重イオン衝突実験と 非ガウスゆらぎ

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重イオン衝突実験と 非ガウスゆらぎ. 北沢正清 ( 阪 大理). MK, Asakawa , Ono, in preparation. 松本研究会 , 2013/Jun./22. 北沢の生い立ち . 信州新町 小2~小6. 長野市 中、高. 大町市 誕生~ 1.5 歳. 南箕輪村 1.5 歳~小1. 飯田市 実家. 茨城県へ 大学. Beam-Energy Scan. T. Hadrons. Color SC. m. 0. Beam-Energy Scan. STAR 2012. high. beam energy. T. - PowerPoint PPT Presentation

Transcript of 重イオン衝突実験と 非ガウスゆらぎ

QCD

MK, Asakawa, Ono, in preparation, 2013/Jun./22

1.51.5 Beam-Energy Scan 0Color SCmTHadrons Beam-Energy Scan 0Color SCmTHadronshighlowbeam energy

STAR 2012 Fluctuations Observables in equilibrium are fluctuating.P(N)VNN

5 Fluctuations P(N)VNN

Skewness:Variance:

Kurtosis:

Observables in equilibrium are fluctuating.6 Event-by-Event Analysis @ HIC Fluctuations can be measured by e-by-e analysis in experiments.

DetectorV Event-by-Event Analysis @ HIC Fluctuations can be measured by e-by-e analysis in experiments.

Detector

STAR, PRL105 (2010) Fluctuations Fluctuations reflect properties of matter.Enhancement near the critical pointStephanov,Rajagopal,Shuryak(98); Hatta,Stephanov(02); Stephanov(09);Ratios between cumulants of conserved charges Asakawa,Heintz,Muller(00); Jeon, Koch(00); Ejiri,Karsch,Redlich(06)Signs of higher order cumulantsAsakawa,Ejiri,MK(09); Friman,et al.(11); Stephanov(11)

Fluctuations Free Boltzmann Poisson

10 Fluctuations Free Boltzmann Poisson

RBC-Bielefeld 0911 Central Limit Theorem Large system GaussianHigher-order cumulants suppressedas system volume becomes larger?CLT Central Limit Theorem :Gaussian

CLT

Cumulants are nonzero.Their experimental measurements are difficult.In a large system,

Proton # Cumulants @ STAR-BES No characteristic signals onphase transition to QGP nor QCD CP

STAR,QM201214 Charge Fluctuations @ STAR-BES

STAR, QM2012No characteristic signals onphase transition to QGP nor QCD CP

Charge Fluctuation @ LHC ALICE, PRL110,152301(2013)D-measureD ~ 3-4 HadronicD ~ 1 Quarkis not equilibrated at freeze-out at LHC energy!

LHC:significant suppressionfrom hadronic value

Dh Dependence @ ALICE ALICEPRL 2013tzDhrapidity acceptane Dissipation of a Conserved Charge

Dissipation of a Conserved Charge

Time Evolution in HIC

Quark-Gluon PlasmaHadronizationFreezeout

Time Evolution in HIC

Pre-EquilibriumQuark-Gluon PlasmaHadronizationFreezeout

Time Evolution in HIC

Pre-EquilibriumQuark-Gluon PlasmaHadronizationFreezeout

Dh Dependence @ ALICE ALICEPRL 2013tzDhHigher-order cumulants as thermometer?HotQCD,2012rapidity acceptaneDh dependences of fluctuation observablesencode history of the hot medium!

Conserved Charges : Theoretical Advantage Definite definition for operatorsas a Noether currentcalculable on any theoryex: on the lattice

Conserved Charges : Theoretical Advantage Definite definition for operatorsSimple thermodynamic relationsas a Noether currentcalculable on any theoryex: on the latticeIntuitive interpretation for the behaviors of cumulants

ex: Fluctuations of Conserved Charges tzDyUnder Bjorken expansionVariation of a conserved charge in Dh is slow, since it is achieved only through diffusion.NQDhPrimordial values can survive until freezeout.The wider Dh, more earlier fluctuation.Asakawa, Heintz, Muller, 2000Jeon, Koch, 2000Shuryak, Stephanov, 2001 and < dNp2 > @ LHC ?

should have different Dh dependence.

@ LHC ?

Left(suppression)How does behave as a function of Dh?

Right(hadronic)or

Hydrodynamic Fluctuations Diffusion equation

Stochastic diffusion equation

Landau, Lifshitz, Statistical Mechaniqs IIKapusta, Muller, Stephanov, 2012 Hydrodynamic Fluctuations Diffusion equationStochastic diffusion equation

Landau, Lifshitz, Statistical Mechaniqs IIKapusta, Muller, Stephanov, 2012

Conservation LawFicks Law Fluctuation-Dissipation Relation

Stochastic forceLocal correlation (hydrodynamics)

Equilibrium fluc.

Dh Dependence

Initial condition:

Translational invariance

initialequilibriumequilibriuminitialShuryak, Stephanov, 2001

Dh Dependence Initial condition:

Translational invariance

initialequilibrium

equilibriuminitialShuryak, Stephanov, 2001

Non-Gaussian Stochastic Force ?? Local correlation (hydrodynamics)Equilibrium fluc.

Stochastif Force : 3rd order

Caution!

diverge in long wavelength No a priori extension of FD relation to higher orders Caution! Theoremcf) Gardiner, Stochastic MethodsHydrodynamicsLocal equilibrium with many particlesGaussian due to central limit theoremMarkov processcontinuous variableGaussian random force

diverge in long wavelength No a priori extension of FD relation to higher orders Three NONs Non-Gaussian

Non-critical

Non-equilibriumPhysics of non-Gaussianity in heavy-ioncollisions is a particular problem.Non-Gaussianitiy is irrelevant in large systemsFluctuations are notequilibratedfluctuations observed so fardo not show critical enhancement Diffusion Master Equation Divide spatial coordinate into discrete cells

probability

Diffusion Master Equation Divide spatial coordinate into discrete cells

Master Equation for P(n)

x-hat: lattice-QCD notationprobabilitySolve the DME exactly, and take a0 limit

No approx., ex. van Kampens system size expansion

Solution of DME

Appropriate continuum limit with ga2=Dinitial

1st

Deterministic part diffusion equationat long wave length (1/a