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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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