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Hadron emission source functions measured by PHENIXWorkshop on Particle Correlations and FluctuationsThe University of Tokyo, Hongo, Japan, September 22, 2011

Oak Ridge National LaboratoryAkitomo Enokizono

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Outline

• Physics motivation• Imaging procedure• 1D and 3D source functions for charged

pion• 1D source function for charged kaon• Experimental systematic uncertainties• Theoretical descriptions• Summary

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Many reasons not to be a simple Gaussian

Traditional HBT analyses assume the Gaussian source, but no reason for the emission source to be Gaussian, and more reasonable to expect the source is a non-Gaussian shape in relativistic heavy-ion collisions due to resonance decay, rescattering effect, time-dependent expansion etc…

halo

Core

“Core-Halo” model

Anomalou diffusion

Normaldiffusion

Lavy type distribution

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M. Csanád, T. Csörgő and M. Nagy hep-hp/0702032

Coulomb

Strong FSI

BEC

p-p correlation function

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Imaging correlation function

2

q(q, r) (r) 1K

P (r)S

obs obsP P P(q) (q) 1 dr (q, r) (r)R C K S

is kernel which can be calculated from BEC and known final state interactions of pairs.

is source function which represents the emission probability of pairs at r in the pair CM frame.

D.A. Brown and P. Danielewicz, Phys. Rev. C 64, 014902 (2001)

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Optimization (parameters)rmax : Maximum r (minimum q) to be imaged.

qscale = /2Δr

ImageRestore

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1D source for charged pions

• The imaged source function deviate from the 3D angle averaged Gaussian source function at > 15-20 fm.

• Resonance (omega) effect?, Kinetic effect?

PHENIX Au+Au 200GeVPhys. Rev. Lett. 98, 132301 (2007)

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Centrality and momentum dependence of non-Gaussian

• Long components (Rlr) depend on both kT and centrality.• Not consistent with a

naïve assumption of omega resonance contribution.

PHENIX Au+Au 200GeVPhys. Rev. Lett. 98, 132301 (2007)

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Theoretical explanation (1)

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D.A. Brown, R. Soltz, J. Newby, A. Kisiel Phys. Rev. C 76, 044906 (2007)

It is hard to figure out the origin of non-Gaussian structure just by looking at 1-D space.

Each component (e.g. life time, omega, kinetics. etc) seems to have different magnitude of contribution in the 3-D space.

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Pion 3D source function

• Charged pion 3D S(r) is measured for the central Au+Au collision at 200GeV and compared with blast-wave model.

• A model calculation with resonance decay + a finite emission duration agrees with the experimental result.

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PHENIX Au+Au 200GeV Phys. Rev. Lett. 100, 232301 (2008)

Outwards

Sidewards

Longitudinal

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1D source for charged kaons

• The result is suggesting non-Gaussian structure in kaon emission function also.

• Experimental systematic errors are big…

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PHENIX Au+Au 200GeV Phys. Rev. Lett. 103, 142301 (2009)

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Experimental Uncertainties (1)• Two track separation capability

• Significant at low-q (large r) region• PID (e.g pion/kaon separation)

• Pion contamination into Kaon data is more significant• Normalization factor (N)

• C2 = N*A/B is obtained from 3D Gaussian (core-halo) fit.• Can avoid the uncertainty by imaging directly raw distributions

(A. Kisiel & D.A Brown, Phys. Rev. C 80, 064911 (2009))

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Experimental Uncertainties (2)Momentum resolution: Real pair and background pair q distributions are smeared and enhance pairs in small-q.

Z vertex resolution: Only background pairs are are affected by finite Zvertex. resolution for mixed event, and enchance pair in small-q.

Central AuAu (~0.7mm), p+p (~2-3cm)

Smeared/Unsmeard

Num

. of P

air SignalQ (q) BackgroundQ (q)

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Theoretical explanation (2)

The time dependent mean free path naturally creates non-Gaussian tails which depends on PID (largest for kaons - that have the smallest cross sections)

M. Csanád, T. Csörgő and M. Nagy, hep-hp/0702032

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The tail by hadronic rescattering reproduce the experimental non-Gaussian structure. (the Core-Core rescattering creates a significant non-Gaussian part)

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Theoretical explanation (3)

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14Without hadronicscattering and decay

With hadronicscattering and decay

Without hadronicscattering and decay

With hadronicscattering and decay

Pion Pion

Kaon Kaon

T. Hirano, WPCF2010

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Summary• PHENIX has measured 1D source function for charged pions,

kasons and 3D source function for charged pions in Au+Au 200GeV

• Non-Gaussian tails are observed for both pions and kaons which still has a large experimental uncertainty

• Non-Gaussian tail is not simply explained by omega resonance decay only.

• Data are reasonably reproduced by hydro models with resonance decay + rescattering

• Need to be careful about the experimental systematic errors which is most significant at small q, i.e large r of the S(r).

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