Transcript STRING COLOR FIELDS PREDICTIONS for pp at LHC

Long Range Correlations,Parton
Percolation and Color Glass
Condensate
C.Pajares
Dept Particle Physics and IGFAE
University Santiago de
Compostela,Spain
The Ridge Correlation in High-Energy Collisions,
INT workshop Seattle,May 7-11 2012
Introduction to long range correlations
STAR data and string like models
nF-nB,nF-ptB,ptF-ptB correlations
Clustering of color sources
Scales of pp and Pb Pb collisions
Similarities between CGC and percolation
Ridge Structures
Conclusions
LONG RANGE CORRELATIONS
• A measurement of such correlations is the backward–forward dispersion
D2FB=<nB nF> - <nB> <nF>
where nB(nF ) is the number of particles in a backward (forward) rapidity
2
DFB
 N    n1B n1F    n1B  n1F      N 2    N  2   n1F  n1B 
B
F

<N> number of collisions: <n1B>,<n1F> F and B multiplicities in one collision
2
• In a superposition of independent sources model, DBF
is proportional to
the fluctuations ( DN2 )on the number of independent sources (It is assumed
that Forward and backward are defined in such a way that there is a rapidity
window   1.0 to eliminate short range correlations).
 nB  a  bnF
with
2
2
b  DBF
/ DFF
• b in pp increases with energy. No LRC at RHIC.In hA increases with A
,also in AA,increases with centrality
The dependence of b with rapidity gap is quite interesting:
In AA central is flat for large values of the rapidity window.
.Existence of long rapidity correlations at high density and/or high energy
.It is possible to eliminate short range correlations even with no very large
rapidity gap,by looking correlations of particles of very different azimuthal
angle
•
1/K is the squared normalized fluctuations on
effective number of strings(clusters)contributing to
both forward and backward intervals
The heigth of the ridge structure is proportional to n/k
--- Any model describing k and dn/dy and the systematics
of their dependence on y,centrality and energy should
give a good description of long range correlations
--- The rapidity length of long range correlations is the
same that the plateau of dn/dy(Assuming that k do not
change in this rapidity range)
--- As dn/dy for protons is much smaller than for pions,
b for protons is much smaller than for pions(not at inter pt)
--- Given a rapidity range and energy,k, is proportional
to the inverse of the width of the multiplicity distribution,
P(n)(very sensitive to the tail of the distribution)
--- In some events,(for instance events with at least one
high pt particle)the associated multiplicity distribution is
nP(n)/mean(n),implying higher mean(n) and and therefore
larger long range correlations
-- The strings must be extended in both
hemispheres,otherwise either they do not
obtained LRC(Hijing)or they have to include
parton interactions(PACIAE).(PACIAE
reproduces well b for central but not for
peripheral)
--Without parton interactions,in this model,
the length in rapidity of the LRC is the same
in pp than AA.In CGC this is not true due to
the running couplig constant,which allows
an increase of b with Na
Short range correlations are eliminated
by using different azimuthal regions and/or
rapidity gaps
Sizable long range n-n ,pt-n and pt-pt
correlations
(M.A.Braun et al Eur Phys C32 535 2004,
PRL 85 4864 (2000)
CLUSTERING OF COLOR SOURCES
• Color strings are stretched between the projectile and target
• Strings = Particle sources: particles are created via sea qqbar production in
the field of the string
•
Color strings = Small areas in the transverse space filled with color field
created by the colliding partons
•
With growing energy and/or atomic number of colliding particles, the
number of sources grows
•
So the elementary color sources start to overlap, forming clusters, very
much like disk in the 2-dimensional percolation theory
• In particular, at a certain critical density, a macroscopic cluster appears,
which marks the percolation phase transition
(N. Armesto et al., PRL77 (96); J.Dias de Deus et al., PLB491 (00); M. Nardi and H.
Satz(98).
• How?: Strings fuse forming clusters. At a certain critical density ηc
(central PbPb at SPS, central AgAg at RHIC, central pp at LHC ) a
macroscopic cluster appears which marks the percolation phase transition
(second order, non thermal).
• Hypothesis: clusters of overlapping strings are the sources of
particle production, and central multiplicities and transverse momentum
distributions are little affected by rescattering.
n 
nSn
1 ;  pT2 n 
S1
nS1
 pT2 1
Sn
Energy-momentum of the cluster is the sum of the energy-momemtum of
each string. As the individual color field of the individual string may be
oriented in an arbitrary manner respective to one another, Q2  nQ2
n
1
•
Scales of pp and AA
Why Protons?
In String Percolation…
 AA
43
NA
r
r
s
  N  23 
R
N A  R p
2
2

 N ps


 AA ( s )  N A2 3 pp ( s )
and
N ~ s2 7
PbPb ( s )  20GeV  200Gev
PP ( s )  6TeV 14Tev
LHC
2
Transverse size
r02 F ()
1
CGC
Qs2
Effective number of clusters
1
 RA 
(1  exp( )) RA2
2
 N 

(
1

exp(
))



F ( ) r02
r
0


2
2
4
R 
  A  , N A 3 , exp( 2 )
 r0 
low density
2
R 
  A  , N A , exp(  )
 r0 
high density
CGC
1
S
2
RA
QS2 , N A , exp(  )
rapidity extension
yN  y1  2lnNS
CGC
1
s
,
lnN A , ln s
ln N A , ln s
 N 2

 N 2    N 2
k 
low density
k 
high density
k=
<N>
(1-exp(- ))
3
2
2
high density
low density
CGC
R 
  A  , N A , exp(  )
 r0 
2
1  RA 


  r0 
k=RS2Qs2 , N A , exp(  )
1
b
1
low density
d
(1  e

2
b 0
b 1
high density (energy)
CGC
)
3
b 
high density (energy)
1
1   S2 c
b 1
1 d
MULTIPLICITY DISTRIBUTIONS
NEGATIVE BINOMIAL
k  N  k0
(k0 , single effective string)
low density
k   , k0  
Poisson
high density
k   , k0  1
Bose-Einstein
CGC
k

k0  1
B:E
,
k=<N>
first decreases with density (energy)
Above an energy(density) k increases
Multiplicity distributions (normalized,
n/  n
i.e.  n  Pn as a function of
will be narrower (Quantum Optical prediction)

Ridge Structure
• In both CGC and string percolation the
heigth of the ridge increases with energy
and centrality
At the same value of string density same
value of the heigth (it was predicted ridge
structure in high multiplicity pp events at LHC,as
far the string density in pp at LHC is similar to
Au-Au peripheral collisions at RHIC)
Triggering a high pt particle, it means that you
change the multiplicity distribution in a very define
way.Now is larger (dn/dy)/k
Conclusions
--- For pp high multiplicity events at LHC should occur the same phenomena
observed at RHIC in Au-Au
--- Normalized multiplicity distributions in pp will be narrower at higher
energy
--- Long range correlations extended more than 10 units of rapidity at LHC
for AA.Large LRC in pp, extended several units of rapidity.
--- There are pt-n and pt-pt long range correlations which can be
distinguished from short range correlations using different azimuthal and
rapidity regions
--- Large similarities between CGC and percolation of strings.Similar
predictions corresponding to similar physical picture.Percolation
explains the transition low density-high density
9
s  5.5TeV
2/Npart dn/d
8
7
6
5
4
0
100
200
Npart
300
400
12