Recent Results on the Quark Coalescence Model
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Károly Ürmössy and Tamás S. Bíró MTA KFKI RMKI, ELTE Fürstenfeld 15-17 April 2009 Recent Results on the Quark Coalescence Model
description
Károly Ürmössy and Tamás S. Bíró MTA KFKI RMKI , ELTE Fürstenfeld 15-17 April 2009. Recent Results on the Quark Coalescence Model. Content. Thermalized Hadrons and Quarks at RHIC ? Hadronisation by Coalescence, quasi-particles of the quark-gluon matter Comparison with pQCD - PowerPoint PPT Presentation
Transcript of Recent Results on the Quark Coalescence Model
Károly Ürmössy and Tamás S. BíróMTA KFKI RMKI, ELTE
Fürstenfeld 15-17 April 2009
Recent Results on the Quark Coalescence Model
Content
• Thermalized Hadrons and Quarks at RHIC ?
• Hadronisation by Coalescence, quasi-particlesof the quark-gluon matter
• Comparison with pQCD • Why power-laws?
Intro: From thermal quarks to hadron spectra
The detector sees - Cooper-Fry formula
sconstraint)(4 iiqi
iH pEfpdEF
22
3
1
tt
tt
pmm
pvmE
EFupFdpEpd
dN
Instant hadronisation at propertime τ, radial flow v║r (Blastwave)
Ansatz:
Co-moving Energy:
Ansatz for the Transverse Spectra
In the co-moving system the energy is minimal at the maximal yield:
The value of the maximum is proportional to the mass :
Flow
Max:
Antiproton spektrum (RHIC)
Adler S S, et al. (PHENIX Collaboration) 2004 Phys. Rev. C69 034909
PT [GeV]
dN/p
Tdp
T
Thermal hadrons at RHIC
(Qmesons – 1)*2 = 3*(Qbaryons - 1)
Vflow = 0.42 – 0.55Thermal up to 6-10 GeV
Thermalisation at the Level of Quarks?
→ Quarks, hadrons have power-law asymptotics→ The hadron power scales with the quark number:
(Qmesons – 1)*2 = 3*(Qbaryons - 1)
jiqqH qcpEfpEfEF ,2211 ,
PpppEqqc iiiiji
jiji
,,,,
Instant hadronisation → no time evollution of the fqs during the hadronization
11
1
1111
q
n
QnqH T
p
n
q
T
pQnpfpF
IF for pT » m
THENcoalescence constraint quark disp no p pick-up from the plasma
Non-Extensivity q Scaling
Qquark - 1 = (Qmeson – 1)2 = 3(Qbaryon - 1)
T.S.Biro, K. Ürmössy: Pions and kaons from stringy quark matter arXiv:0812.2985v1 [hep-ph]
Tslope - m Scaling
Tslope = T0 + (Qhadron - 1)mT.S.Biro, K. Ürmössy: Pions and kaons from stringy quark matter arXiv:0812.2985v1 [hep-ph]
22
22
ii
H
mnPE
MPE
)()()( 11 nnHH EfEfEF
Quasi-particles at Low pT
Simple product does not work! mi << M.
nHqHH
Hq
nEfEF
nEE
P
We need something like
Let’s Try Quarks With Mass-distribution!
)(*)( mMgmg
J Zimányi et al 2005 J. Phys. G: Nucl. Part. Phys. 31 711-718
have a maximum around M/2 for mesons
To achieve that
MmqPpmgEfpddmEF
mgEfEf
ijiiiiiiH
q
,3
,
Power-law quasi-particles, with distrbuted mass:
T. S. Biró, P. Lévai, P. Ván, J. Zimányi: PRC,vol.75, Issue 3, id. 034910, 03/2007.
2
20
20 1
m
m
m
mmg
Coalescence - pQCD
T. S. Bíró, G. G. Barnaföldi, K. Ürmössy: J. Phys. G: Nucl. Part. Phys. 35 044012, 2008.
Why Power Laws?Superstatistics
C. Beck, E. Cohen, H. L. Swinney: Phys. Rev. E 72, 056133 (2005)
Tamás Bíró’ Talk
Kinetic model
Langevin problem:
Kinetic modelThe equivalent Fokker-Planck problem:
To get our power-law distribution as stacionary sollution
Let G, D depend on p through the energy!
we have to enter a linear spectral slope T(E)
Kinetc model
into the equation for G and D.
All D(E) – G(E) pairs result in our power-law distribution.
T. S. Biró, G. Györgyi, A. Jakovác, G. Purcsel 2005 J.Phys.G:Nucl.Part.Phys. 31 S759-S763
Then we know what stochastic equation drives the quasi-particles of the plasma.
Non-additive Energy Composition
T. S. Biró, G. Purcsel 2008 Phys. Lett A 372 1174
Equilibration
Variation and energy distribution:
konst
The termodynamic temperature is the intercept of the spectral slope:
Conclusion
• There can be thermalisation at RHIC at the quark level, because: Under 6-8 GeV the power of Mesonic to Baryonic spectra goes as 2 to 3.
• T(hadron) scales with m linearly: T(m) = To + (q - 1)m
• Our calculations are in qualitative agreementwith pQCD calculations
• We use power-law distributed quarks because:pQCD, Addition Rules, T fluctuations,Fokker-Planck with D(E)
Refrences
T. S. Bíró, G. G. Barnaföldi, K. Ürmössy: Pion and Kaon spectra from distributed mass quark matter, J.Phys.G: Nucl. Part. Phys. 35044012 (6pp) doi: 10.1088/ 0954-3899/ 35/ 4/ 044012, 2008.
T. S. Bíró, K.Ürmössy: From quark combinatorics to spectral coalescence, The European Physical Journal, Special Topics, Volume1 55, Number 1/ March, 2008.
T.S.Biro, K. Ürmössy: Pions and kaons from stringy quark matterarXiv:0812.2985v1 [hep-ph] Submitted: 16 Dec 2008.
Tamas S. Biro, Gabor Purcsel and Karoly Urmossy: Non-Extensive Approach to Quark MatterarXiv:0812.2104 Submitted: December 2008.
)(~
~)(
3
222
3
q
qqC
Coalescence Factor
Lattice EOS – Mass Distribution
T. S. Biró, P. Lévai, P. Ván, J. Zimányi: PRC,vol.75, Issue 3, id. 034910, 03/2007.
Lattice-EOS with u, d, s Quarks (μ=0)
Thermodynamic Consistency
T. S. Biró, P. Lévai, P. Ván, J. Zimányi: J. Phys. G: Nucl. Part. Phys. 32 No 12 (Dec. 2006) S205-S212.
μ and T Independent Mass-distribution from Lattice EOS
T. S. Biró, A. László, P. Ván: http://arxiv.org/abs/heph-ph/0612085v1
Mass-Distribution from the Inversion of the Meier-transform
T. S. Biró, A. László, P. Ván: http://arxiv.org/abs/heph-ph/0612085v1
T. S. Biró, P. Lévai, P. Ván, J. Zimányi: PRC,vol.75, Issue 3, id. 034910, 03/2007.
μ, T Independency→Mass-Gap
