Analysis of Low Energy Pion SpectraAnalysis of Low Energy Pion Spectra

Suk ChoiSuk ChoiProf.: Kang Seog LeeProf.: Kang Seog Lee

Chonnam National UniversityChonnam National University

HIM Apr. 18, 2007 at Yonsei Univ.HIM Apr. 18, 2007 at Yonsei Univ.

PurposePurpose Low pLow ptt pion enhancement is either from pion enhancement is either from resonan resonan

ce contribution or Coulomb interaction.ce contribution or Coulomb interaction.

Near pion production threshold energy, pions are Near pion production threshold energy, pions are produced through produced through resonance.resonance.

Charged pion spectra in Au+Au collision at 2, 4, Charged pion spectra in Au+Au collision at 2, 4, 6, and 8 GeV/A by E895 Collaboration were analy6, and 8 GeV/A by E895 Collaboration were analyzed by zed by ellipsoidal Blastwave Modelellipsoidal Blastwave Model with with resonancresonance contributione contribution && Coulomb Correction. Coulomb Correction.

-/-/+ is used as a fitting parameter to study bea+ is used as a fitting parameter to study beam energy dependence.m energy dependence.

2

2

51.94

5

N N NZ

N Z NZ

Blast-Wave ModeBlast-Wave Modell

Ellipsoidally expanding fireball model.Ellipsoidally expanding fireball model.

Thermal SpectrumThermal Spectrum )cosh(

2

max

max

max )(

00

2

yrdrdm

g

dydmm

Nd r

TTT

)sinh

().cosh)cosh(

exp( 0 T

pI

T

ym TT

),()(23

3

pxfxdpg

pd

NdE

f

Cooper-Frye FormulaCooper-Frye Formula

0, , , , , ,b cT V P

Fit Parameters Fit Parameters

Lorentz-Transformed Boltz

Lorentz-Transformed Boltz

man distributionman distribution

Spectrum is determinedSpectrum is determined

by freeze-out values.by freeze-out values.

ParametersParameters

is longitudinal rapidity.is longitudinal rapidity.

V is overall constant. Vis overall constant. V++ , V , V-- each parameters are fitted. each parameters are fitted.

Herald Dobbler et alHerald Dobbler et al

0 is transverse rapidity at (Ris transverse rapidity at (R00, z=0), z=0)

2

0 2max

( ) 1

Inside Inside 1

0

tanh ( )( )r

R

: linear transverse rapidity profile: linear transverse rapidity profile

ellipsoidal expansionellipsoidal expansion

Spectrum CalculationSpectrum Calculation

CoulombCoulomb

CorrectionCorrection ResonanceResonance

ContributionContribution

Resonance conResonance contribution by J. Stribution by J. S

ollfrank ollfrank

pd

NdE

3

3Thermal Thermal SpectrumSpectrum

,, 94.1 effeff VV

94.15

52

2

NZZ

NZN

N

N

N=118 ,Z=79 in Au+AuN=118 ,Z=79 in Au+Au

Coulomb CorrectionCoulomb Correction

2 12

ch

cf

dNp p e

dy R ,0t t cp p p

3 3 3

0 03 3 3( ) ( ) ( )

d N d N dp EE Edp dp E dp

is the unshifted invariant cross sectionis the unshifted invariant cross section3

03( )d N

Edp

2,0

,0 ,0

t

t t t t t

pdN d Ndy

p dp p dp dy p

2,0

,0 ,0,0 ,0

( ) tt t

t t t

pdN d Nm dm

dy p dp p

Fitted Values for each parametersFitted Values for each parameters

22 1.411.41 1.121.12 0.880.88 4646 2525 1.961.96 1.31.3

44 0.930.93 1.321.32 0.920.92 5757 2424 1.951.95 2.92.9

66 1.441.44 1.501.50 1.111.11 5454 1818 1.401.40 2.42.4

88 1.621.62 1.581.58 1.121.12 5555 1515 1.381.38 1.81.8

beamE V5( 10 )

cPT0m/MeV c

2

n

( )GeV ( )MeV

Transverse Mass SpectrumTransverse Mass SpectrumE895, Au+Au at 2 GeV/A E895, Au+Au at 2 GeV/A

mmt t - m- m00

Transverse Mass SpectrumTransverse Mass SpectrumE895, Au+Au at 8 GeV/A E895, Au+Au at 8 GeV/A

mmt t - m- m00

Rapidity SpectrumRapidity Spectrum

for comparisonfor comparison

TTchch = 50MeV and = 50MeV and bchbch=850MeV at 1GeV/A Au+Au =850MeV at 1GeV/A Au+Au

from pfrom particle ratio analysisarticle ratio analysis

Cleymans et al., Phys. Rev. C59, 1663(1999)Cleymans et al., Phys. Rev. C59, 1663(1999),0tm

ConclusionConclusion

,0tm

1.1.Small freeze-out temperature with large expansioSmall freeze-out temperature with large expansion velocities are obtained and thus resonance conn velocities are obtained and thus resonance contribution is negligible.tribution is negligible.

2.2. Difference in the low momentum region of the twDifference in the low momentum region of the two oppositely charged pions are due to the final sto oppositely charged pions are due to the final state Coulomb interaction. Effect of Coulomb interaate Coulomb interaction. Effect of Coulomb interaction decreases as beam energy increases.ction decreases as beam energy increases.

3.3. Near 2 GeV/A, Near 2 GeV/A, -/-/+ is about 1.94. As energy in+ is about 1.94. As energy increases the ratio decreases.creases the ratio decreases.