Rapidity window and centrality dependences of higher order

Rapidity window and centrality dependences of higher order cumulants Masakiyo Kitazawa (Osaka U. ) MK, Asakawa, Ono, Phys. Lett. B 728, 386 -392 (2014) Sakaida, Asakawa, MK, PRC 90, 064911 (2014) MK, ar. Xiv: 1505. 04349, Nucl. Phys. A, in press HIC for FAIR workshop, Frankfurt, 30/Jul. /2015

In “haiku”, a Japanese short style poem, a poet wrote… Even on one blade of grass the cool wind lives Issa Kobayashi 1814 一本の草も涼風宿りけり 小林一茶

Physicists can feel hot early Universe 13 800 000 years ago in tiny fluctuations of cosmic microwave

Physicists can feel the existence of microscopic atoms behind random fluctuations of Brownian pollens A. Einstein 1905

Feel hot quark wind behind fluctuations in relativistic heavy ion collisions 2010 -

Feel hot quark wind behind fluctuations in relativistic heavy ion collisions 2010 -

Outline 1. A poem 2. Electric charge fluctuation @ ALICE 3. Thermal blurring in momentum-space rapidity Ohnishi+, in preparation 4. Dh dependences of higher order cumulants MK, Asakawa, Ono, PLB(2014); MK, NPA(2015) 5. Effect of global charge conservation Sakaida, Asakawa, MK, PRC(2014)

Electric charge fluctuations @ ALICE

Charge Fluctuation @ LHC ALICE, PRL 110, 152301(2013) hadronic D-measure STAR • D ~ 3 -4 Hadronic • D ~ 1 -1. 5 Quark Suppression v ic n o r d a h m o r f alue at LHC energy! is not equilibrated at freeze-out at LHC energy!

Fluctuations and Elemental Charge Asakawa, Heinz, Muller, 2000 Jeon, Koch, 2000 Ejiri, Karsch, Redlich, 2005 Free Boltzmann Poisson

Shot Noise e* charge of quasi-particles Total charge Q:

Shot Noise e* charge of quasi-particles Superconductors with Cooper Pairs Jehl+, Nature 405, 50 (2000) Higher order cumulants: doubled! Fractional Quantum Hall Systems Saminadayar+, PRL 79, 2526 (1997) 3 rd order: ex. Beenakker+, PRL 90, 176802(2003) up to 5 th order: Gustavsson+, Surf. Sci. Rep. 64, 191(2009)

Various Contributions to Fluctuations p Initial fluctuations p Effect of jets Enhance p Negative binomial (? ) Enhance to Poisson p Final state rescattering p Coordinate vs pseudo rapidities p Particle miss. ID Enhance to Poisson MK Enhance to Poisson Ono, Asakawa, PRC(2013) p Efficiency correction Enhance to Poisson p Global charge conservation Suppress Sakaida, Asakawa, MK, PRC(2014) The suppression is most probably a consequence of the small fluctuation in deconfined medium.

Dh Dependence @ ALICE PRL 2013 t Dh z Same information as rapidity window p 2 particle corr. : p Balance function

Dh Dependence @ ALICE PRL 2013 has to be a constant in equil. medium Fluctuation of NQ at ALICE is not the equilibrated one. rapidity window

Dh Dependence @ ALICE PRL 2013 Dh dependent thermometer? large small rapidity window

Time Evolution of Fluctuations Quark-Gluon Plasma Hadronization Freezeout Fluctuations continue to change until kinetic freezeout!!

Time Evolution of Fluctuations Quark-Gluon Plasma Hadronization Freezeout Variation of a conserved charge is achieved only through diffusion. The larger Dh, the slower diffusion

Conversion of Rapidities Quark-Gluon Plasma Hadronization Freezeout detector conversion from coordinate-space to momentum-space rapidities

Conversion of Rapidities Quark-Gluon Plasma Koch, 0810. 2520 Hadronization Freezeout detector conversion from coordinate-space to momentum-space rapidities

Dh Dependence @ ALICE PRL 2013 Dh dependent thermometer? large small Dh dependences of fluctuation observables Higher-order cumulants as thermometer? encode history of the hot medium!

Dh Dependence @ ALICE PRL 2013 Dh dependent thermometer? large small Even on one blade of gras the cool wind lives Dh dependences of fluctuation observables Higher-order cumulants as thermometer? encode history of the hot medium!

Thermal blurring in momentum-space rapidity

Conversion of Rapidities Quark-Gluon Plasma Hadronization Freezeout detector conversion from coordinate-space to momentum-space rapidities “Thermal blurring”

Thermal distribution in h space nucleon pion Blast wave squeezes the distribution in rapidity space Y. Ohnishi, MK, + in preparation • pions • nucleons • blast wave • flat freezeout surface

Thermal distribution in h space nucleon • pions • nucleons width pion Y. Ohnishi, MK, + in preparation • blast wave • flat freezeout surface

Centrality Dependence More central lower T larger b Smaller blurring Is the centrality dependence understood solely by thermal blurring at kinetic f. o. ?

Centrality Dependence Assumptions: • Centrality independent cumulant at kinetic f. o. • Thermal blurring at kinetic f. o. p Centrality dep. of blast wave parameters may not be large enough to describe the one of Ø Existence of another physics having centrality dep. Ø More accurate data is desirable!!

Rapidity Window Dependences of Higher Order Cumulants

<d. NB 2> and < d. Np 2 > @ LHC ? should have different Dh dependence. NEW normalization!

<d. NB 2> and < d. Np 2 > @ LHC ? should have different Dh dependence. Baryon # cumulants are experimentally observable! MK, Asakawa, 2012

<d. NQ 4> @ LHC ? How does suppression behave as a function of Dh? or enhancement

Hydrodynamic Fluctuations Landau, Lifshitz, Statistical Mechaniqs II Kapusta, Muller, Stephanov, 2012 Stochastic diffusion equation Stephanov, Shuryak, 2001 Markov (white noise) + continuity Fluctuation of n is Gaussian in equilibrium Gaussian noise cf) Gardiner, “Stochastic Methods”

How to Introduce Non-Gaussianity? Stochastic diffusion equation p Choices to introduce non-Gaussianity in equil. : p n dependence of diffusion constant D(n) p colored noise p discretization of n

How to Introduce Non-Gaussianity? Stochastic diffusion equation p Choices to introduce non-Gaussianity in equil. : p n dependence of diffusion constant D(n) p colored noise p discretization of n our choice Fluctuations measured in REMARK: HIC are almost Poissonian.

A Brownian Particles’ Model Freezeout ① Describe time evolution of Brownian particles exactly ② Obtain cumulants of particle # in Dh Time evolution Hadronization (specific initial condition)

10~20 fm mesons baryons time kinetic f. o. chem. f. o. hadronize Baryons in Hadronic Phase e k i l e v a h e b s Baryon r e t a w n i s n e l l o p n a i n w o Br

Diffusion Master Equation MK, Asakawa, Ono, 2014 MK, 2015 Divide spatial coordinate into discrete cells probability

Diffusion Master Equation MK, Asakawa, Ono, 2014 MK, 2015 Divide spatial coordinate into discrete cells probability Master Equation for P(n) Solve the DME exactly, and take a 0 limit No approx. , ex. van Kampen’s system size expansion

A Brownian Particles’ Model Time evolution Initial Final p Each particle are uncorrelated p A particle moves x x’ with probability P(x-x’) Formula of cumulants

Diffusion + Thermal Blurring Hadronization Kinetic f. o. (coordinate space) Kinetic f. o. (momentum space) p Diffusion and thermal blurring can be treated simultaneously

Net Charge Number Prepare 2 species of (non-interacting) particles Time evolution of Q up to Gauusianity is consistent with the stochastic diffusion equation

Time Evolution in Hadronic Phase Hadronization (initial condition) p Boost invariance / infinitely long system p Local equilibration / local correlation suppression owing to strongly dependent on local charge conservation hadronization mechanism

Time Evolution in Hadronic Phase Time evolution via DME Hadronization (initial condition) p Boost invariance / infinitely long system p Local equilibration / local correlation Freezeout suppression owing to strongly dependent on local charge conservation hadronization mechanism

Dh Dependence at Freezeout Initial fluctuations: 2 nd 4 th parameter sensitive to hadronization

Total Charge Number In recombination model, 6 quarks 6 antiquarks p can fluctuate, while does not.

Dh Dependence: 4 th order MK, ar. Xiv: 1505. 04349 Initial Condition Charcteristic Dh dependences! Cumulants with a Dh is not the initial value.

Dh Dependence: 4 th order MK, ar. Xiv: 1505. 04349 Initial Condition at ALICE baryon #

Dh Dependence: 3 rd order MK, ar. Xiv: 1505. 04349 Initial Condition at ALICE baryon #

4 th order : Large Initial Fluc. MK, ar. Xiv: 1505. 04349 Initial Condition at ALICE baryon #

Dh Dependence @ STAR Figure from Jochen Thäder, Yesterday Non monotonic dependence on Dh ?

Effect of Global Charge Conservation (Finite Volume Effect) Sakaida, Asakawa, MK, PRC, 2014

Global Charge Conservation Conserved charges in the total system do no fluctuate! 1 0

Global Charge Conservation Conserved charges in the total system do no fluctuate! 1 0 An Estimate of GCC Effect Jeon, Koch, PRL 2000; Bleicher, Jeon, Koch (2000)

Diffusion in Finite Volume Solve the diffusion master equation in finite volume Infinite Sys. (No GCC Effect) : Average Diffusion Length : Diffusion Coefficient

Diffusion in Finite Volume Solve the diffusion master equation in finite volume : Average Diffusion Length Infinite Sys. (No GCC Effect) effect of GCC : Diffusion Coefficient suppression only for

Physical Interpretation slide by M. Sakaida : Averaged Diffusion Distance : Diffusion Coefficient : Total Length of Matter Time Passes… Condition for effects of the GCC Effects of the GCC appear only near the boundaries.

Comparison with ALICE Result without initial fluc. with initial fluc. e tim • No GCC effect in ALICE experiments! • Same conclusion for higher order cumulants

Very Low Energy Collisions p Large contribution of global charge conservation p Violation of Bjorken scaling detector Careful treatment is required to interpret fluctuations at low beam energies! Many information should be encoded in Dh dep.

Summary Plenty of information in Dh dependences of various cumulants and those of non-conserved charges, mixed cumulants… With Dh dep. we can explore Øprimordial thermodynamics Ønon-thermal and transport property Øeffect of thermal blurring

Future Studies p Experimental side: Ø rapidity window dependences Ø baryon number cumulants Ø consistency between RHIC and LHC p Theoretical side: Ø rapidity window dependences in dynamical models Ø description of non-equilibrium non-Gaussianity Ø accurate measurements on the lattice p. Both sides: Ø Compare theory and experiment carefully Ø Do not use a fixed Dh cumulant for comparison!!!

The noise is the signal. R. Landauer 1998