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MSU

Perspectives of elliptic flow studies in AA and p-p collisions with CMS

V.L. Korotkikh (SINP MSU)

14-19 September 2008, RDMS CMS, Minsk

V.L. Korotkikh

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MSU

Perspectives of elliptic flow studies in AA and p-p collisions with CMS
1.

Azimuthal Anisotropy in Heavy Ions Collisions with CMS Tracker,

CMS Analysis Note 2007/004, Report QM2008 submitted to Yad. Fiz. 2008
G. Eyyubova , V.L. Korotkikh, I.P. Lokhtin, S.V.Petrushanko, L.I. Sarycheva, A.M. Snigirev (SINP MSU), D. Krofcheck(University of Auckland)
2.

Elliptic flow in pp collisions and proton structure
Publication in preparation

,

D. d'Enterria (CERN), G.Kh. Eyyubova, V.L. Korotkikh, I. P. Lokhtin, S.V. Petrushanko, L.I. Sarycheva,A. M. Snigirev (SINP MSU)

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V.L. Korotkikh

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V2 in A+A

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_______________________________________________________________

Non central - - collisions

transverse plane

y x

z

Kolb P.F., Heinz U., nucl-th/0305084 (2003).

Initial spatial anisotropy results in elliptic flow of finite particles. Azimuthal anisotropy of particles is a signature of termalizasion
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RHIC data in Au+Au

r ­ azimuthal angle of reaction plane

3 2 d1 Nd N E 1v n r c( 1 y c v o , t ) 2 s o s 2 r ( ) a p n 2 n 3 p d p 1 p tt 2 dn d p y x


n =2,





2

--

elliptic flow,

V2 =0.02-0.05
5

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V.L. Korotkikh


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RHIC data in Au+Au

The most bright RHIC result scaled elliptic flow V2/nq is the same for all hadrons. It is signature of termalizasion on quark level !
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Energy dependence

V2 = 0.07 (LHC)

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RHIC data on elliptic flow

Elliptic flow V2 normalized on initial space eccentricity as a function of particle density in a unity of transverse overlap square AT of two nuclei. The curves are predictions of hydrodynamics with QGP and Hadron gas as initial states.
Kolb P.F., Heinz U., nucl-th/0305084 (2003).

For lower energies (SPS, 17 GeV/A) thermodynamic equilibrium is not achieved.

For RHIC energies (62-200 GeV-A) the produced system is closed to equilibrium (see plato for STAR, PHOBOS data)
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Elliptic flow measurements with CMS Tracker at LHC
_______________________________________________________________

Our study
·

100000 Pb+Pb events (HYDJET 1.0) are generated at energy 5500 GeV/A at impact parameter value b=9 fm.
Elliptic flow in HYDJET generator
(I.P. Lokhtin and A.M.Snigirev, Eur. Phys. J. C 46, 211 (2006).)

The flow is introduces for soft part of HYDJET generator. Spatial freeze out eccentricity is considered to be connected with initial eccentricity.
The results are published in CMS AN 2007/004 "Azimuthal Anisotropy in Heavy Ions Collisions with the CMS Tracker"

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Elliptic flow measurements with CMS at LHC

Pb+Pb
* Simulated Reconstructed

,

5500 GeV, 100k events

Our analysis is based on:
CMS HI Group MIT data-base (HYDJET 1.0, jet quenching off) ORCA 8_13_3 b=9fm pT >0.9 GeV/c Track selection: nhit>12, cl>0.01

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Elliptic flow measurements with CMS at LHC
_______________________________________________________________

V2 determination of CMS Tracker efficiency

- simulated values by HYDJET - reconstructed in CMS Tracker by Event Plane method

The uncertainties of CMS Tracker detector is not higher than 3%
Methods of V2 extraction - v2{EP} in simulated events - original events - Li-Yang method

Large non-flow corrections
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V2 in p+p
Questions: 1. What for ? 2. Is it possible to measure ?

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Motivation

·There are expectations that gluon density in the nucleon is comparable to one in nuclei .
·Ratio V2/ as a function of density 1/S dN/dy is comparable in p+p and A+A collisions. Thremalization regime may be achieved also in p-p collision in order to measure V2/ . ·There are the theoretical prediction (Frankfurt,2004) an impact parameter dependence of parton-proton interaction in the black disk regime (BDR ) . This regime will be increased at LHC. · Our first results of V2 in pp show a strong dependence of V2(b) from spatial structure of proton. So it may be important in problem of nucleon structure.

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Time evolution of the ratio v2/ _______________________________________________________________
In hydro, at a time of order R/cs where R = transverse size cs= sound velocity

Au-Au R(Au)=6 fm

b

Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009

In hydro model the ratio doesn't depend on size S of transverse overlap region
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Formalism of impact parameter dependence in p-p collision
____________________________________________________________________________

Cross section of p-p generic inelastic interaction

The inelastic probability of p-p interaction is

pp 2 in (s) d B (1 e

0 t1,

2

( B)

)
)
( B)

where 0 -- parton-medium cross-section. The proton-proton thickness function is equal to

(1 e 0 Pinpp ( s, B) P , 2 ( B) 1 2 d B (1 e

t1

,2

( B)

0 t1

,2

)

B B t1, 2 ( B) dxdy t1 ( x , y) t2 ( x , y) 2 2
Here B ­ impact parameter between the centers of proton.

t1 (b)= t2 (b)
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­ parton-proton thickness function.
V.L. Korotkikh 15


Formalism of impact parameter dependence in p-p collision
___________________________________________________________________________

t1 ( x , y ) t ( b) dz ( x , y, z )


FM

(r)

e

0 ( r R) /



1

diffuse edge of Fermi density sharp edge of density (hard sphere)

HS

1 /( 4 / 3R 3 ), r R (r) 0, r R

Then we calculate multiplicity N12 (B) , eccentricity (pp) of p-p and transverse overlap area S(pp).
We fit the probability of proton -proton inelastic interaction Pin the parameters of spatial density distribution (r) = (x,y,z) . We have three parameters: 0 , R and
14-19 Sep 2008, RDMS CMS, Minsk V.L. Korotkikh 16

(B)

and find


Formalism of impact parameter dependence in p-p collision
____________________________________________________________________________

So, a density of binary parton-parton collisions is

B B n1, 2 ( x, y, B) 0 t1 ( x , y) t2 ( x , y) 2 2
And we can calculate the eccentricity of p-p

y2 x2 1, 2 ( B) 2 2 2 2 dxdy ( y x )n1, 2 ( x , y, B) y x
where B is an impact parameter of two black body disks.



dxdy ( y 2 x 2 )n1, 2 ( x , y, B)

Transverse overlap area of two disks is

S1, 2 ( B) x 2 y 2
The average number of binary parton-parton collisions is

d N1, 2 N1, 2 ( B) dxdy n1, 2 ( x, y, B) 2 dB
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Inelastic probability Pin(b) from pp- collision

It is possible to find the impact parameter dependence of the generic inelastic probability Pin(b) from experimental data of p-p collision at high energies. (Frankfurt,2004)

We can do the inverse analysis and find nucleon thickness function
t1,(b)= t2,(b) from Pin(b) , where t1,2(b) is overlap function of two nucleons.

(1 e Pin ( b) 2 d b (1 e
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0 t

1, 2

(b )

)

0 t

1, 2

(b )

)
V.L. Korotkikh 18


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Fit Pin(b) at LHC energies

pp,LHC Fit Pin(b)

R,fm 1.05 ,fm 0.29 0,mb 7.8
R
rms

,fm

1.34

/R = 0.27
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Nucleon density parameters from p+p collisions (CDF, SLAC)
_______________________________________________________________

Different form of nucleon spatial density and different ratio diffuseness/radius
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Nucleon parameters

e+p (DESY) (charge density)

p+p (SLAC) p+p p+p [Abe, CDF] (SLAC) (SLAC) Fermi, set 1 [Abe, CDF] [Abe, CDF]
Fermi , set 2 Fermi , set 3

p+p (SLAC) [Abe, CDF] Hard sphere

Rrms, ,fm 0.77

0.60

0.64

0.64

0.56

/R

FM

?
e
0 ( r R) /

0.20

0.50

0.80

0.

(r)



F. Abe et al, Phys.Rev. C56(1997) 3811

1
pp,LHC Fit Pin(b) Fermi , set Hard 2 sphere

Our study:

Rrms,fm 1.34 /R 0.27

0.90 0.10

0.81 0.
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Eccentricity at different size of proton edge

R = 0.


R =0.10

>0


R = 0.27



<0

y2 x2 1, 2 ( B) y2 x2
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FM

(r)

e

0 ( r R) /



1

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2

Eccentricity scaling and incomplete thermalization model
_______________________________________________________________

There is a simple model based on eccentricity scaling and incomplete thermolization as a consequence of ideal-fluid dynamics.

V2

V2

hyd r o

1 1 K / K
s

Here are
0

where

1 0 dN c K S dy

0 -- parton-medium cross-section (V2 / )hydro -- thermodynamic limit value S --- transverse overlap area of nuclei dN/dy ­ multiplicity at y=0
Cs=1/sqrt(3) -- velocity of sound K0=0.7 (transport calculations)

dN/dy(y=0) from RHIC data S calculated in A+A geometry

H.J. Drescher et al, Phys.Rev. C76(2007)024905, [nucl-th/0704.3553] (see also S.A. Voloshin, Report QM 2008)
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Eccentricity scaling and incomplete thermalization
_______________________________________________________________

There is a simple model based on eccentricity scaling and incomplete thermolization (see [3]). hydro

V2

V2

hyd r o

Two free parameters: (V2 / )

and

0

1 1 K / K
s

0

where

1 0 dN c K S dy
hydro

(V2 / )

0 , mb

0.22 0.01

5.5 0.5 (7.8)
H.J. Drescher et al, Phys.Rev. C76(2007)024905, [nucl-th/0704.3553]

Fit of RHIC data
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Eccentricity and elliptic flow (diffuse edge)

R= 0.10

C=1.8
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C=1.

C=0
25

B2 C 4R2


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Hard sphere
R= 0. R= 0.10

Eccentricity and elliptic flow

Diffuse edge
R= 0.27

C=1
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C=0

C=1.8
V.L. Korotkikh

C=0

C=1.8

C=0
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Conclusion ___________________ ____________________________________________
· Elliptic flow V2 in Pb+Pb at LHC energies can be reconstructed with CMS Tracker with high accuracy( ±3% ). Error of flow V2 is about 10-20% depending on v2 calculation method.

· Elliptic flow in p+p collisions is very sensitive to the form of nucleon spatial density. If there is possibility to measure the V2 centrality dependence then it will be powerful tool to study a nucleon structure.

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Back up slides

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Formalism of impact parameter dependence in p-p collision
___________________________________________________________________________

Differential multiplicity of p-p is proportional to average number of binary parton-parton collisions
pp N1, 2 ( B) dN ch dN 0 ( y, B) ( y) 2 2 dy dyd B d BN1,2 ( B)

or
pp N1, 2 () dN ch dN 0 ( y, ) ( y) dyd dy dc N1,2 (c)

B2 4R2
We use

­ centrality parameter of p-p collision

dNppch (y=0)=5.

from approximation data RHIC to LHC energy.
V.L. Korotkikh 29

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Transverse overlap area of two protons

R =0.10

R = 0.27

0.

0.

S1, 2 ( B) x y
2 2
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_______________________________________________________________ Hard sphere (- - - - -) and Fermi (_________) distribution

Transverse overlap area and eccentricity of p-p collision

S

1,2

0.

0.
R =0.10



1,2

R =0.27

S1, 2 ( B) x 2 y 2
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y2 x2 1, 2 ( B) y2 x2
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Differential multiplicity as function of centrality c

Hard sphere (- - - - -) and Fermi (_________) distribution

R= 0.27 R= 0.10

R= 0.

R= 0.

pp dN ch dN 0 ( y, ) / ( y) dyd dy

|

y 0
V.L. Korotkikh



N 1, 2 ( ) dc N 1, 2 ( c)
32

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Multiplicity density as function of centrality c

Hard sphere (- - - - -) and Fermi (_________) distribution

R= 0.

R= 0.

R= 0.27 R= 0.10

pp 1 dN ch (0, ) S1, 2 dyd

B2 C 4R2

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Eccentricity and elliptic flow (hard sphere)

R= 0.0

C=1.8
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C=1.

C

B 4R

2 2

C=0
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Eccentricity and elliptic flow (diffuse edge)

R= 0.27

C=1.
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C=0

B2 C 4R2

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Some excerpts of recent theoretical works

At LHC energies the soft parton interactions take place in the disk edges and the hard parton interactions happen in more central region.

L. Frankfurt et al, Phys.Rev. D69(2004)114010, [hep-ph/031123]
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