Rapidity dependence of particle densities in pp-AA collisionscrunch.ikp.physik.tu-darmstadt.de/qghxm/talks/... · The multiplicity in pp and AA collisions Rapidity dependence Conclusions

The String Percolation ModelThe multiplicity in pp and AA collisions

Rapidity dependenceConclusions

Rapidity dependence of particle densities inpp-AA collisions

Irais BautistaIn collaboration of J. Dias de Deus, C. Pajares and G. MilhanoWorkshop ”Quarks, Gluons, and Hadronic Matter under

Extreme Conditions”

19th of March 2013St. Goar, Germany

Irais Bautista In collaboration of J. Dias de Deus, C. Pajares and G. Milhano Workshop ”Quarks, Gluons, and Hadronic Matter under Extreme Conditions”Rapidity dependence of particle densities in pp-AA collisions



Table of contents

The String Percolation Model

The multiplicity in pp and AA collisions

Rapidity dependence

Conclusions




I Multi-particle production is described in terms of color ofstrings stretched between the partons of the projectile andtarget. Color strings will decay into new ones by qq̄, qq − q̄q̄production.S1 = πr20 , r0 ∼ 0.25 fm.




I The number of strings grows with the energy and with thenumber of nucleons of participating nuclei.

I Color strings may be viewed as small disks in the transversespace filled with the color field created by colliding partons.

I Particles are produced by the Schwinger mechanisms.

I With growing energy and size of the colliding nuclei thenumber of strings grow and start to overlap forming clusters.

I At a critical density a macroscopic cluster appears and marksthe percolation phase transition.




I The formation of clusters behaves like disks in the continuumtwo dimensional percolation.

I ηtc = 1.1− 1.5I ηt = Ns

S1SA

I We assume a cluster of n strings behaves as a single stringwith higher color field, and momentum.

I < µn >=√

nSnS1

< µ1 >

I < p2Tn >=√

nS1Sn

< p2T1 >




I In SPM the relevant quantity is the transverse impactparameter density ηt for pp collisions

I ηt ≡ ( r0Rp )2N̄ sp

I The particle density dn/dy at mid rapidity is related to theaverage number N̄s of stringsdndy ∼ F (ηt)N̄s

F (ηt) =√

1−e−ηtηt




I The overlap area is given by SNA = SA(NA/A)5/3,

N sA ' N s

pN(α+1)A (1)

with

N sp = 2 + 4

(r0Rp

)2(√smp

)2λ

, (2)




Notice that it would be expected

N sA ' N s

pN4/3A (3)

instead ofN sA = N s

pN(α+1)A (4)

but the energy in pp is√s and in AA is A

√s, therefore at not very

high energy some strings have not enough energy to be formed.The number should increase from A to A4/3 with a ln s (phasespace) dependence as is has α(s).




I With the string density

ηtNA = ηtpN(α(s))A

A

N2/3A

(5)




I

1

NA

dn

dy

∣∣∣∣y=0

=dnpp

dy

∣∣∣∣y=0

(1 +

F (ηtNA)

F (ηtp)(N

α(√s)

A − 1)

), (6)

I with

α(s) =1

3(1− 1

1 + ln(√s/s0 + 1)

), (7)

anddnppchdη

∣∣∣∣η=0

= κF (ηtp)Nsp , (8)




s210 310 410

=0

ηηddn

A

N1

0

2

4

6

8

10

12

Figure: Multiplicity dependence on√s. Data from p− p, Cu− Cu,

Au−Au and P −Pb is shown in circles, triangles and starts respectively.(NA = 1, A = 1) for is used for pp (grey line); (NA = 50, A = 63) forCuCu (blue line); and (NA = 175, A = 200) for AuAu/PbPb (red line)




partN0 50 100 150 200 250 300 350 400

=0

ηηddn

pa

rtN

2

0

2

4

6

8

10




N̄s ∼ e2λY , (9)

for the particle density, at y ' 0,

dn

dy∼ eλY , (10)

and for the full rapidity distribution,

dn

dy|pp = aeλY

dn

dy|s, (11)

where dndy |

s is the single string density, dndη |pp

dn

dy|s =

1

eη−(1−α)Y

δ + 1, (12)




dn

dη|pp = J

dn

dy|pp, (13)

with J = coshη√k+sinh2η

, k =m2+p2Tp2T

and by assumption fix k at the

effective value 1.2. It corresponds to mπ ' 0.14 GeV and p̄π ' 0.3GeV.




dnppchdη

∣∣∣∣η

= κ′J F (ηtp)Nsp

1

exp (η−(1−α)Yδ ) + 1(14)

0 2 4 6 8 100

1

2

3

4

5

6

7

8

η

ηd

n/d

CMS 7 TeVCMS 2.36 TeV

TOTEM 7 TeV

CDF 1.8 TeV NSDCDF 630 GeV NSDUA5 900 GeV NSDUA5 546 GeV NSDUA1 540 GeV NSDP238 630 GeV NSDUA5 200 GeV NSDUA5 53 GeV NSD

Comparison of the results from the evolution of the dnchdη with

dependence in pseudorapidity for p− p collisions at differentenergies (lines).




I Evolution in pseudorapidity for AA collisions

dndη =

κ′J(NA)dn

pp

dy |y=0(1 +F (ηtNA

)

F (ηtp)(N

α(√s)

A − 1)) 1

exp (−η−(1−α)Y

δ)+1

with κ′ = κJ(η=0)(exp (−(1−α)Yδ ) + 1).




In all the computations we have used the following values of theparameters: κ = 0.63± 0.01, λ = 0.201± 0.003,

√s0 = 245± 29

GeV, α ' 0.34, δ ' 0.84 and k1 = 1.2 to describe the particledensity dn

dη |NANA in the same power law as dndη |pp. We had made

here an extension to these descriptions to add the pseudo rapidityevolution.




-10 -5 0 5 100

20

40

60

80

100

120

140

ηd

n/d

η

Cu-Cu 22.4 GeV

-10 -5 0 5 100

20

40

60

80

100

120

140 Cu-Cu 62.4 GeV

ηd

n/d

η

-10 -5 0 5 100

20

40

60

80

100

120

140

160

180

200

220Cu-Cu 200 GeV

η

ηd

n/d

Figure: Evolution of the dnch/dη with pseudorapidity for Cu-Cu collisionsat 22.4 GeV, 62.4 GeV, and 200 GeV energies, data from ref. [1]. Errorbars in color blue, green, pink, red, purple and black are used for thecorresponding centralities 45− 55%, 35− 45%, 25− 35%, 15− 25%,6− 15%, 0− 6% respectively, black lines show our results.




-10 -5 0 5 100

50

100

150

200

250

300

350

400Au-Au 19.6 GeV

ηd

n/d

η -10 -5 0 5 100

50

100

150

200

250

300

350

400

450

500Au-Au 62.4 GeV

ηd

n/d

η

-10 -5 0 5 100

100

200

300

400

500

600

700Au-Au 130 GeV

ηd

n/d

η-10 -5 0 5 10

0

100

200

300

400

500

600

700

800

ηd

n/d

η

Au-Au 200 GeV

Figure: Evolution of the dnch/dη with pseudorapidity for Au-Au collisionsat 19.6 GeV, 62.4 GeV, 130 GeV and 200 GeV energies. Error bars incolor blue, green, pink, red, purple and black are used for thecorresponding centralities 45− 55%, 35− 45%, 25− 35%, 15− 25%,6− 15%, 0− 6% respectively, black lines are the model results [2]




-10 -5 0 5 100

1

2

3

4

5

6

7

8

9

10

/2)

par

t(N

ηd

n/d

η

Figure: Comparison of the results CMS [3] from the evolution of thednch

dη1

(Npart/2)with the pseudorapidity for Pb-Pb collisions at 2.76 TeV.

Error bars in color green, blue, pink and red are used for thecorresponding centralities 85− 95%, 50− 55%, 0− 90% and 0− 5%respectively, lines in black are the corresponding results from the modelto the respective centrality, for the smaller centrality we use the numberof participants corresponding to the 85-95% showed in dot and dashedline and in dashed line is the minimum number of participants equal 2.




-10 -5 0 5 100

2

4

6

8

10

12

14

/2)

par

t(N

ηd

n/d

η

Pb-Pb 5.5 TeVPb-Pb 3.8 TeVPb-Pb 3.2 TeV

Figure: Predictions on the evolution of the dnch

dη1

(Npart/2)with

pseudorapidity for Pb-Pb collisions at 3.2, 3.9 and 5.5 TeV energies at0− 5% centrality.




Conclusions

I We have discussed in a general way the physics of particledensities in pp and AA collisions.

I Our model gives a non-linear dependence of 1NAdn/dη|AA on

dn/dη|pp.

I Particle densities, as a function of η and Y give a gooddescription of Pb-Pb data at LHC in a wide region in η. Thesame is observed for pp in a wide range of rapidity Y .

I Notice that recent data from TOTEM experimentmeasurements in the charged particle pseudorapidity densitydNch/dη in pp collisions at

√s = 7 TeV for 5.3 < |η| < 6.4 is

consistent with this results.




Thank you...




Bibliography

I B. Alver, B. B. Back, M. D. Baker, M. Ballintijn,D. S. Barton, R. R. Betts, R. Bindel and W. Busza et al.,Phys. Rev. Lett. 102 (2009) 142301

I B.B Back, et. al. Phys. Rev. Lett. 91, 052303 (2003).B. B. Back et al. [PHOBOS Collaboration], Phys. Rev. C 74(2006) 021901

I S. Chatrchyan et al. [CMS Collaboration], JHEP 1108 (2011)141

I I. Bautista, C. Pajares, J. G. Milhano and J. D. de Deus,Phys. Rev. C 86 (2012) 034909.

I I. Bautista, J. G. Milhano, C. Pajares and J. Dias de Deus,Phys. Lett. B 715 (2012) 230.


Documents

Rapidity dependence of particle densities in pp-AA collisionscrunch.ikp.physik.tu-darmstadt.de/qghxm/talks/... · The multiplicity in pp and AA collisions Rapidity dependence Conclusions