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YThermal

Tsukuba-Yonsei Workshop Program

Inst. of Physics,Univ. of Tsukuba

D.J .Kim /Y.Kwon

YONSEI UNIVERSITY

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Outline

• Motivation• Introduction to Thermal Model• Introduction to YThermal • Physics Issues of YThermal• YThermal Howto• Furture Work

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Develop a model calculator for PHENIX based on the work

of P. BraunMunzinger et al.’s work.

--- One of the circumstantial evidence for the QGP formation is

the chemical equilibrium of the produced hadron multiplicity

including the strangeness sector ( Phys. Lett. B465, 15-20, 1999 ).

--- Rejection or confirmation of this conclusion will be within the reach

of PHENIX run1 measurements

if we can account for the the kinematics of the whole phase space properly.

   --- Hence we decided to reproduce the model and study the basic aspects

of the model parameters relavant to the experiment. [( T, ) ,volume correction]

--- Proper handling of the whole kinematics are under progress.

Motivation

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Thermal Model

Free Parameter : ( T, )+ volume correction

System Parameter : ( N , Z)Proton,neutron number of the colliding nuclei

GCE +

strangeness +

baryon number +

charge conservation+

excluded volume correction

m;mass(Chiral symmetry restoration) , r;radius for the volume correction

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As model and data agree very well, one can assume, that the system is in thermal and chemical equilibrium at the time of chemical freeze-out

The freeze-out point is characterized by different temperatures and baryochemical potentials in the different collision system, but is very close to the predicted quark-gluon phase boundary

CERN press Release :New State of Matter created at CERN

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After this,

PRC 56,p2210,1997

For volume correction

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Entropy conservation

(T, s) ( S, nB )

S/N, nB

Net baryon number

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pi+/pi- K+/K- pbar/p pi+/p

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Introduction of YThermal

>> Technically the model is built upon ROOT frame work (http://root.cern.ch/)

with two objectives(YThermal, Yparticle )

First , to generate a user friendly system which any PHENIX collaborator can understand and use easily.

This include

     1. the automatic documentation

     2. the usage of the object inspector & graphics

     3. free usage of the declared classes

Second, to prepare the model as a part of the bigger hydrodynamic model calculation which is under steady progress.

* note all units follows hbar = c = 1 unless dictated otherwise;

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Ythermal HowTo

1.1. Design scheme Design scheme

•> Production of the particle objects and simple initialization.

•    YThermal *thermal = new YThermal(0.168,0.266);

•> Decides the baryon number of the fireball

•    thermal->Set_Btotal(200);

•> Input isospin balance for Iz calculation

•   thermal->Set_Isobalance(0.66949153);

•> Set default experimental feed-down

•   thermal->Experiment();

•> Clears data block for each particle species

•   thermal->Clear();

•> Perform the iteration and do the calculation

•> iteration over all particles.

•   thermal->DoIt();

memo:

• important input :

[(T,mu_B), Btotal]

• With (T,mu_B), thermal model predicts the absolute particle densities.

• When Btotal ( the baryon umber of the fireball ) is decided, it subsequently decides the absolute multiplicities of all particles. Experimentally Btotal will have close relationship with the collision centrality in the thermal model.

memo:

• important input :

[(T,mu_B), Btotal]

• With (T,mu_B), thermal model predicts the absolute particle densities.

• When Btotal ( the baryon umber of the fireball ) is decided, it subsequently decides the absolute multiplicities of all particles. Experimentally Btotal will have close relationship with the collision centrality in the thermal model.

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Generation of the html filesGeneration of the html files

1. How to insall :

http://ipap.yonsei.ac.kr/~npl/thermal/install.html)

After the system is properly installed, you can load

     % thermal

(This is root with the dynamic library

for the thermal model calculation ).

    then execute

        root [0] .x GenerateHtmlDoc.C

        What's in the html file? You can try

       % netscape html/USER_Index.html  

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Usage of the object inspectorUsage of the object inspector• % thermal

• root [0] .x CaseTEST.C

• root [1] gP->Inspect();

• root [2] TF1 *fun1 = (TF1 *)gPIP->Fnid;

• root [3] fun1->Draw();

• gPIP->Fnid is the pointer to the function used to get PIP total multiplicity ( i.e. integrand ). x axis correspond to k/m and y axis are the integrand function.

• root [4] fun1->Print();

• This shows the parameters of the distribution.

• Par 0 = mu/mass

• Par 1 = T/mass

• Par 2 = eta ( 1 for Fermi stat, -1 for Bose stat ).

• If you like to access the model values, you can try

• root [5] thermal->PrintInfo(0);1~9

• Each one explains what is being printed...

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YPariclesROOT

YThermal

STABLE(12) Ythermal.Primary:

Gamma, pi+ ,pi-,pi0, K+,K-,p ,n ,pbar,nbar, Deuteron , Deuteron b

WEAK (16)Ythermal.Experiment

K0 ,K0b,Lambda,Lambdab, SigmaP Sigma0 SigmaM SigmaPb Sigma0b SigmaMb Cascade0 CascadeM Cascade0b CascadeMb, OMEGA OMEGAb

STRONG Ythermal Strong: the others

M(mesons)<1.5GeV

M(baryons)<2 GeV

This limits the temperature upto which thermal model calculations are trustworthy to Tmax< 185GeV

(<> heavier hadrons is not sufficiently well known)

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Physics Issues

1. Volume correction

2. Finding out the most probable (T, )

3. Particle ratios

4. pi+ pt spectrum

5. Weak-decay feed-down and its reconstruction efficiency

6. Chiral symmetry restoration

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1.Volume correction • Volume correction is adhoc, but may be needed especially when we estimate the

absolute particle density. However there seems to be possible debate on the volume parameter ( PRC 56, 2210, 1997 , ~0.8fm ).

• Change of the volume parameter ruins the predictability of the model. The radius parameters of the particles has 0.3 fm as the the default value as chosen in Phys. Lett. B465, 15-20, 1999.

• Physicswise volume correction can change the relative abundance of particles.

(volume has to be chosen appropriately to simulate the repulsive interactions between hadrons)

• As we turn down the volume correcrtion, the absolute density increases by almost constant factor close to 50% w.r.t the default choice. When we change only the pion volume factor, pion multiplicity almost exclusively increase. Small discrepancy with the red points is due to the volume effect of the other particles.

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All particles with r=0.3fm

pi+,pi-,pi0 with r=0

No volume correction(or ideal gas limit)

Nu

mb

er D

end

isy

charge x mass

pi+

K+ p

(1232)++

pbar

(1232)++b

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2.Finding out the most probable (T, )

• The work of P. BraunMunzinger et al. uses the Chi2/DOF as the measure to find the best choice

for (T, ).

• find the most probable (T, ) for the given set of input data. Also the histograms hChi2_ndf0, hChi2_ndf1,and hChi2_ndf2 shows Chi2/DOF in three different scale.

• As the experimental input, we used the data of ( Phys. Lett. B465, 15-20, 1999 ). But this procedure can be easily modified to any set of measurements.

• For this case, we find T = 157 (MeV) and = 245 (MeV) as the most probable ( though Chi2/DOF is not close to 1 ).

• Experimental reconstruction efficiency as discussed can play a role. (hyperon,decay reconstruction factor, weak decaying neutral meson)

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3.Particle ratios

• Particle densities at freeze-out.

• For the RHIC condition, we used (T,mu) = (0.17,0.01) as used by

P. BraunMunzinger et al.

• As the data analysis further developes, we will be able to conclude on the goodness of the thermal model and these parameters.

pbar p , K+ K-

Note02 : (data?)

K+ K- : small

pbar p ? (stopping?)

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4.+ pt spectrum • Integrated pt spectrum assuming

 1. isotropic fireball  (development in progress )

  2. feed-down from the resonance & higher mass mesons.

• By running the model,

we observe rho,omega,Kshort play the important role to the pi+ multiplicity, and

generate the pair decay spectrum for rho and Kshort

(1/pt dN/dpt distribution with the arbitrary normalization.)

• These plots are generated with the 3 different reconstruction efficiencies.

This will be equivalent to changing the selection cuts for tracks and studying the pt

spectral shape assuming the primary multiplicity and the kinematics are correct

( also we need to assume perfect tracking )

http://www.phenix.bnl.gov/phenix/WWW/p/draft/janebh/ talks/pt/global-hadron-092100/outline_092100.htm

• Kinematic distributions is affected by the hydrodynamic motion and it's likely to be

included in the next release.

• In fact this will be of importance to the high pt particle ( pt > 2 GeV/c ),

where description by the perturbative physics can be claimed.

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Pt ;careful study will be needed to get the proper interpretation ( Weak decay )

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Weak-decay feed-down and its reconstruction efficiency

Weak-decay feed down efficiency can be handled and the macro SetWeakDecayFeedDown.C shows how. We also show the resulting systematics.Particle list reports c tau values for the following particles.

To estimate the potential systematics due to these feed-down, we can vary the reconstruction efficiencies of the daughter particles ( say 0% : SetWeakDecayFeedDownEfficiency0.C,                      50% : SetWeakDecayFeedDownEfficiency50.C,                      and 100% : SetWeakDecayFeedDownEfficiency100.C ).For (T,mu) = (0.17,0.01), we can look at these systematics from the example. N- : negative particles One of the good candidate for the effect on N- is Kshort. p,pbar is affected from the feed-down of the hyperons.The effect is less drastic than the lower energies at CERN and AGS. At AGS and CERN, mu_B is relatively big and the consequential mu_S is also relatively big. In the scheme of hadron thermal model, the abundance of the multi-strange antibaryon is explained by this big mu_S.

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Chiral symmetry restoration

• If hadro-chemical transition occurs at fairly high Temperature ( baryon density is not that high at RHIC ), there might be some modification in particle properties. • ThermalChiralSymmetryRestoration.C shows how we can change the mass of the particles and study the effect.

nominal mass excitation

mass reduction by 20%

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Furture Work

• Address Physics Issues

• Developement of Ythermal including hydrodynamic model

> Prediction for the kinematic spectrum

• Implementation of the decay into lepton channels