Time evolution of QGP via photon observables
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TIME EVOLUTION OF QGP VIA PHOTON OBSERVABLES
PRESENTER: IMRE MÁJER – EÖTVÖS UNIVERSITY PHYSICS STUDENT SUPERVISOR: MÁTÉ CSANÁD – DEPARTMENT OF ATOMIC PHYSICS
ZIMÁNYI WINTER SCHOOL 2011
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RHIC MILESTONES
New, strongly interacting medium(Nucl.Phys., A757:184–283, 2005)
Collective behaviour (Phys.Rev.Lett., 91:182301, 2003)
Perfect fluid hydro(Phys.Rev.Lett., 98:172301, 2007)
Quark degrees of freedom(Phys.Rev.Lett. 98, 162301,2007)
Direct photon data, time evolution can be analyzed(Phys.Rev.Lett., 104:132301, 2010)
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TIME DEVELOPMENT - SPECTRA
freeze-out
expansion, cooling
Photon spectrum: information on the time development
Thermalization time Equation of state Initial
temperature
• Freeze-out time• Freeze-out temperature• Expansion at freeze-out
Hadronic spectrum information on the
final state
thermalization
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SPECTRA INFORMATION
Physical quantities we can get from different spectra: Hadronic spectra
Freeze-out temperature () Freeze-out time () Freeze-out expansion velocities (, , , , )
Photon spectra Equation of state () Thermalization time () Initial temperature ()
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PHYSICAL QUANTITIES
1.• Source function for a particle type • Unknown functions (, , , )
2.• Hydrodynamic model• We get the unknown functions (, , , )
3.• Observables: spectra • Free parameters are the physical quantities (eg. , , , …)
4.• Comparing to data• Fitting the spectra free parameters
How do we get the physical quantities describing the system?
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The probability of particle creation at a given place and time with a given momentum:
Photons: bosons Bose-Einstein distribution
– Cooper-Frye factor gives the integration measure
Integrate the source function: invariant momentum distribution
One of the most important observable!
1. SOURCE FUNCTION 2. 3. 4.
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Relativistic hydro for perfect fluids:
Equation of state ()
Assuming an avarage constant
Ideal solution: Relativistic
1+3 dimensional
Realistic (eg. ellipsoidal) geometry
Anisotropic Hubble-flow ( const.) after some time
Accelerating at the start of the time development
1. 2. HYDRODYNAMICS 3. 4.
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Solutions Basic properties Equation of state
Landau-Khalatnyikov 1+1D, accelerating, implicit
Hwa-Björken1+1D, non-accelerating,
estimate of the initial energy density
Csörgő, Nagy, CsanádPhys.Rev.C77:024908, 2008
1+1D / 1+3D spherical symmetry, accelerating
Bialas et al.Phys. Rev. C76, 054901
(2007).
1+1D, Between Hwa-Björken and Landau-Khalatnyikov
Csörgő, Csernai, Hama, Kodama
Heavy Ion Phys., A21:73–84, 2004
1+3D, ellipsoidal symmetry, non-accelerating
Some known solutions:
1. 2. HYDRODYNAMICS 3. 4.
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The examined solution (Csörgő et al., 2004): Relativistic, 1+3 dimensional
Scaling parameter – ellipsoidal symmetry:
Arbitrary function of the scaling parameter: is the good temperature gradient
Hubble-flow:
Non-accelerating:
1. 2. HYDRODYNAMICS 3. 4.
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3D:
2D:
Fourier series of the azimuthal distribution function
Inverse Fourier-transform transverse momentum distribution and elliptic flow
Bose-Einstein correlation:
correlation radii (HBT radii)
– rapidity()
1. 2. 4.3. OBSERVABLES
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Parameter Symbol Value Type
Freeze-out temperature MeV fixed by hadron spectrum
Freeze-out time fm/c fixed by hadron spectrum
Excentricity fixed by hadron spectrum
Transverse expansion fixed by hadron spectrum
Longitudinal expansion fixed by hadron spectrum
Compressibility fitted
Initial time fm/c acceptable interval
Number of datapoints
Fitted parameters
Degrees of freedom NDF
Chi square
Confidence rate
Properties of the fit:
Fixed by hadron spectrum fit: (M. Csanád – M. Vargyas: Eur.Phys.J., A44:473–478, 2010.)
1. 2. 3. 4. COMPARING TO DATA
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Fitting to 0-92% centrality PHENIX data:
EoS from photon spectra:
PHOTON MOMENTUM DISTRIBUTION
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Fixed from hadronic observables
Determined from photon spectra
With and , hydro gives us the initial temperature:
𝑇 𝑖>507±12MeV
QGP INITIAL TEMPERATURE
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Elliptic flow from PHENIX data [arXiv:1105.4126]: Many models fail
Non-hydro effects from 2 GeV
Sign change possible
PHOTON ELLIPTIC FLOW
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Rout/Rside = 1 for hadrons
Rout Rside here, different time evolution!
BOSE-EINSTEIN CORRELATIONHBT radii at freeze-out time ():
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FURTHER ANALYSISOther microscopic models: additional scaling with needed
with (or if velocity is temperature dependent)
Our model already Examined with use of additional minor change, systematic error
N=0
N=1
N=2
N=3
𝒄𝒔=𝟎 .𝟑𝟔 ±𝟎 .𝟎𝟐𝒔𝒕𝒂𝒕 ±𝟎 .𝟎𝟒𝒔𝒚𝒔
𝑻 𝒊>𝟓𝟎𝟕±𝟏𝟐𝒔𝒕𝒂𝒕±𝟗𝟎𝒔𝒚𝒔MeV
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SUMMARY 1+3D realistic relativistic hydro model without acceleration
Calculated , and HBT radii for photon source
Fitted with freeze-out parameters fixed by hadron solution
Important new parameters: EoS and initial temperature:
MeV
Corresponds to other theories (R. A. Lacey, A. Taranenko., PoS, CFRNC2006:021, 2006: ; A. Adare et al., Phys.Rev.Lett., 104:132301, 2010: )
𝒄𝒔=𝟎 .𝟑𝟔 ±𝟎 .𝟎𝟐𝒔𝒕𝒂𝒕 ±𝟎 .𝟎𝟒𝒔𝒚𝒔
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THANK YOU FOR YOUR ATTENTION!
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The exact analitic result of the second order Gaussian approximation:
are the coefficients of the first kind modified Bessel-functions
THE ANALYTIC SOLUTION
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Sensitivity to EoS
Small dependence on initial time
DEPENDENCIES OF N1(pt)
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DEPENDENCIES OF v2(pt)
Initial time
EoS
Eccentricity
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SIGN CHANGE OF v2 AT LOW pt-S
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AZIMUTHAL DEPENDENCE OF HBT RADII