1. V.L. Korotkikh (SINP 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

2. 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)
14-19 September 2008, RDMS CMS, Minsk
V.L. Korotkikh

3. V2 in A+A
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

4. Non central А-А - collisions _______________________________________________________________x y z
transverse plane px py
Kolb P.F., Heinz U., nucl-th/ (2003).
Initial spatial anisotropy results in elliptic flow of finite particles.
Azimuthal anisotropy of particles is a signature of termalizasion
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

5. r – azimuthal angle of reaction plane
RHIC data in Au+Au _______________________________________________________________
r – azimuthal angle of reaction plane
n =2, 2 -- elliptic flow, V2 =
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

6. 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 !
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

7. _______________________________________________________________
Energy dependence
_______________________________________________________________
V2 = (LHC)
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

8. 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/ (2003).
For lower energies (SPS, 17 GeV/A) thermodynamic equilibrium is not achieved.
For RHIC energies ( GeV-A) the produced system is closed to equilibrium (see plato for STAR, PHOBOS data)
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh 8

9. _______________________________________________________________
Elliptic flow measurements with CMS Tracker at LHC
_______________________________________________________________
Our study
Pb+Pb events (HYDJET 1.0) are generated at energy 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”
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

10. Elliptic flow measurements with CMS at LHC _______________________________________________________________
Pb+Pb ,
5500 GeV, 100k events
* Simulated
▲ Reconstructed
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
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

11. 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
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

12. V2 in p+p Questions: 1. What for ? 2. Is it possible to measure ?
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

13. 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.
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

14. 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/
In hydro model the ratio doesn’t depend on size S of transverse overlap region
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

15. t1 (b)= t2 (b) – parton-proton thickness function.
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
where  parton-medium cross-section.
The proton-proton thickness function is equal to
Here B – impact parameter between the centers of proton.
t1 (b)= t2 (b) – parton-proton thickness function.
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

16. Formalism of impact parameter dependence in p-p collision ___________________________________________________________________________
 diffuse edge of Fermi density
 sharp edge of density (hard sphere)
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(B) and find 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

17. Formalism of impact parameter dependence in p-p collision ____________________________________________________________________________
So, a density of binary parton-parton collisions is
And we can calculate the eccentricity  of p-p
where B is an impact parameter of two black body disks.
Transverse overlap area of two disks is
The average number of binary parton-parton collisions is
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

18. 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.
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

19. Fit Pin(b) at LHC energies _______________________________________________________________
pp,LHC
Fit Pin(b)
R,fm
1.05
,fm
0.29
0,mb
7.8
Rrms,fm
1.34
/R = 0.27
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

20. Nucleon density parameters from p+p collisions (CDF, SLAC) _______________________________________________________________
Different form of nucleon spatial density and different ratio diffuseness/radius
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

21. Nucleon parameters _______________________________________________________________
e+p (DESY)
(charge density)
p+p (SLAC) [Abe, CDF]
Fermi, set 1
Fermi , set 2
Fermi , set 3
Hard sphere
Rrms, ,fm
0.77
0.60
0.64
0.56
/R ?
0.20
0.50
0.80 0.
F. Abe et al, Phys.Rev. C56(1997) 3811
pp,LHC
Fit Pin(b)
Fermi , set 2
Hard sphere
Rrms,fm
1.34
0.90
0.81
/R
0.27
0.10 0.
Our study:
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

22. Eccentricity at different size of proton edge _______________________________________________________________
>0
  R = 0.
  R =0.10 
<0
  R = 0.27
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

23. 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.
Here are
 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)
where
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/ ]
(see also S.A. Voloshin, Report QM 2008)
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

24. Eccentricity scaling and incomplete thermalization _______________________________________________________________
There is a simple model based on eccentricity scaling and incomplete thermolization (see [3]).
Two free parameters: (V2 /  )hydro and 0
where
(V2 /  )hydro
0 , mb
0.22  0.01
5.5  0.5
(7.8)
Fit of RHIC data
H.J. Drescher et al, Phys.Rev. C76(2007)024905, [nucl-th/ ]
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

25. Eccentricity and elliptic flow (diffuse edge) ______________________________________________________________
  R= 0.10
C=1.8
C=1.
C=0
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

26. Eccentricity and elliptic flow _______________________________________________________________
Hard sphere
Diffuse edge
  R= 0.
  R= 0.10
  R= 0.27
C=0
C=1
C=1.8
C=0
C=1.8
C=0
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

27. 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.
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh 27 27

28. Back up slides
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

29. Formalism of impact parameter dependence in p-p collision ___________________________________________________________________________
Differential multiplicity of p-p is proportional to average number of binary parton-parton collisions or
– centrality parameter of p-p collision
We use dNppch (y=0)=5. from approximation data RHIC to LHC energy.
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

30. Transverse overlap area of two protons _______________________________________________________________
  R = 0.27
  R =0.10 0. 0.
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

31. Transverse overlap area and eccentricity of p-p collision _______________________________________________________________
Hard sphere ( ) and Fermi (_________) distribution
S 1,2 0. 0.
  R =0.10
1,2
  R =0.27
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

32. Hard sphere (- - - - -) and Fermi (_________) distribution
Differential multiplicity as function of centrality c _______________________________________________________________
Hard sphere ( ) and Fermi (_________) distribution
  R= 0.27
  R= 0.10
  R= 0.
  R= 0.
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

33. Multiplicity density as function of centrality c _______________________________________________________________
Hard sphere ( ) and Fermi (_________) distribution
  R= 0.
  R= 0.
  R= 0.27
  R= 0.10
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

34. Eccentricity and elliptic flow (hard sphere) _______________________________________________________________
  R= 0.0
C=1.8
C=1.
C=0
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

35. Eccentricity and elliptic flow (diffuse edge) ______________________________________________________________
  R= 0.27
C=1.
C=0
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh

36. 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]
14-19 Sep 2008, RDMS CMS, Minsk
V.L. Korotkikh