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本審査・公開発表(10/31/2007)

金野正裕（数理物質科学研究科）

Proton and Antiproton ProductionProton and Antiproton Productionin High Energy Heavy Ion Collisions at RHICin High Energy Heavy Ion Collisions at RHIC

(RHIC(RHICでの高エネルギー重イオン衝突における陽子反陽子生成）での高エネルギー重イオン衝突における陽子反陽子生成）

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1. Introduction2. Motivation

- Baryon/Meson difference- Hadron production in heavy ion collisions

3. Methods- PHENIX detector- Charged hadron measurement & PID

4. Results & Discussions- Freeze-out properties- (Anti-)Proton production at intermediate pT

5. Conclusion

Outline

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-　 Quarks can exist as an apparent degree of freedom? => Quark Gluon Plasma (QGP)

- Matter under high temperature and high energy density.- Quarks and gluons are freely moving in a large volume.

- Relativistic heavy ion collisions is a method to approach the QGP.- QCD transition : Hadron gas <=> QGP

Tc ~ 175 MeVεc ~ 0.6 GeV/fm3

Introduction - QGP

(predicted by lattice QCD calculations)

QCD phase diagramJHEP 04 (2004) 050

PLB 478 (2000) 447

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Relativistic Heavy Ion Collider (RHIC)

• RHIC located at Brookhaven National Lab (USA) • A first collider for heavy ion beam• 2 circulating rings (circumference: 3.83 km) • Colliding nuclei: Au+Au, Cu+Cu, d+Au, p+p• Top energy (Au+Au): sNN = 200 GeV • Peak luminosity: ~ 3x1027 cm-2s-1

• Experiments: PHENIX, STAR, BRAHMS, PHOBOS

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Space-time evolution of a heavy-ion collision (time scale: ~10 fm/c)

Picture of Relativistic Heavy Ion Collisions

Hadron gas

QGP

Pre equilibrium

Incoming nuclei

Freeze-outHadronic scatterings

HadronizationExpansion & Cooling

Thermalization

Hard scatteringInitial collision

There are some stagesand dynamic changes.

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- Longitudinal expansion (parallel to beam axis) is dominant.- Longitudinal boost invariance partly holds at mid-rapidity.

Phys. Rev. C 67 (03) 044903, Phys.Rev.Lett.91 182301 (2003)

RHIC Findings (1)

A bulk system is expandinglongitudinally & transversely.

Rapidity distributions of charged hadron multiplicity (PRL 91, 052303 (2003))

- Hydrodynamic calculations reproduce elliptic flow behavior at low pT.- Small viscosity (/s) estimated => Nearly perfect fluid

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RHIC Findings (2) Jet Quenching

- In central Au+Au collisions, hadrons are suppressed at high pT.- The suppression is a final state effect (parton energy loss).- Away-side jet peak disappeared in central Au+Au collisions.

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0.5

1.0

Particles & Medium Effects

- Suppression/Enhancement has particle-type dependence. => Baryon/Meson difference in yields and emission patterns at intermediate pT (2-5 GeV/c).

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Baryon enhanced B/M Splitting of v2

RHIC Findings (3)

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Hadron Production in RHI Collisions

HadronizationInteractions

in the medium

Low-pT (soft)Thermal emission

Quark recombination

Thermalization

Collective flow

High-pT (hard) Jet fragmentationHard scattering

Jet quenching

- There are multiple hadronization mechanisms at intermediate pT.- The relative contributions and particle-type dependence are not yet fully understood.

Current understanding:

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Motivation

- Measurement of Proton and Antiproton pT Spectra - Sensitive to collective flow due to its relatively large mass. - Indicator of baryon number transport at lower energies. => Enhance the high-pT PID capability with new detector.- Systematic Study - Au+Au/Cu+Cu/p+p collision systems at √sNN = 62.4/200 GeV (system size, energy dependence).

- What pT does hydrodynamic contribution exist up to?- Quark recombination process is really necessary?- Can we separate hadron radial flow and quark radial flow ?

- Understanding Baryon/Meson difference at intermediate pT. => What is the origin?

What we should do:

Outstanding questions:

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My Activities- Construction and Installation of Aerogel Cherenkov detector in PHENIX for high-pT PID upgrade (2002~2004)

- Participation in PHENIX experiment during data taking periods (Run3-Run7)- Staying at BNL for ~2 years- Data analysis (2005~current): + Calibrations, Software developments + Proton spectra using Aerogel detector- Presentations (QM05, HQ06, QM06, etc.)- Papers, proceedings (NPA 774 (2006) 461, EPJC 49, 29 (2007)) (Preparing full papers)

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Aerogel Cherenkov (PID)

EM Calorimeter (PID)

TOF (PID)

Drift Chamber (momentum meas.)

Pad Chambers(tracking)

- Global detectors (event characterization)- Central Arm Detectors (||<0.35) (magnetic spectrometer)

PHENIX

Beam Beam Counter (trigger, centrality, t0, z-vertex, RP) (efficiency: A+A: ~90%, p+p: ~50%)

Zero Degree Calorimeter (centrality)

Global detectors:

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Data Analysis

Data sets: Au+Au at sNN = 62.4, 200 GeV (Run-4) Cu+Cu at sNN = 62.4, 200 GeV (Run-5)

p+p at sNN = 200 GeV (Run-5) p+p at sNN = 62.4 GeV (Run-6)

Analysis methods:(1) Event selection (z-vertex, centrality)(2) Tracking, Momentum determination(3) Track selection(4) Particle Identification (TOF, ACC)(5) MC corrections (acceptance, efficiency)

=> Invariant yield pT distributions (/K/p) at mid rapidity ||<0.35

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- Minimum Bias Trigger (BBC coin.)- Centrality determination (BBC, ZDC)Event Selection

Participant-Spectator model

Participant

Spectator

Spectator

ZDC

BBC

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Track Reconstruction

- Drift chamber provides 12 hits in (x,y) plane- Giving the bending angle (R=220cm) after passing in magnetic field- Giving pT with field-integral value

- PC1 hits and collision z-vertex fix the polar angle

- Momentum resolution:

- Find intersection points between the trajectory and outer detectors. Projected points are then matched to measured points.

€

pT =q Bdl∫α

=101mrad • GeV /c

α

€

p =pTsinθ

€

δpp

≈ 0.7%⊕1%p x

y

R

z

r

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Track Selection- Residual distribution between hit point and projection point.- Centroid and width are parameterized as a function of pT (position ~8 mm at r = 5m).

- Require tracks to be within 2.

Background subtraction for charged hadron measurement

Background sources (dominant at high pT): - e+, e- from conversion in materials - Weak decays mostly K+, K-

- Matching residual distribution has a tail.- Asymmetric shape comes from residual bend.- Background is subtracted with shape of the distribution. MC study was done.

DC tracks at PC3

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Particle IdentificationTime of Flight (~120 ps), p(p) ID up to 4 GeV/c

Aerogel Cherenkov (n=1.011), p(p) ID up to 7 GeV/c

m2 distributions(3.5-4.0 GeV/c)

Veto for proton ID+

K+pClear proton line 0 2 4 6 8

pT [GeV/c]

TOF

ACC

proton & antiproton ID

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Corrections for:

- Geometrical acceptance - Decays in flight - Momentum resolution - Detector efficiency - Occupancy effect (tracking efficiency is reduced in high multiplicity environment.)

Real data / MC matching: - Dead areas are removed - Detector stability is checked - Same cuts are applied to obtain efficiency

Acceptance (TOF)

Acceptance (ACC)

Occupancy (TOF, ACC)

Monte Carlo Corrections

* MC simulation based on Geant-3.

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Feed-down: Weak decays take place very close to the vertex. Since heavier particles take most of the decay momentum, these tracks are inseparable from tracks coming from the vertex of a collision.

Feed-down from weak decays

Evaluation of the fraction: - Effective lambda spectra measured including higher resonances (~33%) - Decays in PHENIX acceptance (MC)

- Fraction in measured p(p) : ~15%

p+p 200 GeV TOF

Proton and Lambda pT spectra

Fraction of Feed-down ( from ’s)

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Evaluation: Systematic errors are evaluated by varying cut conditions in data analysis. Some parts can be canceled when taking particle ratios etc.

Systematic Errors

Systematic errors (TOF)

Systematic errors (ACC)

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Proton and Antiproton pT spectra

pT reach extended up to 6 GeV/c

for p(p) with fine centrality bins. (1) Aerogel Cherenkov (2) High statistics

NOTE: No weak decay feed-down correction applied.

Au+Au sNN = 200 GeV Cu+Cu sNN = 200 GeV

p+p sNN = 200 GeV

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Freeze-out Properties

Characterizing bulk properties: - Chemical Freeze-out - Kinetic Freeze-out

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Particle Yield dN/dy at mid rapidity

- Particle yields are (roughly) scaled with Npart btw. Au+Au and Cu+Cu.- dN/dy(Cu+Cu) >~ dN/dy(Au+Au) at smaller Npart.- Statistical model describes their ratios with few parameters (T,).

Au+Au/Cu+Cu/p+p(sNN = 200 GeV)

Au+Au/Cu+Cu/p+p(sNN = 62.4 GeV)

K

p

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Statistical Model Fit- Extracting chemical freeze-out properties with statistical model fit.- Fitting particle ratios of dN/dy (/K/p) at y~0.- Assuming local chemical equilibrium of light quarks (u,d,s), s=1.- Partial feed-down correction taken into account.

- Tch, q : relatively stable

- s, s : not determined with this set of ratios (/K/p). Strangeness info is short.

Phys. Rev. C71 054901, 2005 nucl-th/0405068

Au+Au 200 GeV (0-5%)

-/+: 1.02 +/- 0.05 K+/K-: 1.09 +/- 0.05 p/p: 0.74 +/- 0.05 K-/-: 0.16 +/- 0.02 p/-: 0.08 +/- 0.01

1.00 +/- 0.011.09 +/- 0.080.74 +/- 0.080.16 +/- 0.020.08 +/- 0.02

Tch: 157 +/- 8 MeVq: 9 +/- 1 MeV2/ndf: 1.1/2

data model

Au+Au 62.4 GeV (0-5%)

-/+: 0.84 +/- 0.04 K+/K-: 1.19 +/- 0.06 p/p: 0.48 +/- 0.03 K-/-: 0.17 +/- 0.02 p/-: 0.08 +/- 0.01

1.01 +/- 0.011.20 +/- 0.130.48 +/- 0.090.17 +/- 0.020.08 +/- 0.02

Tch: 167 +/- 10 MeVq: 24 +/- 3 MeV2/ndf: 9.2/2

data model

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pp annihilation rate

thermal motion (+ collective flow)T = 120 MeVp ~ 500 MeV, ~ 0.4ann ~ 100 mb

dNch/d ~ 700 at mid rapiditydNp/d ~ 18 (2.5 %)

V = 8.4 x 103 fm3 (freeze-out, 10 fm/c) ~ 8n = dNp/d/(V/) ~ 1.7 x 10-2 fm-3

= 1/n ~ 5.9 fm

exp(- (t)/) = exp(- (0.4x4)/5.9) ~ 0.76survival rate(hadronic phase)

cross section

particle density

limiting case

small for high-p particles

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- Tch ~160 MeV, flat centrality dependence.- Npart scaling of Tch between Au+Au and Cu+Cu.

- Almost same Tch at √sNN = 62.4, 200 GeV.

Au+Au/Cu+Cu/p+p(sNN = 200 GeV)

Au+Au/Cu+Cu/p+p(sNN = 62.4 GeV)

Chemical Freeze-out Temperature

Tch ~160 MeV

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- Clear hadron mass dependence: larger <pT> for heavier particles. => Consistent with radial flow picture.- <pT> increases with Npart. it is clearly seen for (anti)proton.

Mean Transverse Momentum

K

p

Au+Au/Cu+Cu/p+p(sNN = 200 GeV)

Au+Au/Cu+Cu/p+p(sNN = 62.4 GeV)

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Blast-wave model is a parameterization within a simple boost-invariant model with transverse collective flow. pT spectra reflecting thermal freeze-out temperature and transverse flow at final state. * Ref: PRC48(1993)2462

(* Resonance decay feed-down correction not applied. Instead, tighter pT fitting range used. ; 0.6-1.2 GeV/c K; 0.4-1.4 GeV/c, p/pbar; 0.6-1.7 GeV/c)

Spectra for heavier particleshas a convex shape due to radial flow.

2 map

€

dN

mTdmT∝ rdrmTK1

mT coshρ

Tfo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟I00

R

∫ pT sinhρ

Tfo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

ρ =tanh−1βT

€

T = β sr

R

⎛

⎝ ⎜

⎞

⎠ ⎟n

Blast-wave Model Fit

Tfo ~120 MeV, T ~0.7

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- <T>: increasing with Npart.- Npart scaling of <T> between Au+Au and Cu+Cu.

- Almost same <T> at √sNN = 62.4, 200 GeV.

<T> ~0.5

Transverse Flow Velocity

Au+Au/Cu+Cu/p+p(sNN = 200 GeV)

Au+Au/Cu+Cu/p+p(sNN = 62.4 GeV)

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- Tfo: decreasing with Npart.- Npart scaling of Tfo between Au+Au and Cu+Cu.

- Almost same Tfo at √sNN = 62.4, 200 GeV.

Tfo ~120 MeV

Kinetic Freeze-out Temperature

Au+Au/Cu+Cu/p+p(sNN = 200 GeV)

Au+Au/Cu+Cu/p+p(sNN = 62.4 GeV)

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Summary - Freeze-out properties

Characterizing bulk properties: - Chemical freeze-out - Kinetic freeze-out

=> Hadron production at low pT : “Thermal emission + Radial flow”

Scaling properties between different systems: - Chemical/kinetic freeze-out properties show similarities between different collision systems.

- Npart scaling of freeze-out properties (Au+Au, Cu+Cu), * even though the overlapped region has a different shape. => System volume Npart is a control parameter. * Particle yield: (Cu+Cu) > (Au+Au) at smaller Npart

- Similarity at sNN = 200 and 62.4 GeV.

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Baryon Enhancement

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- (Anti-)proton enhancement observed/confirmed in 200 GeV Au+Au/Cu+Cu.- Larger than expected from jet fragmentation (measured in pp, e+e-).- p/ (p/) ratios turn over at 2~3 GeV/c ,and fall towards the ratio in p+p.

Baryon enhancement at sNN = 200 GeVp/

p/

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Baryon enhancement at sNN = 62.4 GeVp/

p/

- (Anti-)proton enhancement observed/confirmed in 62.4 GeV Au+Au/Cu+Cu.- Similar pT dependence as at 200 GeV.

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Cu+Cu vs. Au+Au (200 GeV)

- Npart scaling of p/ (p/) at same √sNN.- The ratios are controlled by the initial overlap size of colliding nuclei, even though overlap region has a different geometrical shape.

p/ ratio vs. Npart1/3

Cu+Cu vs. Au+Au (62.4 GeV)

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- Comparison with p+p spectra (reference) in binary collision scaling.- Proton, antiproton are enhanced at 1.5 - 4 GeV/c for all centralities. - Suppression is seen for , K.

Nuclear Modification Factor

RAA

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- Proton is enhanced for all centralities, while /K are suppressed.

Comparison of RAA in Au+Au/Cu+Cu

Pion RAA (pT=2.25 GeV/c) Proton RAA (pT=2.25 GeV/c)

RAA (Cu+Cu) > RAA (Au+Au)

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(Cu+Cu: b=0.0 fm, Au+Au: b=8.6 fm)

<Npart> ~117

Comparison of Au+Au and Cu+Cu

<Npart> ~100

Cu+Cu: good resolution at smaller Npart

Glauber model calculation

Even though Ncoll-Npart relation is almost same between Au+Au and Cu+Cu, the geometrical overlap shape is different.

- RAA (Cu+Cu) > RAA (Au+Au) - Geometrical shape : Au+Au more deformed - No. of N-N scatterings per N : narrow peak in Cu+Cu

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Beam energy dependence

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Beam energy dependence of enhancement

- p/+ ratio : decreasing as a function of sNN.

- p/- ratio : increasing as a function sNN.

- Antiproton is a good probe to study the baryon enhancement.

* No weak decay feed-down correction applied.

p/

p/

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- No Npart scaling of p/ (p/) in Au+Au between 62.4 and 200 GeV.- Transverse energy density dET/d scaling of p/ is favored.- dET/d is a connection key between different √sNN.

p/ ratio vs. (dET/d)1/3

Proton production at 62.4 GeV is partly from baryon number transport, not only proton-antiproton pair production.

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Energy loss per nucleon: 73±6 GeV

Net proton distribution

it drastically changeswith beam energy.

BRAHMS, PRL 93 (2004) 102301

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Au+Au/Cu+Cu/p+p(sNN = 200 GeV)

Au+Au/Cu+Cu/p+p(sNN = 62.4 GeV)

Chemical Potential

- q (200 GeV) : ~8 MeV, independent of Npart

- q (62.4 GeV) : increasing with Npart => more baryon stopping at central

€

p

p= exp(−6μq /Tch )

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Summary - Baryon enhancement

Baryon enhancement: - Proton and antiproton enhancement confirmed at intermediate pT (2-5 GeV/c) in Au+Au/Cu+Cu. A turnover of p/ ratio seen at pT = 2-3 GeV/c. - In terms of binary collision scaling, (anti)protons are enhanced while pions/kaons are suppressed.

Low energy 62.4 GeV data: - At lower energy 62.4 GeV, proton production seems to be more affected by baryon number transport process. => Antiproton is a good indicator of the baryon enhancement.

Scaling properties between different systems: - Npart scaling of p/ (p/) - dET/d scaling of p/

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Two-component model(Soft+Hard)

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high-pT

particleslow-pT

particles

Particle production in expanding matter

z-axis

time

x-axis

time

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Soft component : Thermal emission + Radial flow - Described by Blast-wave model - Npart scaling seen - Thermal distribution extrapolated up to high pT

Hard component : Jet fragmentation + Jet suppression - Measured p+p spectra - Ncoll scaling - Constant suppression factor (power-law distribution & fractional energy loss)

Two-component Model (Soft+Hard)

€

dN totpTdpT

=dNsoftpTdpT

+dNhardpTdpT

€

dNsoftpTdpT

= A rdrmTK1

mT coshρ

Tfo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟I00

R

∫ pT sinhρ

Tfo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

dNhardpTdpT

= RAA ×Ncoll ×dN p+ p

pTdpT

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- Hard component (in p+p) at high pT depends on s.- In Au+Au, suppression effect should be taken into account.

Hard component in p+p and Au+Au

p+p sNN = 200 GeV

200 GeV

62.4 GeV

Au+Au 200 GeV

(pi0: diamond, h+h-: circle)

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Pion pT spectra Au+Au 200 GeV

+

-

Soft Line Hard Line

Reproduce the measured pion pT spectra.

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Pion fraction vs. pTAu+Au 200 GeV

+

-

Soft HardResidual

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Proton pT spectra Au+Au 200 GeV

p

p

Soft Line Hard Line

Reproduce the measured proton pT spectra.

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Proton fraction vs. pTAu+Au 200 GeV

p

p

Soft HardResidual

RAA vs. Npart

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Proton pT spectra Au+Au 200 GeV

p

p

Soft Line Hard Line

Using pion’s RAA for suppression factor.

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Proton fraction vs. pTAu+Au 200 GeV

p

p

SoftHard

ResidualNeed 3rd component ?

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Fraction of soft and hard components

€

hard

soft + hard

€

soft

soft + hard

+

-

p

p

- Both soft and hard components are necessary to reproduce the hadron spectra at intermediate pT (2-5 GeV/c).- Soft component is extended to higher pT in central.- Intermediate pT: Hard pions vs. Soft protons

- Cross point (S=H) vs. pT -

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Summary - Two-component modelTwo-component model: - Reproduce the measured pT spectra for pions and protons with a consistent way. - Identify crossover region from soft to hard hadron production at intermediate pT (2-5 GeV/c).

Baryon/Meson difference: - Intermediate pT: “Hard” pions vs. “Soft” protons - Origin of baryon enhancement is radial flow. It pushes heavier particles to higher pT. Baryon/Meson difference is trivial?

=> Next question: Radial flow developed at partonic or hadronic phases?

Energy loss & Fragmentation function:- Quarks and gluons have similar energy loss when traversing the nuclear medium, and parton fragmentation function does not change.

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Quark Flow vs. Hadron Flow

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Quark recombination- One of the hadronization mechanisms.- Recombination of thermal quarks in local phase space: qq Meson, qqq Baryon- At intermediate pT, (recombination) > (fragmentation) because quark distribution is thermal: ~exp(-mT/T).- At high pT, fragmentation (power-law shape) would be dominant.

€

Ed3NMd3p

=CMw2(pT /2)

€

Ed3NBd3p

=CBw3(pT /3)

€

vM 2(pT ) = 2v q2(pT /2)

€

vB 2(pT ) = 3v q2(pT /3)

Fries, R et al PRC 68 (2003) 044902Greco, V et al PRL 90 (2003) 202302Hwa, R et al PRC 70(2004) 024905

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p/ vs. pT

- Baryon enhancement & quark number scaling of v2

explained by “Quark recombination”- v2 at quark level => Collective flow at quark level

Applicability of quark recombination model

- In a simple recombination picture, radial flow cannot be distinguished between hadron and quark phases. => Can we separate hadron flow and quark flow ?

v2/n vs. KET/n

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- Ideal gas: P=(1/3)- Entropy conservation- Longitudinal expansion & Transverse expansion

z

x

y

1+1D Adiabatic Expansion

bj vs. Np

- cooling curves -

tfo fixed at 10 fm/cat most central

T scaled with (bj)1/4

at t = 1 fm/c Cooling stopped at Tfo

€

bj (τ ) =1

τπR2

dET (τ )

dy

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- More central collisions freeze-out later at lower temperature.- Consistent with freeze-out condition: (t)=R(t)- Even if quark phase is created before hadronization, hadronic scattering should be taken into account.

Freeze-out Time & TemperatureFreeze-out time vs. Np

- As expected, Tfo is lower than Tch. Different centrality dependences.- Tfo dropping is consistent with 1+1D adiabatic expansion.

Freeze-out temperature vs. Np

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Summary - Quark flow & Hadron flow

Quark recombination: - In a simple recombination picture, hadron and quark radial flow effects cannot be separated. Since the constituent quark number scaling of elliptic flow v2 is indicative, quark recombination process is thought to be a possible hadronization mechanism.

Quark flow vs. Hadron flow: - We see the sum of quark and hadron flow. - The difference of chemical and kinetic freeze-out temperatures shows a finite expansion time at hadronic stage.

=> Hadron radial flow should exist even though quark flow exist before hadronization.

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Conclusions- Systematic measurement of proton and antiproton pT spectra (Au+Au, Cu+Cu, p+p at sNN = 200/62.4 GeV)

- Proton and antiproton enhancement confirmed at intermediate pT (2-5 GeV/c).

- Antiproton is a good indicator for study of the baryon enhancement.

- p/ ratio & freeze-out properties show Npart scaling between Au+Au and Cu+Cu at same sNN. The Initial volume (~Npart) of colliding nuclei is a control parameter.

- Baryon enhancement is caused by transverse radial flow - pT and centrality dependences are described by two-component model. - Intermediate pT (2-5 GeV/c): hard pions vs. soft protons - Chemical/Kinetic Freeze-out temperatures provide a hint for further expansion at hadronic stage.