linear fit


+π+π+-π-π

freeα

linear fit


+π+π+-π-π

freeα

linear fit


+π+π+-π-π

freeα

linear fit

0-10%10-20%20-30%30-40%40-50%50-60%

PH ENIXpreliminary

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

]2[1

/fm 2

/ R 1

0

0.05

0.1

0.15

0.2

0.25


+π+π+-π-πlinear fit









= 1.096 fixedα0-10% , = 1.247 fixedα10-20% , = 1.373 fixedα20-30% , = 1.422 fixedα30-40% , = 1.403 fixedα40-50% , = 1.348 fixedα50-60% ,

PH ENIXpreliminary

R [f

m]

2

3

4

5

6

7

8

9

0-10%10-20%20-30%30-40%


0-10%10-20%20-30%30-40%


0-10%10-20%20-30%30-40%


0-10%10-20%20-30%30-40%

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

R/R

δ

-0.2-0.1

00.10.2 rel. syst. uncertaintiesrel. syst. uncertaintiesrel. syst. uncertaintiesrel. syst. uncertainties

PH ENIXpreliminary

R [f

m]

2

3

4

5

6

7

8

9

0-20%

20-40%


0-20%

20-40%

]2 [GeV/cTm0.3 0.4 0.5 0.6 0.7

R/R

δ

-0.2-0.1

00.10.2 rel. syst. uncertaintiesrel. syst. uncertainties

PH ENIXpreliminary



“Hole” in λ: all energies and centralities

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

λ

0.5

1

1.5

2


+π+π+-π-π freeα









0-10%10-20%20-30%30-40%40-50%50-60%

PH ENIXpreliminary

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

max

λ / λ

0.6

0.7

0.8

0.9

1

1.1

1.2


+π+π+-π-π


+π+π+-π-π


+π+π+-π-π


+π+π+-π-π


+π+π+-π-π


PH ENIXpreliminary

λ

0.4

0.6

0.8

1

1.2

1.40-10%10-20%20-30%30-40%




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

λ/λ δ -0.4-0.20


PH ENIXpreliminary

λ

0.4

0.6

0.8

1

1.2

1.40-20%

20-40%


0-20%

20-40%

]2 [GeV/cTm0.3 0.4 0.5 0.6 0.7

λ/λ δ -0.4-0.20


PH ENIXpreliminary



R̂ scaling for all energies & centralities

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

[1/fm

]

R 1

/

0.2

0.4

0.6

0.8

1

1.2

)α(1+⋅λR = R


+π+π+-π-π

freeα

linear fit

)α(1+⋅λR = R


+π+π+-π-π

freeα

linear fit

)α(1+⋅λR = R


+π+π+-π-π

freeα

linear fit

)α(1+⋅λR = R


+π+π+-π-π

freeα

linear fit

)α(1+⋅λR = R


+π+π+-π-π

freeα

linear fit

)α(1+⋅λR = R

0-10%10-20%20-30%30-40%40-50%50-60%

PH ENIXpreliminary

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

[1/fm

]

R 1

/

0.2

0.4

0.6

0.8

1

1.2

)α(1+⋅λR = R


+π+π+-π-π

linear fit

)α(1+⋅λR = R


+π+π+-π-π

linear fit

)α(1+⋅λR = R


+π+π+-π-π

linear fit

)α(1+⋅λR = R


+π+π+-π-π

linear fit

)α(1+⋅λR = R


+π+π+-π-π

linear fit

)α(1+⋅λR = R


PH ENIXpreliminary

[1/fm

]R

1/

0

0.1

0.2

0.3

0.4

0.5

0.6

)α(1+⋅λR = R

0-10%10-20%20-30%30-40%


)α(1+⋅λR = R

0-10%10-20%20-30%30-40%


)α(1+⋅λR = R

0-10%10-20%20-30%30-40%


)α(1+⋅λR = R

0-10%10-20%20-30%30-40%

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

-1R/

-1Rδ -0.2-0.1


PH ENIXpreliminary

[1/fm

]R

1/

0

0.1

0.2

0.3

0.4

0.5

0.6

)α(1+⋅λR = R

0-20%

20-40%


)α(1+⋅λR = R

0-20%

20-40%

]2 [GeV/cTm0.1 0.2 0.3 0.4 0.5 0.6 0.7

-1R/

-1Rδ -0.2-0.1


PH ENIXpreliminary



Outline






6 Summary



Summary

I B-E correlation functions, run-10 200 GeV Au+Au, ∼7 billion evts.I Levy fits yield statistically acceptable description

I Fine mT binned Levy source parameters (R, λ, α)I Nearly constant α, away from 2, 1 and 0.5 ↔ distance to CEP?I Linear scaling of 1/R2(mT )↔ hydro?I Low-mT decrease in λ(mT )↔ resonances, η′ in-medium mass?

I New empirically found scaling parameter R̂ = R/(λ · (1 + α))I Centrality and

√sNN dependence also explored

I No α decrease down to√sNN = 39 GeV

I Non-monotonic α vs Npart dependenceI “Hole” in λ(mT ) present down to

√sNN = 39 GeV (c.f. SPS result!)

I No change in 1/R2 and R̂ scaling


Outline


Run4 preliminary&Gauss → Run10 preliminary&Lévy

λ (π+ π+) RUN4 200GeV Au+Au

0

0.1

0.2

0.3

0.4

0.5

0.6

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 mT

m*η’ = 958 MeVm*η’ = 600 MeVm*η’ = 500 MeVm*η’ = 400 MeVm*η’ = 300 MeVm*η’ = 200 MeV

Gauss fit

PHENIX PRELIMINARY

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

max

λ/λ

0

0.2

0.4

0.6

0.8

1

1.2


PRL105:182301(2010),

PRC83:054903(2011)

2(0.5-0.7) GeV/c〉λ〈 = maxλ

-π-π+π+π

=958 MeV'ηm=900 MeV'ηm=700 MeV'ηm=500 MeV'ηm=250 MeV'ηm= 50 MeV'ηm

freeα

PH ENIXpreliminary(data only)


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

I More smooth trend

I Smaller systematic errors

I Saturation at large mTI Decrease (“hole”) for smaller mT values


Backup slides

[STAR] Abelev et al., PRC80, 024905[NA44] Beker et al., PRL74, 3340

STAR centrality dependent results (left) and the comparison of STARresults in different energye with NA44 data (right)


The PHENIX experimentBose-Einstein correlationsLévy-type HBT and the critical pointPHENIX Lévy HBT results: sNN=200 GeV, MinBiasPHENIX Lévy HBT results: sNN & centrality dependenceSummary

phenix results on the lévy analysis of bose-einstein ...balaton workshop 2017 { tihany m at e csan...

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