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Phenomenology of multi-hadron and jet production in heavy ion collisions at Large Hadron Collider

I.P. Lokhtin

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

The XXII International Workshop «High Energy Physics and Quantum Field Theory» June 24­ July 1, 2015, Samara, Russia


Deconfinement of nuclear matter

F. Karsch, arXiv:0711.0656

Deconfinement of nuclear matter and quark-gluon matter (QGM) formation ­ the prediction of Lattice Quantum Chromodynamics (QCD) for systems with high enough temperature and/or baryon density

2


Study of quark-gluon matter in relativistic heavy ion collisions
SPS (CERN) RHIC (BNL) LHC (CERN)

3


Heavy ion physics at the LHC
2010, 2011: PbPb (sNN = 2.76 TeV); 2012/2013: pPb (sNN = 5.02 TeV); 2015: PbPb (sNN = 5.1-5.5 TeV);... New regime of heavy ion physics with the important role of hard QCD-processes in hot and long-lived quark-gluon medium complementary measurements from ALICE & CMS/ATLAS ALICE ALICE ATLAS ATLAS CMS CMS

ALICE (low-p charged particle tracking, hadron ID, central e, forward (J/), soft ,...) soft probes + selected hard probe

s

CMS/ATLAS (high-pT charged particle tracking, central (J/, Z, W), hard , calorimetric jets...) hard probes + selected soft probes 4


Basic probes of hot and dense quark-gluon matter formation in PbPb collisions at Large Hadron Collider at sNN=2.76 TeV

Hydrodynamical (collective) properties of multi-particle system


Anisotropic flow Two-particle azimuthal correlations ("ridge")

Medium-induced energy loss of hard quarks and gluons ("jet quenching")


Transverse momentum imbalance in jet+jet, +jet, Z+jet production Suppression of hard hadron and jet yields Modification of internal jet structure

Debye screening of colour charge and thermal charmonium production


Specific pattern of quarkonium suppression (J/ , ) Regeneration and anisotropic flow of J/ mesons

5 5


HYDJET and HYDJET++ relativistic heavy ion event generators
HYDJET (HYDrodynamics + JETs) - event generator to simulate heavy ion event as merging of two independent components (soft hydro-type part + hard multi-partonic state, the latter is based on PYQUEN - PYthia QUENched).
http://cern.ch/lokhtin/hydro/hydjet.html
(latest version 1.9)

Original paper: I.Lokhtin, A.Snigirev, Eur. Phys. J. C 46 (2006) 2011

______________________________________________________
HYDJET++ (HYDJET v.2.*) ­ continuation of HYDJET (identical hard component + improved soft component including full set of thermal resonance production).
http://cern.ch/lokhtin/hydjet++
(latest version 2.2)

Original paper: I.Lokhtin, L.Malinina, S.Petrushanko, A.Snigirev, I.Arsene,
K.Tywoniuk, Comp. Phys. Comm. 180 (2009) 779

6


HYDJET++ (soft component): physics frames
Soft (hydro) part of HYDJET++ is based on the adapted FAST MC model: Part I: N.S.Amelin, R.Lednisky, T.A.Pocheptsov, I.P.Lokhtin, L.V.Malinina, A.M.Snigirev, Yu.A.Karpenko, Yu.M.Sinyukov, Phys. Rev. C 74 (2006) 064901 Part II: N.S.Amelin, R.Lednisky, I.P.Lokhtin, L.V.Malinina, A.M.Snigirev, Yu.A.Karpenko, Yu.M.Sinyukov, I.C.Arsene, L.Bravina, Phys. Rev. C 77 (2008) 014903


fast HYDJET-inspired MC procedure for soft hadron generation multiplicities are determined assuming thermal equilibrium hadrons are produced on the hypersurface represented by a parameterization of relativistic hydrodynamics with given freeze-out conditions chemical and kinetic freeze-outs are separated decays of hadronic resonances are taken into account (360 particles from SHARE data table) with "home-made'' decayer written within ROOT framework (C++) contains 16 free parameters (but this number may be reduced to 9)
7






HYDJET++ (hard component): PYQUEN (PYthia QUENched)
Initial parton configuration PYTHIA6.4 w/o hadronization: mstp(111)=0
Parton rescattering & energy loss (collisional, radiative) + emitted g PYQUEN rearranges partons to update ns strings Parton hadronization and final particle formation PYTHIA6.4 with hadronization: call PYEXEC
Three model parameters: initial maximal QGP temperature T0, QGP formation time 0 and number of active quark flavors in QGP N
f

(+ minimal pT of hard process Ptmin to specify the number of hard NN collisions)
I.P.Lokhtin, A.M.Snigirev, Eur. Phys. J. 45 (2006) 211 (latest version 1.5.1)
8


Centr of eus ality nucleus-nucl interactions
Participant Region Spectators

b

2 R ~ 1 5 fm
Spectators

central collision
, b = 0

riphersi, b 2R pe al colli on

9


Charged multiplicity vs. centrality and pseudorapidity

PPb b

Pb Pb

Pb Pb

PPb b

Open points: ALICE data (PRL 106 (2011) 032301), closed points: CMS data (JHEP 1108 (2011) 141); histograms: HYDJET++

Tuned HYDJET++ reproduces multiplicity vs. event centrality (down to very peripheral events) with contribution of hard component to multiplicity in mid-rapidity 10 for central PbPb ~30%, as well as approximately flat pseudorapidity distribution.


PT-spectrum and nuclear modification factor R for inclusive charged hadrons
0-5%
PPb b

AA

0-5%
||<0.8
PPb b

||<1.0

R

AA

=



inel pp coll

N

d 2N d 2

AA pp

/ dpT d / dpT d

~

"QCD Medium" "QCD Vacuum"

RAA>1: enhancement RAA=1: no medium effect RAA<1: suppression

HYDJET++ reproduces pT-spectrum and R

Points: ALICE (left) (PL 696 (2011) 30) & CMS (right) (EPJ C 72 (2012) 1945) data; histograms: HYDJET++ 11
AA

for central PbPb in mid-rapidity up to pT~100 GeV/c


PT-spectra of identified hadrons
PPb b

||<0.5

Pb Pb

Points: ALICE data (APP B 43 (2012) 555); histograms: HYDJET++

HYDJET++ reproduces pT-spectrum of pions, kaons and (anti-)protons as well

12


Azimuthal correlations and flow
Event plane

(contains the impact parameter)

Reaction plane

beam

participants

Elliptic flow

Triangular flow

13

2


Anisotropic flow generation in HYDJET++ (soft component)
Elliptic flow v
2

spatial modulation of freeze-out surface fluid velocity modulation
Spatial anisotropy

Momentum anisotropy

R(b) ­ surface radius

u : azimuthal angle of fluid velocity : spatial azimuthal angle
3

Triangular flow v

Spatal modulation of freeze-out surface as cos(3) with independent phase 3 and parameter 3

Three parameters (b0), 3(b0) (b0) is tuned to fit the data

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Anisotropic flow generation in HYDJET++ (soft component)

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Anisotropic flow generation in HYDJET++ (hard component)

Some anisotropic flow for hard component (v2 and higher even harmonics at high transverse momenta) is generated due to partonic rescattering and energy loss in azimuthally-asymmetric volume of the medium 16


Elliptic flow of inclusive charged hadrons
||<0.8
PPb b

Pb Pb

Closed circles and squares: CMS data v2{2} & v2{LYZ} (PRC 87 (2013) 014902); histograms and open circles: HYDJET++ ("true" v2(2) & v2{EP})

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Triangular flow of inclusive charged hadrons
||<0.8
PPb b

Pb Pb

Closed circles and squares: CMS data v3{2} & v3{EP} (PRC 89 (2014) 044906); histograms and open circles: HYDJET++ ("true" v3(3) & v3{EP})

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Quadrangular flow of inclusive charged hadrons
||<0.8
PPb b

Pb Pb

Closed circles and squares: CMS data v4{2} & v4{LYZ} (PRC 89 (2014) 044906); histograms and open circles: HYDJET++ ("true" v4(2) & v4{EP})

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Pentagonal flow of inclusive charged hadrons
||<0.8
PPb b

Pb Pb

Closed circles and squares: CMS data v5{2} & v5{EP} (PRC 89 (2014) 044906); histograms and open circles: HYDJET++ ("true" v5(3) & v5{EP})

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Hexagonal flow of inclusive charged hadrons
||<0.8
PPb b

Pb Pb

Closed circles and squares: CMS data v6{EP/2} & v6{LYZ} (PRC 89 (2014) 044906); 21 histograms: HYDJET++ ("true" v6(2))


Correlations between elliptic and triangular flows

PPb b

Pb Pb

Points: ATLAS data (arXiv:1504.01289); histogram: HYDJET++

HYDJET++ reproduces the correlation between elliptic and triangular flows

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Elliptic and triangular flows of identified hadrons

PPb b

Pb Pb

||<0.8

Points: ALICE data (JPG 38 (2011) 124047); histograms: HYDJET++

HYDJET++ reproduces v2 and v3 for kaons and (anti-)protons, but rather underestimates
2 the data for pions (stronger non-flow correlations in the data than in the model?) 3


Dihadron angular correlations

PPb b

Pb Pb

ridge!

Points: CMS data (EPJC 72 (2012) 2012); histograms: HYDJET++

Interplay of elliptic and triangular flows in HYDJET++ yields long-range 2-partilce azim4 hal 2 ut correlations (ridge effect), but centrality dependence of the correlation strenght seems to strong


1) Thermal charm production in HYDJET++ (soft component)
Thermal charmed hadrons J/, D , 0, D+, D- , Ds+, Ds-, c+, c- are generated within the statistical hadronization model
0

D

(A.Andronic, P.Braun-Munzinger, K.Redlich, J.Stachel, Phys.Lett. B 571 (2003) 36; Nucl. Phys. A 789 (2007) 334)

ND=cNDth(I1(cNDth)/I0(cNDth)),

NJ/=c2 N
th J/

th J/

c - charm enhancement factor is obtained from the equation:

Ncc=0.5cNDth(I1(cNDth)/I0(cNDth))+c2 N

where number of c-quark pairs Ncc is calculated with PYTHIA (the factor K~2 is applied to take into account NLO pQCD corrections) and multiplied by the number of NN sub-collisions for given centrality

2) Non-thermal charm production in HYDJET++ (hard component)
Non-thermal charmed hadrons are generated within PYTHIA/PYQUEN taking into account medium-induced rescat2ering t5 and energy loss of heavy quarks (b, c)


PT-spectra and elliptic flow of D0-mesons
PPb b

PPb b

Pb b P

Pb Pb

Points: ALICE data (JHEP 1209 (2012) 112; PRC 90 (2014) 034904); histograms: HYDJET++

HYDJET++ reproduces pT-spectrum & v2(pT) of D-mesons with the same freeze-out parameters as for inclusive hadrons significant part of D-mesons (thermal component) is in the kinetic equilibrium with the medium; non-thermal component is important at high pT 26


D mesons at LHC (nuclear modification factor RAA)
R
AA

=



inel pp

N

coll

d 2N d 2

AA pp

/ dpT d / dpT d

~

"QCD Medium" "QCD Vacuum"

RAA>1: enhancement RAA=1: no medium effect RAA<1: suppression

PPb b

Points: ALICE data (JHEP 1209 (2012) 112); histograms: HYDJET++

HYDJET++ reproduces RAA(pT) of D-mesons up to very high pT treatment of heavy quark energy loss in hard component of HYDJET++ (PYQUEN) seems quite successful
27


Medium-induced partonic rescattering and energy loss («jet quenching»)
Collisional loss
(high momentum transfer approximation)

Radiative loss
(BDMPS model, coherent radiation)

28


Angular structure of energy loss in PYQUEN

Radiative loss, three options (simple parametrizations) for angular distribution of in-medium emitted gluons: Collinear radiation Small-angular radiation Wide-angular radiation =0
-( -0 )2 dN g sin e x p ( ), 2 d 2 0 05
o

dN g d



1

Collisional loss always "out-of-cone" (energy is absorbed by medium)
29


Suppression factor of inclusive jets

PPb b

ATLAS (PRL 114 (2015) 072302) PYQUEN (small-angle radiation) PYQUEN (wide-angle radiation)

Pb Pb

30

30


Suppression factor of inclusive jets
PPb b

CMS (PAS HIN-12-004 ) PYQUEN (small-angle radiation) PYQUEN (wide-angle radiation)

Pb Pb

31

31


Suppression factor of b-jets
PPb b

CMS (PRL 113 (2014) 132301) PYQUEN (small-angle radiation) PYQUEN (wide-angle radiation)

Pb Pb

32 32


Jet fragmentation function
Pb Pb

CMS (PRC 90 (2014) 024908) PYQUEN (small-angle radiation) PYQUEN (wide-angle radiation)

PPb b

The modification of longitudinal jet profile (ETjet>100 GeV, R=0.3): 33 excess at low pT ; suppression at intermediate pT; high pT is slightly enhanced. 33 Reproduced well by PYQUEN with wide-angle radiative + collisional partonic energy loss.


Jet shapes
Pb Pb



CMS (PLB 730 (2014) 243) PYQUEN (small-angle radiation) PYQUEN (wide-angle radiation)

PPb b

The modification of radial jet profile (ETjet>100 GeV, R=0.3): excess at large radii; suppression at intermediate radii; core is unchanged. 34 ic energy loss. 34 Reproduced well by PYQUEN with wide-angle radiative + collisional parton


Main publications (2011-2015)


[1] I.P. Lokhtin, A.V. Belyaev, A.M. Snigirev, "Jet quenching pattern at LHC in PYQUEN model", Eur. Phys. J. C 71 (2011) 1650 [2] I.P. Lokhtin, A.V. Belyaev, L.V. Malinina, S.V. Petrushanko, E.P. Rogochaya, A.M. Snigirev, "Hadron spectra, flow and correlations in PbPb collisions at the LHC: interplay between soft and hard physics", Eur. Phys. J. C 72 (2012) 2045 [3] L.V. Bravina, B.H. Brusheim Johansson, G.Kh. Eyyubova, V.L. Korotkikh, I.P. Lokhtin, L.V. Malinina, S.V. Petrushanko, A.M. Snigirev, E.E. Zabrodin. "Hexagonal flow v6 as a superposition of elliptic v2 and triangular v3 flows", Phys. Rev. C 89 (2014) 024909 [4] L.V. Bravina, B.H. Brusheim Johansson, G.Kh. Eyyubova, V.L. Korotkikh, I.P. Lokhtin, L.V. Malinina, S.V. Petrushanko, A.M. Snigirev, E.E. Zabrodin. "Higher harmonics of azimuthal anisotropy in relativistic heavy ion collisions in HYDJET++ model", Eur. Phys. J. C 74 (2014) 2807 [5] I.P. Lokhtin, A.A. Alkin, A.M. Snigirev, "On jet structure in heavy ion collisions", arXiv 1410.0147, submitted to Eur. Phys. J. C [6] G. Eyyubova,V.L. Korotkikh, I.P. Lokhtin, S.V. Petrushanko, A.M. Snigirev, L.V. Bravina, E.E. Zabrodin, "Angular dihadron correlations as interplay of elliptic and triangular flows", Phys. Rev. C 91 (2015) 064907 [7] I.P. Lokhtin, A.V. Belyaev, G.Kh. Eyyubova, G. Ponimatkin, E. Pronina, "Thermal and non-thermal charmed meson production in heavy ion collisions at the LHC", in preparation [8] V.L. Korotkikh, I.P. Lokhtin, L.V. Malinina, E.N. Nazarova, S.V. Petrushanko, A.M. Snigirev, E.S. Fotina, "Anisotropic flow fluctuations in hydro-inspired freeze-out model for relativistic heavy ion collisions", in preparation
35
















SUMMARY

36 36


SUMMARY
Two-component model of relativistic heavy ion collisions HYDJET++ reproduces basic physical observables measured in PbPb collisions at the LHC:


multiplicity and momentum spectra of inclusive and identified hadrons anisotropic flow of inclusive and indentified hadrons (including odd and higher harmonics) two-particle angular correlations of inclusive hadrons (including "ridge") momentum spectra and elliptic flow of D-mesons femtoscopic correlation radii of pion pairs transverse momentum imbalance in dijet production suppression of hard hadron and jet yields (including b-jets) modification of internal jet structure (longitudinal and radial profiles)

37 37


SUMMARY
Two-component model of relativistic heavy ion collisions HYDJET++ reproduces basic physical observables measured in PbPb collisions at the LHC:


multiplicity and momentum spectra of inclusive and identified hadrons anisotropic flow of inclusive and indentified hadrons (including odd and higher harmonics) two-particle angular correlations of inclusive hadrons (including "ridge") momentum spectra and elliptic flow of D-mesons femtoscopic correlation radii of pion pairs transverse momentum imbalance in dijet production suppression of hard hadron and jet yields (including b-jets) modification of internal jet structure (longitudinal and radial profiles)

The pattern of multi-hadron and jet production in most central PbPb collisions at the LHC agrees with the formation of hot strongly-interacting matter with hydrodynamical properties ("quark-gluon fluid") , which absorbs energetic quarks and gluons due to their multiple scattering and wide-angle radiative and collisional medium-induced energy loss.

38 38


SUMMARY
Two-component model of relativistic heavy ion collisions HYDJET++ reproduces basic physical observables measured in PbPb collisions at the LHC:


multiplicity and momentum spectra of inclusive and identified hadrons anisotropic flow of inclusive and indentified hadrons (including odd and higher harmonics) two-particle angular correlations of inclusive hadrons (including "ridge") momentum spectra and elliptic flow of D-mesons femtoscopic correlation radii of pion pairs transverse momentum imbalance in dijet production suppression of hard hadron and jet yields (including b-jets) modification of internal jet structure (longitudinal and radial profiles)

The pattern of multi-hadron and jet production in most central PbPb collisions at the LHC agrees with the formation of hot strongly-interacting matter with hydrodynamical properties ("quark-gluon fluid") , which absorbs energetic quarks and gluons due to their multiple scattering and wide-angle radiative and collisional medium-induced energy loss. Works in progress and near plans related to phenomenological analysis of LHC heavy ion data and the model improvements:


event-by-event fluctuations of anisotropic flow azimuthal dependence of femtoscopic correlation radii momentum spectra and elliptic flow of J/-mesons ...

39 39


BACKUP SLIDES

40 40


Period Dec. 2010 Dec. 2011 Mar. 2011 Jan. 2013 Fev. 2013

Species Pb+Pb Pb+Pb p+p p+Pb p+p

Energy 2.76 TeV 2.76 TeV 2.76 TeV 5.02 TeV 241 TeV .76

Lumi 7 b­1 150 b­1 230 nb­1 35 nb­1 5.4 pb­1
41


PYQUEN: physics frames
General kinetic integral equation:
L

E L , E = dx
0

dP dE x x x , E , dx dx

dP 1 x = exp - x / x dx x

1. Collisional loss and elastic scattering cross section:
dE 1 = dx 4T
t
max



2 D

2 2 t d d 12 s dt t, C , S = 2 dt dt t 3 3 - 2 N f ln t /

2 Q CD



, C =9 / 4 gg , 1 gq , 4 / 9 qq

2. Radiative loss (BDMPS):
2 C dE m q = 0 = s dx L
E F E


LPM

~ g

2 D

C y2 16 4 d 1- y ln os 1 1, 1= i 1- y F y 2 ln , = D g , 1= L , y = , C F = c k k 2 3 k 1- y 2 g E 3

[

]







2

"dead cone" approximation for massive quarks:
dE 1 m q 0 = dx 1 l 3
/2 2



dE m =0 , dx q

l= 2 D


1/ 3

mq E

4/ 3

42


Nuclear geometry and QGP evolution
impact parameter b|O1O2| - transverse distance between nucleus centers

(r1,r2) TA(r1) TA(r2) (TA(b) - nuclear thickness function)

Space-time evolution of QGP, created in region of initial overlaping of colliding nuclei, is descibed by Lorenz-invariant Bjorken's hydrodynamics J.D. Bjorken, PRD 27 (1983) 140
43


Monte-Carlo simulation of parton rescattering and energy loss in PYQUEN


Distribution over jet production vertex V(r cos, r sin) at im.p. b
dN b = d dr T A r 1 T A r 2
2 r
m ax


0

d


0

rdrT A r 1 T A r 2
T



Transverse distance between parton scatterings li=(i+1-i) E/p
dP = -1 dl i
l
i

i 1

exp - -1 i s ds , -1=
0



Radiative and collisional energy loss per scattering

E


tot , i

= E

rad , i

E

col , i

Transverse momentum kick per scattering
ti 2 k t ,i = E - 2m



0i



2

ti E ti - p- - -m p 2m0i 2p



2

2 q

44


HYDJET(soft): physics frames & simulation procedure
The final hadron spectrum are given by the superposition of thermal distribution and collective flow assuming Bjorken's scaling. 1. Thermal distribution of produced hadron in rest frame of fluid element

f E0 E

0



E 0 -m exp - E 0 / T f , - 1 cos 0 1, 0 0 2


2

2

2. Space position r and local 4-velocity u

- - Y 2Y

f r = 2r / R R A , b , 0 r R f ,

u r =sinh Y r / Reff R A , b R A , u t = 1 u cosh , u z = 1 u sinh
2 r 2 r

2 f max T

f e

max 2 L max 2 L





, 0 2

3. Boost of hadron 4-momentum p in c.m. frame of the event

p x = p 0 sin 0 cos 0 u r cos [ E 0 u p 0 / u t 1 ] , p y = p0 sin 0 sin 0 u r sin [ E 0 ui p i0 / u t 1 ] , p z = p 0 cos 0 u z [ E 0 u i pi0 / u t 1 ] ,
i i 0 i i 0

i

i

E = E 0 u t u p ,

4 u p =u r p 0 sin 0 cos -0 u z p 0 cos 50


Monte-Carlo simulation of hard component (including nuclear shadowing) in HYDJET/HYDJET++


Calculating the number of hard NN sub-collisions Njet (b, Ptmin, s) with Pt>Ptmin around its mean value according to the binomial distribution. Selecting the type (for each of Njet) of hard NN sub-collisions (pp, np or nn) depending on number of protons (Z) and neutrons (A-Z) in nucleus A according to the formula: Z=A/(1.98+0.015A2/3). Generating the hard component by calling PYQUEN njet times. Correcting the PDF in nucleus by the accepting/rejecting procedure for each of Njet hard NN sub-collisions: comparision of random number generated uniformly in the interval [0,1] with shadowing factor S(r1,r2,x1,x2,Q2) 1 taken from the adapted impact parameter dependent parameterization based on Glauber-Gribov theory
(K.Tywoniuk et al.,, Phys. Lett. B 657 (2007) 170).
46








HYDJET: model parameters
Minimal external input A - beam and target nucleus atomic weight; energy - c.m.s. energy per nucleon pair; ifb, bmin, bmax, bfix ­ parameters to fix event centrality selection; nh- total mean multiplicity of primary hadrons for soft component (PbPb, b=0); (multiplicity for other centralities and atomic weights is calculated automatically). Parameter can be varied by user ytfl - maximum transverse collective rapidity, controls slope of low-pt spectra; ylfl - maximum longitudinal collective rapidity, controls width of -spectra; Tf ­ hadron thermal freeze-out temperature; fpart - fraction of soft multiplicity proportional to # of participants (fpart(D)=1); sigin ­ inelastic NN cross-section (calculated by PYTHIA by default); ptmin - minimal transverse momentum of "non-thermalized" initial parton-parton scatterings (=ckin(3) in PYTHIA; other PYTHIA parameters also can be varied); T0, tau0, nf, ienglu, ianglu ­ PYQUEN parameters; nhsel - flag to switch on/off jet production and jet quenching; ishad - flag to switch on/off nuclear shadowing. Internal sets for soft component poison multiplicty distribution; thermal particle ratios.
47


HYDJET++ (soft): main physics assumptions
A hydrodynamic expansion of the fireball is supposed ends by a sudden system breakup at given T and chemical potentials. Momentum distribution of produced hadrons keeps the thermal character of the equilibrium distribution. 3 0 d Ni 3 eq Cooper-Frye formula: p 3 d ( x) p f i ( p u ( x); T , i ) d p ( x) - HYDJET++ avoids straightforward 6-dimensional integration by using the special simulation procedure (like HYDJET): momentum generation in the rest frame of fluid element, then Lorentz transformation in the global frame uniform weights effective von-Neumann rejection-acception procedure.

Freeze-out surface parameterizations

1. The Bjorken model with hypersurface u 2. Linear transverse flow rapidity profile 3. The total effective volume for particle producti
- Veff
(x

(t 2 z 2 )1/ 2 const

r onRat

max u



R d 3 ( x )u ( x ) r rdr d d 2 max ( u ) 0 0 min
R
max

2



2

max u

si n h

max u

cosh

max u

1)

48


HYDJET++ (soft): hadron multiplicities
1. The hadronic matter created in heavy-ion collisions is considered as a hydrodynamically expanding fireball with EOS of an ideal hadron gas. 2. "Concept of effective volume" T=const and µ=const: the total yield of particle species is N i i (T , i )Veff . 3. Chemical freeze-out : T, µi = µB Bi + µS Si + µc Ci + µQ Qi ; T, µB ­can be fixed by particle ratios, or by phenomenological formulas
4 T ( B ) a b B c B ; B ( s NN

)

d 1 e s

NN

4. Chemical freeze-out: all macroscopic characteristics of particle system are determined via a set of equilibrium distribution functions in the fluid element rest frame: 1 g eq 0*
f i ( p ; T , i )

(T , i ) d p * f i eq ( p 0* ; T ( x* ), ( x* ) i ) 4 dp * p *2 f i eq ( p 0* ; T , i )
eq i 3 0 0



(2 ) exp([ p i ] / T ) 1
3 0*

i



49


HYDJET++ (soft): thermal and chemical freeze-outs
1. The particle densities at the chemical freeze-out stage are too high to consider particles as free streaming and to associate this stage with the thermal freeze-out 2. Within the concept of chemically froz conservation of the particle number ratios ieq (T ch , ich ) e c q (T ch , h ) en evolution, assumption of the from the chemical to thermal freeze-out : th ieq (T th , i ) e th q (T th , )

3. The absolute values ieq (T th , ith ) are determined by the choice e of the free parameter of the model: effective pion chemical potential ff ,th at T th Assuming for the other particles (heavier then pions) the Botzmann approximation : e e ieq (T ch , ich ) q (T th , ff ,th ) ith T th ln eq th (T , 0) eq (T ch , ch ) i i i
Particle momentum spectra are generated on the thermal freeze-out hypersurface, the hadronic composition at this stage is defined by the parameters of the system at chemical freeze-out
50


HYDJET++ (soft): input parameters
1-5. Thermodynamic parameters at chemical freeze-out: Tch , {µB, µS, µC,µQ} (option to calculate Tch, µB and µs using phenomenological parameterization µB(s), Tch( µB) is foreseen). 6-7. Strangeness suppression factor S 1 and charm enchancement factor c 1 (options to use phenomenological parameterization S (Tch, µB) and to calculate c are foreseen). 8-9. Thermodynamical parameters at thermal freeze-out: Tth , and µ- effective chemical potential of positively charged pions. 10-12. Volume parameters at thermal freeze-out: proper time f , its standard deviation (emission duration) f , maximal transverse radius Rf . 13. Maximal transverse flow rapidity at thermal freeze-out
ma x u

. .

14. Maximal longitudinal flow rapidity at thermal freeze-out 15. Flow anisotropy parameter: (b) u = u ((b),)

max

16. Coordinate anisotropy: (b) Rf(b)=Rf(0)[Veff((0),(0))/Veff((b),(b))] 1/2[Npart(b)/Npart(0)] For impact parameter range bmin-bmax: Veff(b)=Veff(0)Npart(b)/Npart(0), f(b)=f(0)[Npart(b)/Npart(0)]
1 /3

1/3

51


Higher harmonic flow
Non-zero high Fourier coefficients carry information about the details of the space-time evolution of QCD-matter and initial state fluctuations.

n=2

n=3

n=4

n=5

n=6

52

3


Elliptic flow of inclusive charged hadrons
||<2.5
PPb b

Pb Pb

Closed circles: ATLAS data v2{EP} (PRC 86 (2012) 014907); 53 histograms and open circles: HYDJET++ ("true" v2(2) & v2{EP})

53


Triangular flow of inclusive charged hadrons
||<2.5
PPb b

Pb Pb

Closed circles: ATLAS data v3{EP} (PRC 86 (2012) 014907); 54 histograms and open circles: HYDJET++ ("true" v3(3) & v3{EP})

54


Quadrangular flow of inclusive charged hadrons
||<2.5
PPb b

Pb Pb

Closed circles: ATLAS data v4{EP} (PRC 86 (2012) 014907); 55 histograms and open circles: HYDJET++ ("true" v4(2) & v4{EP})

55


Pentagonal flow of inclusive charged hadrons
||<2.5
PPb b

Pb Pb

Closed circles: ATLAS data v5{EP} (PRC 86 (2012) 014907); 56 histograms and open circles: HYDJET++ ("true" v5(3) & v5{EP})

56


Hexagonal flow of inclusive charged hadrons
||<2.5
PPb b

Pb Pb

Closed circles: ATLAS data v6{EP} (PRC 86 (2012) 014907); 57 histograms: HYDJET++ ("true" v6(2))

57


Femtoscopic momentum correlations (pion pairs)
CF=1+exp(-Ro2qo2 ­Rs2qs2 -Rl2ql2 -2Rol2qo ql)
0-5%
PPb b

||<0.8

Points: ALICE data (PLB 696 (2011) 328), histograms: HYDJET++

58

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One of first new LHC results from lead-lead collisions at s=2.76 eV was the observation of transverse energy asymmetry for dijet production in most central events. It is interpreted as a signal of partonic jet absorbtion in hot quark-gluon matter.
10% of most central PbPb collisions at, s=2.76 A eV
PPb b

CMS (PRC 84 (2011) 024906) PYTHIA PYQUEN

ETj1>120 GeV, ETj2>50 GeV

ETj1 ETj AJ j1 ET ETj

2 2
59