thermal fits of hadron yields and the qcd phase diagram - talk...

Thermal fits of hadron yields and the QCD phasediagramTalk from Gregor Dentinger

8.11.2012 | Gregor Dentinger | 1

Topics

Heavy-Ion Collisions

Historical Meaning: Perturbation Theory vs Statistical Physics

Thermal fits

Phase diagram


Basic notation

I ’High-Energy’: Energy per nucleon� nucleon massI Spectators and ParticipantsI Rapidity and pseudorapidity


Why do we use high center of mass energies?

Figure: Particle production in dependence of√

sNN [Andronic, 2012]


Heavy Ion collision participants

I Difference between participants and the whole nucleusI All data has been taken from central collision

Figure: Participants and Spectators from [www.hep.lu.se]


Rapidity and pseudorapidity

y =12

ln(E + p‖)(E − p‖)

= arctanh(v‖) (1)

Rapidity is a simplification for dealing with relativistic energies.I replace velocity with rapidityI additive under Lorentz boosts along the beam axisI not an observable

η =12

ln(|p| + p‖)(|p| − p‖)

= − ln(tan θ2

) (2)

I observable scattering angle θI for low hadron masses mH → 0, η = y

Note: η ' 7 means a scattering angle of 0.1 degrees, i.e. close to the beam!


Rapidity and pseudorapidity distribution

dNdηd2p⊥

=|p|E

dNdyd2p⊥

(3)

for midrapidity with y ≈ η ≈ 0

dNdηd2p⊥

∣∣∣∣η=0

=p⊥m⊥

dNdyd2p⊥

∣∣∣∣y=0

(4)


Experimental reference

Figure: Rapidity and pseudorapidity distribution at√

sNN = 200GeV [iopscience.iop.org][BRAHMS, 2004]


Historical: One Pion production

Started with Landau in 1950 - statistical concepts for hadronic collision analysis.Probability S for a state with n particles (also used by Fermi):

S(n) =[

V(2π)3

](n−1) dQ(W )dW

(5)

With W := total energy of the system,dQdW

:= number of states per unit energy and

V := volume of interaction.The n-1 corresponds to n-1 independent momenta.


Probability for states with 2 and 3 particles

In this case we use W = Tkin and V = V0 (not Lorentz contracted↔ low energy)

Q2 =∫

d3q1d3q2θ(

Tkin −q21

2mN− q

22

2mN

)δ(3)(q1 + q2)

=∫

d3q1θ(

Tkin −q21mN

)= 4π

∫ √TkinmN0

q21dq1

=4π3

(TkinmN )3/2

(6)


Two and three particle probability

S(2) =[

V(2π)3

]1 dQ2dTkin

=Vm3/2N

4π2T 1/2kin

(7)

For three particle production one can find

S(3) =V 2m3/2N m

3/2π (∆Tkin)

2

32√

2π3(8)

S(3)S(2) + S(3)

≈ S(3)S(2)

≈ Vmπ8√

2π(Tkin −mπ)2 (9)


One pion model proved

S(3)S(2)

=1

6√

2

(Tkinmπ− 1)2

(10)

I compared to 345MeV beam energy data (proton energy 1950 at Berkeley)I good agreement with dataI statistical idea works very wellI for high energies statistical consideration can be replaced with

thermodynamic arguments


Canonical Ensembles

I Grand canonical:I system depends on µ (for sort of particle), V and TI system can exchange particles and internal energyI in equilibrium with an external reservoir

I Canonical:I system described with N, V and TI only internal energy may exchanged

I Micro canonical:I system with parameters of N, V and internal energyI isolated system


The thermal model

Ni = giV∫

d3p(2π)3

[exp

(Ei (p)− µi

T

)+ �]−1

(11)

with Ni multiplicity for the ith sort of particle, gi spin degeneracy, V fireball volume,µi chemical potential, Ei total energy, T temperature and � variable for fermions(+1) or bosons (-1).

I µi contains all chemical potentials for strong interacting matter⇒ µi = µbBi + µsSi + µI3 Ii + µCCi

I conservation for baryon number, strangeness, isospin and charm reduces thedegrees of freedom in equation (11) to three:⇒ parameters left: µb, T and V


Thermal fit

Calculation for thermal fits with minimizing

χ2 =n∑

k=1

(Rexpk − Rmodelk

)2σ2k

(12)

with Rexpk k-th measured ratio, σk corresponding error and Rmodelk the theoretical

result for the same ratio

I using grand canonical ensemble for the thermal modelI Rk will be replaced with the hadron yields (determine T, µb and V) or hadron

ratios (no V)


A thermal fit

Figure: Thermal fit from [Andronic et al., 2006]


Canonical suppression

Figure: Suppression factor[Andronic et al., 2006]

For low energies strangeness carry-ing particles are suppressed by anenergy depending factor

nCi ,S = nGCi ,S

IsI0

(13)


A thermal fit

Figure: Thermal fit from [Andronic et al., 2006]


More thermal fits

Figure: Thermal fit from [Andronic et al., 2006] [Andronic et al., 2012]


Energy dependence of T, µb

Figure: Energy dependence of T and µb [Andronic et al., 2006]


Values for T and µb

Saturation for Tsat ∼ 164MeV

Tchem =Tsat

1 + exp(2.60− ln

(√sNN [GeV ]

)/0.45

) (14)For µb the empirical parametrization is

µbchem =1303MeV

1 + 0.286√

sNN [GeV ]. (15)


The horn

I the horn is well described in thethermal model[A. Andronic et al., 2009]

I found at about 10GeVI close to the saturation

temperature


The horn structure in K +/π+ ratio with anothermodel

Figure: I - pure initial hardroniccalculation; II - initial partonic calculationfor higher

√sNN [Nayak et al., 2010]

I transport modelI calculation with pure hardronic

assumption does not fit with theexperimental data

I at about 10GeV partonicformation (according to thismodel)


LHC data

Figure: All data fit [Andronic et al., 2012]


What do we see in this picture?

I The ’all data fit’ is good for single strange baryons and also for mesonsI very poor for multi-strange baryonsI underpredicted multi-strange baryons in all thermal fitsI new data implies a much lower value for T than in lower energy experimentsI nothing like a saturation

⇒ what is wrong?⇒ some models showed annihilation at the phase boundary for baryons⇒ fit without p, p̄ yields⇒ annihilation for Λ, Ξ and Ω is not observed?!


Fit with all data vs fit without p, p̄ yields

Figure: Left: thermal fit with all data; right: fit without considering p, p̄ [Andronic et al., 2012]


Conclusions from fit without p, p̄

I overall better agreement with ALICE data⇒ compare χ2

I proton is about 1.4 times below the fitI excellent value for temperature, agrees with all low energy calculations


QCD phase diagram

Figure: Phase diagram [Andronic et al., 2006]8.11.2012 | Gregor Dentinger | 28

What to say about this phase diagram?

I only experimental connection to the phase diagramI the chemical freeze-out describes a snapshot of the time evolution of the hot

fireball created in the collisionI saturation in T leads to a connection to the QCD phase boundaryI probably the chemical freeze-out temperature is the hadronization

temperature


Summary: Thermal fits

I the fits with the thermal model work, for low energies and at high energieswithout respect pp̄, really well

I one can speak of a phase boundary temperature (saturation at (164±4)MeV)I some kind of experimental evidence for the QGP (horn)?I only way to put data on the phase diagramI chemical freeze-out is the earliest part in timeline which is measuredI thermal fit with LHC data is not good, but needs further understanding


Resources

A. Andronic; 2012; The study of quark-gluon matter in high-energynucleus-nucleus collisions; arXiv:1210.8126v1

A.Andronic, P.Braun-Munzinger, J.Stachel; 2006; Hadron production in centralnucleus-nucleus collisions at chemical freeze-out; Nucl.Phys.A772:167-199,2006 -arXiv:nucl-th/0511071

A.Andronic, P.Braun-Munzinger, J.Stachel; 2009; Thermal hadron production inrelativistic nuclear collisions: the hadron mass spectrum, the horn, and the QCDphase transition; Phys.Lett.B673:142,2009 - arXiv:0812.1186

http:

//www.hep.lu.se/staff/tydesjo/physics/theses/lichtml/node6.html

http://iopscience.iop.org/0295-5075/61/6/736


http://www.hep.lu.se/staff/tydesjo/physics/theses/lichtml/node6.htmlhttp://www.hep.lu.se/staff/tydesjo/physics/theses/lichtml/node6.htmlhttp://iopscience.iop.org/0295-5075/61/6/736

Resources

BRAHMS Collaboration; 2004; Charged meson rapidity distributions in centralAu+Au collisions at

√sNN = 200 GeV; Phys.Rev.Lett. 94 (2005) 162301 -

arXiv:nucl-ex/0403050

A. Andronic, P. Braun-Munzinger, K. Redlich, J. Stachel; 2012; The statisticalmodel in Pb-Pb collisions at the LHC; arXiv:1210.7724

Jajati K. Nayak, Sarmistha Banik and Jan-e Alam; 2010; The horn in the kaon topion ratio; Phys. Rev. C 82 (2010)024914 - arXiv:1006.2972

P. Braun-Munzinger, J.Stachel; 2011; Hadron Production in Ultra-relativisticNuclear Collisions and the QCD Phase Diagram: an Update; arXiv:0911.4806


Time left? Volume dependence?

For the LHC energy, thevolume is highly increased.The fits are still good. Thisindicates a fixed densityfor the chemical freeze out.[Braun-Munzinger et al., 2011]


Heavy-Ion CollisionsHistorical Meaning: Perturbation Theory vs Statistical PhysicsThermal fitsPhase diagram

thermal fits of hadron yields and the qcd phase diagram - talk...

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