G.A. Feofilov, O.A. Kochebina

Reporter O.A. Kochebina

The 5th International Nordic "LHC and Beyond" Workshop "The First LHC Physics and Major Spin-Offs", 9 June 2010

St. Petersburg State University

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Phase transitions See NA61. Physics goals. https://na61.web.cern.ch Phases of strongly

interacting matter in AA collisionsPhases of water

The phase diagram of water is well established

butthe properties of the

transition between hadrongas and quark-gluon plasma

still have to be uncovered

1st order phase transitioncritical point

Shape changes little from peripheral to the transition

83-94% 55-65%

ηΔ width

STAR PreliminarySTAR Preliminary

Smaller change from transition to most central

Low-pT manifestation of the “ridge”

0-5%

STAR Preliminary

Variation of low-pT “ridge” with centrality (Npart).(pt> 0.15 GeV/c )

[1]Anomalous centrality variation of minijet angular correlations in Au-Au collisions at 62 and 200 GeV from STAR. M. Daugherity. QM2008.

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Large change within ~10%

centrality

46-55%

STAR Preliminary

The data showed a sharp transition at some definite energy-dependent centrality:growing of peak amplitude and pseudorapidity stretching of width.

Example New threshold (?) phenomena in AA collisions observed by STAR [1]

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Peak Amplitude

Npart Npart

NpartPeak η Width

STAR PreliminarySTAR Preliminary200 GeV62 GeV

refρ

Δρ

Peak η Width

200 GeV “Critical value” Npart≈40

62 GeV“Critical value” Npart≈90

Sd

dNch /2

3~

Transverse Particle Density

~

STAR Preliminary

STAR Preliminary

200 GeV62 GeV

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A sudden increase of the peak amplitude and η width of the near-side low p_t ridge were found at an energy-dependent centrality point at definite number of participating nucleons Npart.

Same-side gaussian peak amplitude, width. Points show eleven centrality bins for each energy (84-93%, 74-84%, 65-74%, 55-65%, 46-55%, 37-46%, 28-37%, 19-28%, 9-19%, 5-9%, and 0-5%) transformed to tranvserse density.

22,06,2~ fmcrit

Anomalous centrality variation of minijet angular correlations in Au-Au collisions at 62 and 200 GeV from STAR. M. Daugherity. QM2008.

Variation of low-pT “ridge” with centrality (Npart).

S

Motivation(theory) Application of string model. Investigations of the charged particles long-range multiplicity correlations, measured for well separated

rapidity intervals, can give us information on the number of emitting centers and hence on the fusion of colour strings[2,3].

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[2] M.A.Braun, C.Pajares and V.V.Vechernin, Low pT Distributions in the Central Region and the Fusion of Colour Strings, Internal Note/FMD ALICE-INT-2001-16 [3] А. Абрамовский, О.В. Канчели// Письма в ЖЭТФ, т.31, 566, 1980

Fig.1. Quark-gluon strings and schematics for studies of Long-Range Correlations[2]

String model. Estimate of string percolation parameter.

With growing energy and/or atomicnumber of colliding particles, the number of strings grows and they start to overlap, forming clusters, new type of particle emitting source. At a critical density a macroscopic cluster appears that marks the percolation phase transition.[3]

- number of strings, πr02 string transverse area, S overlap area of two nucleons.

r0=0,2-0,3 fm – change of string radius value results in different percolation parameter

NStr

[4] J.Dias de Deus and A. Rodrigues// Phys. Rev. C 67, 064903 (2003)[3] C. Pajares // arXiv:hep-ph/0501125v1 14 Jan 2005

)(

)()(

20

bS

rbNb str

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ηс= 1,15([4])

)(/)()( 20 partpartstrpart NSrNNN

Percolation parameter:

S

?strN

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]8[)1()(partcoll

ppstrstr NxNxNN

Number of strings

x – parameterNstr(pp) - the number of strings in pp collisionNcoll – number of nucleon - nucleon collisionsNpart – number of nucleon participants

Npart, Ncoll - from MC calculation [9]Nstr(pp) – theoretical estimates [8]x - ?

ValentSeastr NNN

[8]V.V. Vechernin, R.S. Kolevatov, 2007, published in Yadernaya Fizika, 2007, Vol. 70, No. 10, pp. 1858–1867.[9]G.Feofilov,A.Ivanov //Journal of Physics: Conference Series 5 (2005) 230–237

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New! Our calculation

S-?SrN str /2

0

Percolation parameter

Sd

dNch /2

3~

Transverse particle density

22062 fmcrit ,,~15,1crit

crit

crit

~

Percolation model parameters at the “critical“ point

xr

dydN

N

ch

crit

critcritstr

2

0

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~

Percolation parameter Percolation parameter η vs. number of participants: vs. number of participants:

[7] G.Feofilov,A.Ivanov, “Number of nucleon‐nucleon collisions vs. energy in modified Glauber calculations”,Journal of Physics: Conference Series 5 (2005) 230–237]

)(/)()( 20 partpartstrpart NSrNNN

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GMNstr ≈ 275Ns ≈ 220

Ncoll ≈ 150

x=0,39±0,07

MGM (momentum loss)Nstr ≈275Ns ≈ 216

Ncoll ≈ 168

x=0,34±0,06

√s= 62 GeV, Au+Au

______ - GM - - - - - - - MGM[7]

“Critical value” Npart ≈ 90ηсrit = 1,15

ρсrit = 2,6 GeV/fm-2

r0=0,28 fm

Example of calculation

partcollpp

strstr NxNxNN )1()(

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Extrapolation of percolation model parameters for energy Extrapolation of percolation model parameters for energy 17,3 GeV and 3500 GeV 17,3 GeV and 3500 GeV

tsecba /

Parameter Value Error

d 1,00 0,08

c -0,8 0,1

t 293 107

Parameter Value Error

d 0,80 0,05

c -0,61 0,07

t 296 91

partcollpp

strstr NxNxNN )1()(

GM

MGM

√s= 17,3 GeV => x=0,18±0,02√s= 3500 GeV => x=1,0±0,3

√s= 17,3 GeV => x=0,19±0,02√s= 3500 GeV => x=0,8±0,4

62 GeV 200 GeV

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Percolation parameter vs. number of participants:

It is possible to try to search for the onset of the near-side low p_t “ridge” in the very central Pb+Pb at 17,3 GeV(SPS) or AuAu collisions 19,6 GeV (RHIC) andin very peripheral collisions or maybe even in pp collisions at LHC energies.

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Sd

dNch /2

3~

SrN str /20

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ρ = 0,60+ 1,75 η

From experimental data [11] for dNch/dy

√s, GeV ρ, GeV/fm-2 η Nstr

7000 6,2±0,2 3,2±0,3 18±22360 4,8±0,2 2,4±0,2 14±1900 3,9±0,2 1,9±0,2 11±1

Sd

dNch /2

3~

SrN str /20

Obtained Nstr was checked and has agreement at theoretical predictions for Nstr[12] (for energy 17,3 GeV, 200 GeV, 900GeV)

ValentSeastr NNN

[11] ALICE Collaboration: arXiv:1004.3034[hep-ex], arXiv: 1004.3514[hep-ex][12]N. Armesto, D. Derkach and G. A. Feofilov, Phys. At. Nucl. 71 (2008) 2122–2131

• The hypothesis of percolation transition looks reasonable in the description of the onset of the near side low-pt ridge phenomenon at RHIC energies.

• it is possible to try to search for the onset of the “near-side low p_t “ridge” phenomenon” in the very central Pb+Pb at 17,3 GeV(SPS) or in Au+Au at 19.6 GeV (RHIC).

•At the LHC energy one may expect the observation of the low p_t ridge phenomenon in ALL centrality classes and the onset in peripheral PbPb or pp collisions.

•The method for obtaining the number of sea strings following the concept of valent and sea strings is checked on the data of the ridge onset in Au+Au collisions at RHIC.

• The method for finding the total number of strings for pp collisions at LHC energies is proposed.

• The hypothesis of percolation transition looks reasonable in the description of the onset of the near side low-pt ridge phenomenon at RHIC energies.

• it is possible to try to search for the onset of the “near-side low p_t “ridge” phenomenon” in the very central Pb+Pb at 17,3 GeV(SPS) or in Au+Au at 19.6 GeV (RHIC).

•At the LHC energy one may expect the observation of the low p_t ridge phenomenon in ALL centrality classes and the onset in peripheral PbPb or pp collisions.

•The method for obtaining the number of sea strings following the concept of valent and sea strings is checked on the data of the ridge onset in Au+Au collisions at RHIC.

• The method for finding the total number of strings for pp collisions at LHC energies is proposed.

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Ncoll depends on the model:1.Classical Glauber model (GM)2.Modified Glauber model (MGM) (takes into account moment losses)[7]

Systematic uncertainties:1. String radius (r0=0,2-0,25 fm)2. Estimate of overlap area S 3. Estimate of Ncoll (Classical or Modified Glauber )

[7] G.Feofilov,A.Ivanov //Journal of Physics: Conference Series 5 (2005) 230–237

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ηсrit= 1,15r0=0,2 fm

20/)()()( rNSNNN partpartpartstr

“Critical value” Nstr

New!

b, fm

Npart

S(bcrit)

∙ - sphere nuclear shape∙ - WS nuclear shape

ηсrit /πr0 = Nstr/S(bcrit)

Our calculation

Percolation parameter vs. number of participants:Percolation parameter vs. number of participants:

[7] G.Feofilov,A.Ivanov, “Number of nucleon‐nucleon collisions vs. energy in modified Glauber calculations”, Journal of Physics: Conference Series 5 (2005) 230–237]

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“Critical value” Npart ≈ 40ηсrit= 1,15r0=0,2 fm

√s= 200 GeV, Au+Au

GMNstr ≈ 300Ns ≈ 460

Ncoll ≈ 50

a=5,0±2,2

MGMNstr ≈ 360Ns ≈ 260

Ncoll ≈ 40

a=6,7±2,9

)(/)()( 20 partpartstrpart NSrNNN collpartstr aNNN

______ - r0=0,2 fm (GM)

- - - - - - - r0=0,25 fm (GM)

..-..-..- - line r0=0,2 fm (MGM)[7]

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collpartstr aNNN

62 GeV a = 2,9±0,8

200 GeV a = 5,0±2,2

Preliminary

tsecba /Extrapolation of percolation model parameters to lower Extrapolation of percolation model parameters to lower

energy.energy.

SVstr NNN

17,3 GeV a=1,2±0,1

17,3

Parameter Value Error

d 5,44 0,25

c -5,38 0,24

t 81 1017,3

Parameter Value Error

d 7,40 0,27

c -7,35 0,26

t 86 8

62 GeV a = 3,8±0,8

200 GeV a = 6,7±2,9

Preliminary

17,3 GeV a=1,4±0,1

Classical Glauber model Modified Glauber model

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[8]Terence J. Tarnowsky*, Brijesh K. Srivastava, Rolf P. Scharenberg (for the STAR Collaboration)/ arXiv:nucl-ex/0606019v2 10 Apr 2007

Au+Au, 200 GeV

Au+Au, 62 GeV

Percolation parameter vs. number of participants:Percolation parameter vs. number of participants:

Au+Au62 GeV Npart ≈ 90

200 GeV Npart ≈ 40ηсrit= 1,15

Au+Au62 GeV Npart ≈ 75

200 GeV Npart ≈ 20ηсrit= 1,175

______ - r0=0,2 fm (GM)

- - - - - - - r0=0,25 fm (GM)

..-..-..- - line r0=0,2 fm (MGM)[7]

[7] G.Feofilov,A.Ivanov,”,Journal of Physics: Conference Series 5 (2005) 230–237

Our estimates based on RHIC experimental data

Theoretical estimates made by Tarnowsky (2007)

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Near-side low p_t “ridge” in dihadron correlations that were studied recently in Au+Au collisions at the collision energies √s= 62 and 200 GeV, demonstrate a number of interesting features as a function of collision centrality, transverse momentum and particle composition

New threshold (?) phenomena in AA collisions

Ridge: see J. Putschke et al. [STAR], J. Phys. G 34, S679 (2007). Low-p_t near side ridge: see Daugherity report at QM2008

Onset of manifestation of the near-side low p_t “ridge” (pt> 0.15 GeV/c )

refρ

Δρ

refρ

Δρ Pair densities : Δρ ≡ ρsib−ρref, where ρsib is sibling pair densities, ρref - the uncorrelated reference from different events measures

),( 21 pp

Ref.:[1]   M. Daugherity for the STAR Collaboration//arXiv:0806.2121v2 [nucl-ex] 13 Jun 2008; M. Daugherity// Report on QM2008.[2] J. Putschke et al. [STAR], J. Phys. G 34, S679 (2007). [3] Adams J et al (STAR Collaboration) 2006 Phys. Rev. C 73 064907[4] Adams J et al (STAR Collaboration) 2007 J. Phys. G: Nucl. Part. Phys. 34 799[5] Jana Bielcikova, Acta Physica Polonica B Vol. 1 Proceedings Supplement No 3, (2008) 611-614

~

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]1[2,06,2~ 2 fmcrit

r0 =0.2 fm

Modified Glauber model

~Preliminary

17,3 GeV a= 1,4±0,162 GeV a= 3,8±0,8200 GeV a= 6,7±2,9

623~ 2 forfmcrit

Percolation parameter vs. Transverse Particle Density

~ ~

Sd

dNch /~

2

3

PHOBOS Collaboration, B. B. Back et al., Phys. Rev. C65, 061901 (2002); 70, 021902 (2004).PRL 94(2005) 022002

d

dNch

obtained in our calculations

PbPbGeVs ,3,17

r0=0,2 fm

We obtain a=3,0±0,5

)(/)()( 20 partpartstrpart NSrNNN

Percolation parameter vs. number of participant (J/psi).

collpartstr aNNN

[7] CERN–2005–005 arXiv:hep-ph/0412158v2 26 Jul 2005, p. 428

“Critical value” Npart≈110[7]

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G.Feofilov, O. Kochebina. J/psi suppression, percolation model and the critical energy density in AA collisions at SPS and RHIC energies with the account of centrality.//Baldin ISHEPP XIX. Dubna, Oct 2, 2008

AuAuGeVs ,200

Percolation parameter vs. number of participant:Systematic uncertainties

Uncertainties r0 (0.25 fm)Upper estimate

Modified Glauber[11] estimateUncertainties Nstr

Systematic uncertainties:1. Nstr2. String radius3. S – overlap area

[11] G.Feofilov,A.Ivanov, “Number of nucleon nucleon collisions vs. energy in modified Glauber calculations”, Journal of ‐Physics: Conference Series 5 (2005) 230–237]

Experimental data for J/Psi suppression

“Critical value” Npart ≈ 50

All parameters is the same

)(/)()( 20 partpartstrpart NSrNNN

collpartstr aNNN

r0=0,2 fma= 4,2±0,5

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crit~