Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://lav01.sinp.msu.ru/~igor/seminar/Hydjet_status_2013.pdf Äàòà èçìåíåíèÿ: Tue Mar 12 20:15:58 2013 Äàòà èíäåêñèðîâàíèÿ: Thu Feb 27 21:05:44 2014 Êîäèðîâêà:

PYQUEN, HYDJET HYDJET++
Latest PYQUEN paper: I.P. Lokhtin, A.V. Belyaev, A.M. Snigirev, "Jet quenching pattern at LHC in PYQUEN model", Eur. Phys. J. C 71 (2011) 1650 Latest HYDJET++ paper: 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 HYDJET Works in the frames of CMS Heavy Ion Physics Analysis Group


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 1.8)

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 2.1)

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

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HYDJET/HYDJET++ (hard): 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 QGP temperature T0, QGP formation time 0 and number of active quark flavors in QGP N (+ minimal pT of hard process Ptmin)
I.P.Lokhtin, A.M.Snigirev, Eur. Phys. J. 45 (2006) 211 (latest version 1.5.1)
f

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(«jet quenching»)
Collisional loss
(high momentum transfer approximation)

Radiative loss
(BDMS model, coherent radiation)

Strength of e-loss in PYQUEN is determined mainly by initial maximal temperature T0 of hot matter in central (b=0) PbPb collisions (depends 4 also on formation time 0 and # of quark flavors Nf)


PYQUEN: physics frames
General kinetic integral equation:
L

E L , E = dx
0

dP dE x x x , E , dx dx

dP 1 x = e x p - 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 33 -2N f ln t /

2 QC D



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

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


LPM

~ g

2 D

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

[

]







"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

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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 exp , 2 d 2 0 0 ~ 5
o

dN g d



1

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


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


to t , i

= E

rad , i

E

c ol , 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

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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 9 (K.Tywoniuk et al.,, Phys. Lett. B 657 (2007) 170).








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

ma x 2 L ma x 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 ui p i0 / u t 1 ] , p y = p0 sin 0 sin 0 u r sin [ E 0 ui p i0 / u t 1 ] , ii p z = p 0 cos 0 u z [ E 0 u p0 / u t 1 ] ,
i i 0 i i 0

E = E 0 u t u p ,

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

0


HYDJET: model parameters
Minimal exter A - beam and target nucleus atomic weight; energy - c.m.s. energy per nucleon pair; ifb, bmin, bmax, bfix ­ parameters to fix event nh- total mean multiplicity of primary hadrons (multiplicity for other centralities and atomic nal input centrality selection; for soft component (PbPb, b=0); 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.
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HYDJET (soft): «post-LHC» updates
HYDJET1.8 (July 2011) 1. The set of basic resonances (, , , ', , K*, ) for the soft component is implemented. The ratios between primary hadrons are taken from the thermal model. Previously, only final , K, p and n were considered for the soft component. HYDJET1.7 (April 2011) 1. sp is 2. so The additional von Neumann rejection/acceptance procedure generating hadron ectra of soft component in accordance with the Cooper-Frye freeze-out prescription introduced. The hydro-inspired parametrization for the momentum and spatial anisotropy of ft hadron emission source is implemented.

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HYDJET++ (soft): 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)
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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 µ eq Cooper-Frye formula: p 3 = d µ ( x) p f i ( p uµ ( x); T , µ 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 m ma ma d 3 µ ( x)u µ ( x) = r rdr d d = 2 max ( u ax sinh u x - cosh u x + 1) u ) 0 0 min
R
max

2



2

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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 , µ 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 ( µ B ) = a - bµ B - cµ B ; µ 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: g 1 eq 0*
f i ( p ; T , µi ) =

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



(2 ) exp([ p - µi ] / T ) ± 1
3 0*

i



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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 , µich ) = e c q (T ch , µ h ) en evolution, assumption of the from the chemical to thermal freeze-out : th ieq (T th , µi ) e th q (T th , µ )

3. The absolute values eq (T th , µth ) are determined by the choice i i e of the free parameter of the model: effective pion chemical potential µff ,th at T th Assuming for the other particles (heavier then pions) the Botzmann approximation : e e ieq (T ch , µich ) q (T th , µff ,th ) µith = T th ln eq th (T , µ = 0) eq (T ch , µch ) 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
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HYDJET++ (soft): thermal charm production
Thermal charmed mesons J/, D0, D0, D+, D- , Ds+, Ds-, c+, c- are generated within the statistical hadronization model
(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/

c - charm enhancement factor can be obtained from the equation:

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

th J/

where number of c-quark pairs Ncc is calculated with PYTHIA (the factor K~2 is applied to take into account NLO pQCD corrections)


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

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LHC s=2.76 PbPb, - .
10% PbPb, s=2.76 A CMS (. ) PYQUEN ( ) PYQUEN ( )

ETj1 - ETj AJ = j1 ET + ETj

2 2


Multiplicity vs. centrality and pseudorapidity

Pb Pb

PPb b

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

Tuned HYDJET & HYDJET++ reproduce multiplicity vs. event centrality (down to very peripheral events) with contribution of hard component to multiplicity in mid-rapidity for central PbPb ~25%(~30%), as well as approximately flat pseudorapidity distribution.


PT-spectrum and nuclear modification factor R
||<0.8

AA

||<1.0

Points: ALICE (left) (PL 696(2011) 30) & CMS (right) (EPJ C 72 (2012) 1945 ) data, histograms: HYDJET++ (the same for HYDJET).

HYDJET & HYDJET++ reproduce pT-spectrum of charged particle and nuclear modification factor for central PbPb in mid-rapidity up to pT~100 GeV/c

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Energy density vs. and centrality

Pb Pb

PPb b

CMS Collab., Phys.Rev.Lett. 109 (2012) 152303

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Hadron ratios
ALICE data HYDJET HYDJET++

(JPG 38 (2011) 124025)

PbPb, 0-5%, ||<0.5

K±/

±

0.155 ± 0.012

0.171

0.153

p±/

±

0.0456 ± 0.0036

0.040

0.065

Not perfect (K/ better for HYDJET++, p/ ­ for HYDJET), but depends on treatment of weak decays (off in the models).

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Elliptic flow
10-20% 20-30% 30-40%

Points: ALICE data v2{4} (PRL 105(2010) 252302), histograms: HYDJET HYDJET & HYDJET++ reproduce elliptic flow coefficient v2 up to pT~5 GeV/c and 40% PbPb centrality
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.


Elliptic flow

Points: CMS data v2{4} (archiv:1204.1409), histograms: HYDJET++

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Elliptic flow

Points: CMS data v2{4} (archiv:1204.1409), histograms: HYDJET++

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Femtoscopic momentum correlations
CF=1+ exp(-Ro2qo2 ­Rs2qs2 -Rl2ql2 -2Rol2qo ql)

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

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Jet background fluctuations

PPb b

Pb b P

Pb Pb

Tuned HYDJET event generator reproduces jet background fluctuations, that allows us to use it as the reference for jet quenching analysis in PbPb collisions
­ Use PYTHIA and N
coll

scaling for unquenched reference
28

­ Embed in HYDJET (underlying event)


Validation of background

Pb Pb

PPb b


Validation of background

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Jet momentum dependence of jet quenching
A significantly lower average dijet momentum ratio pT,2/pT,1 in central PbPb collisions than in pp and peripheral PbPb collisions, and in the dijet embedded MC simulations
CMS Collab., Phys.Lett. B712 (2012) 176

The fraction of the energy that a jet loses increases monotonically with increasing collision centrality, and does not dramatically change with jet pT Ejet ~ 0.1Ejet?

Pb Pb

Pb b P

PPb b


Photon+jet correlation
Pb Pb PPb b

RJ =
-jet

/N



>

CMS Collab., Phys.Lett. B718 (2013)
Pb Pb PPb b Pb Pb PPb b

A significant shift of jet­photon pT-ratio (~15%) and reducing the fraction of isolated photons with associated partner jet (~20%) in central PbPb collisions as compared with pp and peripheral PbPb events, and MC simulations jet quenching in hot QCD-matter