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Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 1
Color Glass Condensate and the relation toHERA physics
Edmond IancuIPhT Saclay & CNRS
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 2
Introduction: What is CGC ?
■ The ultimate form of hadronic matter at high energy◆ “parton saturation” (maximal occupation numbers)
■ A firm prediction of first–principle calculations◆ weak coupling (perturbative QCD)◆ strong coupling (AdS/CFT for N = 4 SYM)
■ Interesting conceptual aspects◆ high energy limit of scattering amplitudes◆ multiple scattering, saturation, unitarity◆ relation to modern problems in statistical physics
■ Interesting consequences for the phenomenology◆ rapid growth of the gluon distribution (HERA)◆ geometric scaling (HERA)◆ particle production in pA and AA collisions (RHIC)
■ Decisive tests are coming soon, at LHC !
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 3
Motivation: Gluons at HERA
⊲ The gluon distribution rises very fast at small x ! (∼ 1/xλ)
H1
Col
labo
ratio
n
xG(x,Q2) ≈ # of gluons with transverse size ∆x⊥ ∼ 1/Q and kz = xP
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 4
Motivation: High density = Weak Coupling
H1
Col
labo
ratio
n⊲ High–energy evolution : An evolution towards increasing density.
⊲ High density partonic matter is weakly coupled !
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 5
Motivation: High density = Non-linear
⊲ A challenging problem though !
High density =⇒ weak coupling but strong non–linear effects
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 6
Gluon evolution at small x
■ The ‘infrared sensitivity’ of bremsstrahlung favors the
emission of ‘soft’ (= small–x) gluons
dP ∝ αsdkz
kz= αs
dx
x≡ αs dY
Y ≡ ln1
x∼ ln s =⇒ dY =
dx
x: “rapidity”
■ A probability of O(αs) to emit one gluon per unit rapidity.
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 6
Gluon evolution at small x
■ In turn, the emitted gluon can radiate an even softer one
■ The ‘price’ of such an additional gluon:
P(1) ∝ αs
∫ 1
x
dx1
x1= αs ln
1
x= αsY
■ Ordering in x =⇒ Ordering in (life)time (“glass”) :
∆t ∝ kz
k2⊥
∝ x
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 7
BFKL evolution
■ The blowing–up gluon distribution
xG(x,Q2) ∝∑
n
1
n!
(
αs ln1
x
)n
∼ eωαsY
Y ≡ ln (1/x) ∼ ln s : “rapidity”
■ “BFKL resummation” (Balitsky, Fadin, Kuraev, Lipatov, 75–78)
■ Conceptual difficulties in the high energy limit
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 8
Onset of non–linear dynamics
■ The gluon occupation number (or ‘packing factor’) :
n(x, k⊥, b⊥) ≡ dN
dY d2k⊥d2b⊥∼ 1
Q2× xG(x,Q2)
πR2
■ n ∼ 〈AiAi〉 : when n ∼ 1/αs ⇐⇒ Aia ∼ 1/g
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 9
The Saturation Momentum
■ The gluons must be numerous enough (small x) and
large enough (low Q2) to strongly overlap with each other.
Q2s(x) ≃ αs
xG(x,Q2s)
πR2∼ 1
xλ
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 10
Dipole factorization for DIS
■ At small–x, the struck quark is typically radiated off
the gluon distribution in the proton
■ Lorentz boost to the ‘dipole frame’
γ∗ fluctuates into a qq pair which then scatters off the proton.
■ The proton still carries most of the total energy !
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 10
Dipole factorization for DIS
σγ∗p(x,Q2) =
∫ 1
0
dz
∫
d2r |Ψγ(z, r;Q2)|2 σdipole(x, r)
σdipole(x, r) = 2
∫
d2b T (x, r, b)
■ T ≡ 1 − S : The dipole–proton scattering amplitude
■ Unitarity bound: T ≤ 1 (T = 1 : ‘black disk limit’)
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 11
BFKL evolution: Unitarity violation
■ The ‘last’ gluon at small x can be emitted off any of the
‘fast’ gluons with x′ > x radiated in the previous steps :
∂n
∂Y≃ αsn =⇒ n(Y ) ∝ eωαsY
■ Dipole forward scattering amplitude: T ∼ αsn
■ Unitarity bound (T ≤ 1) is eventually violated by BFKL !
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 12
BFKL evolution: Infrared diffusion
■ The gluon emission vertex is non–local in transverse space:
∂Y n(ρ, Y ) = αsn + αs∂2ρn
=⇒ Diffusion in ρ ≡ ln k2⊥
∼ lnQ2
Y
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 13
Non–linear evolution: Saturation
■ High density: recombination processes leading to saturation
∂n
∂Y≃ αs∂
2ρn + αsn − α2
s n2 = 0 when n ∼ 1
αs≫ 1
■ Non–linear equation =⇒ stable fixed point at high energy !
■ Unitarity restoration & Hard momentum scale (Qs(Y ))
Introduction
Motivation
Gluon evolution at small x
● Small-x evolution
● BFKL
● Saturation momentum
● Dipole frame
● BFKL equation
● Non–linear evolution
● Non–linear evolution
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 14
Non–linear evolution: Saturation
∂Y n(ρ, Y ) = αs∂2ρn + αsn − α2
sn2
■ Cartoon version of BK (Balitsky–Kovchegov) equation (99)
■ Mean field (large–Nc) approx. to JIMWLK equation (CGC)(Jalilian-Marian, E.I., McLerran, Weigert, Leonidov, and Kovner, 97–00)
■ Derived to leading–order in perturbative QCD
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
● Strong coupling
● Saturation line
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 15
DIS at strong coupling(Polchinki, Strassler, 02; Hatta, E.I., Mueller, 07) see talk by R. Peschanski
■ λ ≡ g2Nc ≫ 1 with g2 ≪ 1 =⇒ AdS/CFT correspondence
■ N = 4 SYM ⇐⇒ classical gravity in the AdS5 × S5
■ Parton branching at strong coupling :
No reason to favour special corners of phase–space !
■ All partons have branched down to small values of x !
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
● Strong coupling
● Saturation line
CGC & Geometric scaling
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 16
Saturation line: weak vs. strong coupling
■ No ‘leading–twist’ (no pdf’s !) at Q2 > Q2s(x)
all partons lie within the CGC with occupancy n ∼ O(1)
■ Saturation exponent : Q2s(x) ∝ 1/xλs ≡ eλsY
◆ weak coupling : λs ≈ 0.4 g2Nc (LO BFKL Pomeron)
◆ strong coupling : λs = 1 (graviton)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 17
The Color Glass Condensate(McLerran, Venugopalan, 1994; E.I., Leonidov, McLerran, 2000)
■ An effective theory for the evolution towards saturation
■ Small–x gluons: Classical color fields radiated by fast colorsources (x′ ≫ x) ‘frozen’ in some random configuration ρa
■ WY [ρ] : Probability distribution for the color charge density
■ Functional evolution equation for WY [ρ] : JIMWLK
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 18
Deep Inelastic Scattering off the CGC
■ T (r)[ρ] : scattering off a given configuration ρ of the color
sources (multiple scattering in the eikonal approximation)
■ Average over ρ with weight function WY [ρ] (glass)
〈T (r)〉Y =
∫
D[ρ] WY [ρ] T (r)[ρ]
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 19
Saturation momentum
■ Saturation front : T (ρ, Y ) with ρ = ln(1/r2)
=⇒ a front interpolating between T = 0 and T = 1
ρρ ρ
1/2
1
ss(Y )2)( Y1
T
2YY1> Y1
■ The position ρs(Y ) of the front =⇒ saturation momentum
BK =⇒ ρs(Y ) ≡ lnQ2s(Y ) ≈ λY with λ ≈ 4.88αs ∼ 1
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 20
Gluon occupation number
■ A similar front holds for the ‘unintegrated gluon distribution’
xG(x,Q2) =
∫
d2b
∫ Q
dk k n(x, k)
Y = 15Y = 10Y = 5
log(k2/k20)
n(k
)
35302520151050-5-10
10
1
0.1
0.01
0.001
1e-04
1e-05
log(k2/k20)
kn(k
)
6050403020100-10
1000
100
10
1
0.1
0.01
■ The typical transverse momentum of the gluons is ∼ Qs(Y )
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 21
BK equation: The traveling wave
■ The shape of the front is not altered by the evolution
log(r20/r
2)
T
2520151050-5
1
0.8
0.6
0.4
0.2
0
T (ρ, Y ) ≃ T (ρ− ρs(Y )) ≡ T(r2Q2
s(Y ))
■ ‘Geometric scaling’E.I., Itakura, McLerran (02) ; Mueller, Triantafyllopoulos (02)
■ Traveling wave picture : Munier, Peschanski (03)
■ Relation to Stat Phys : ‘reaction–diffusion’ A ⇋ 2A
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 22
Geometric scaling
ln Qln Λ
Y = ln 1/x
22QCD
ln Q (Y)2s
■ ρ− ρs(Y ) = const : A line of constant gluon occupancy
=⇒ physics must be invariant along any such a line !
■ Saturation makes itself felt in the dilute regime (Q2 > Q2s)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 22
Geometric scaling
■ Strictly true only within a finite ‘scaling window’ above Qs,
which extends with Y : lnQ2g(Y ) − lnQ2
s(Y ) ∝ √αsY
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 23
Geometric Scaling at HERA(Stasto, Golec-Biernat and Kwiecinski, 2000)
σ(x,Q2) ≈ σ(τ) with τ ≡ Q2/Q2s(x), Q2
s(x) = (x0/x)λ GeV2 , λ ≃ 0.3
x ≤ 0.01
Q2 ≤ 450 GeV2
Q2s ∼ 1 GeV2
for x ∼ 10−4
10-1
1
10
10 2
10 3
10-3
10-2
10-1
1 10 102
103
E665
ZEUS+H1 high Q2 94-95H1 low Q2 95ZEUS BPC 95ZEUS BPT 97
x<0.01
all Q2
τ
σ totγ*
p [µ
b]
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 24
Geometric Scaling at HERA (2)(Marquet and Schoeffel 2006)
10-2
10-1
1
β dσ
diffγ*
p /dβ
(µb
)
H1 data (LRG)
ZEUS data (Mx) *0.85
ZEUS data (LPS) *1.23
10-2
10-1
1
10-2
10-1
1
1 10 102
τd1 10 10
2
τd
10-1
1
10
1 10 102
ZEUS dataH1 data
τV
σ DV
CS (
nb)
1
10
10 2
10 102
ZEUS dataH1 data
τV
σ VM
(nb
)
1
10
10 2
1 10
ZEUS data
τV
σ VM
(nb
)1
10
10 2
10 102
ZEUS dataH1 data
τV
σ VM
(nb
)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
● CGC
● DIS off the CGC
● Saturation front
● Gluon distribution
● Traveling wave
● Geometric scaling
● Geometric scaling at HERA
● Qsat at NLO
Some consequences for HERA
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 25
Saturation exponent at NLO
D.N. Triantafyllopoulos, 2002
5 10 15 20 25
0.2
0.4
0.6
0.8
1
a
b
c
d
e
All with running coupling
a. brownb. greenc. blued. magentae. black
: L BFKL with: L BFKL: L BFKL + boundary: L RG BFKL + boundary: NL RG BFKL + boundary
Y0 =0
λ(Y ) ≡ d lnQ2s(Y )
dY≈ 0.3
■ NLO BFKL + Collinear resummation + Saturation Boundary
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 26
The unreasonable effectiveness of the ‘saturation models’
■ “Saturation models” ≡ QCD–inspired models for σdipole
involving saturation and a reasonable # of free parameters
■ The parameters are fixed by fits to the F2 data alone !
■ Satisfactory description of the ensemble of HERA data atx ≤ 0.01
All other observables (FD2 , FL, F
c2 , ρ, J/ψ, DVCS, ...)
emerge as ‘predictions’.
■ Important qualitative predictions of the theory which appearto be consistent with the data.
geometric scaling, the transition towards low Q2 for F2,a nearly constant σdiff/σtot ratio ...
■ A similar success for the relevant data at RHIC
high–p⊥ suppression in forward d–Au collisions (‘RpA’)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 27
Saturation models
■ The Golec-Biernat and Wüsthoff model (1999)
σGBWdipole(x, r) = 2πR2
(
1 − e−r2Q2
s(x)
)
, Q2s(x) = (x0/x)
λ GeV2
◆ Good fit to the early HERA data with only 3 parameters
◆ Exact ‘geometric scaling’ built in : σGBW(r2Q2s(x))
■ More sophisticated models (pQCD evolution, geometricscaling violations)
◆ DGLAP–like (also with b dependence) Bartels, Golec-Biernat,Kowalski (02), Kowalski, Teaney (03), Kowalski, Motyka, Watt (06)
◆ CGC model (BK eq.) E.I., Itakura, Munier (03) : 3 light quarks
◆ Improvements of CGC model: heavy quarks,b–dependence Kowalski, Motyka, Watt (06), Soyez (07)
◆ FS04 saturation model Forshaw, Shaw (04)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 28
A CGC fit to F2 (G. Soyez, 2007)
x ≤ 10−2 , Q2 ≤ 150 GeV2 (281 data points, ZEUS & H1)
10-6 10-5 10-4 10-3 10-2
x
10-1
1
101
F2
(x1.
5n )
0.045
0.065
0.085
0.11
0.15
0.2
0.25
0.3
0.4
0.5
0.65
Q2 (GeV2)
10-4 10-3 10-2
x
1
101
102
F2
(x1.
3n )2
2.5
3.5
56.58.51012152022252735456090120150Q2
4 parameters: R, x0 ≈ 2× 10−5, γ ≈ 0.26 and λ ≈ 0.22 (χ2 = 0.90)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 29
A CGC fit to F2 (G. Soyez, 2007)
0.1
1
10
1e-07 1e-06 1e-05 0.0001 0.001 0.01
Q2 (
GeV
2 )
x
Qs2
limit of geometricscaling window
H1ZEUS
light+heavy (GS)light only (IIM)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 30
A CGC fit to F c2
Forshaw, Sandapen and Shaw (06)
0
0.1
0.2
0.3
0.4
ZEUSm
c = 1.15
mc = 1.35
mc = 1.55
0
0.2
0.4
0.6
H1
0.0001 0.001 0.010
0.2
0.4
0.6
0.8
0.0001 0.001 0.01 0.0001 0.001 0.01
Q2 = 1.8, 2.0 Q
2 = 4.0 Q
2 = 7.0 Q
2 = 11.0
Q2 = 12.0 Q
2 = 18.0 Q
2 = 25.0 Q
2 = 30.0
F2
c
Q2 = 130.0Q
2 = 60.0Q
2 = 45.0
x
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 31
Saturation fits for Diffraction
Forshaw, Sandapen and Shaw (06) Low Q2
0.02
0.04
0.06
ZEUS FPC FS04 sat b= 6.8 GeV-2
FS04 no sat b=8 GeV-2
CGC b=6.8 GeV-2
Q2 = 6 GeV2Q2 = 4 GeV2
=0.6522
Q2 = 2.7 GeV2
xIP
x IP FD
(3)
2
=0.0044 =0.0066
0.02
0.04
0.06
=0.2308
=0.0099 =0.0148
=0.032 =0.0472
0.02
0.04
0.06
=0.0218
=0.1429
0.02
0.04
0.06
=0.0067
=0.3077 =0.4
10-4 10-3 10-2
0.02
0.04
0.06
=0.003
10-4 10-3 10-2
=0.7353
10-4 10-3 10-2 10-1
=0.8065
0.02
0.04
0.06
=0.0698=0.1
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 32
Saturation fits for Diffraction
Forshaw, Sandapen and Shaw (06) High Q2
0.02
0.04
0.06=0.0088
Q2 = 55 GeV2Q2 = 27 GeV2Q2 = 14 GeV2
Q2 = 8 GeV2x
IP
x IP FD
(3)
2
=0.0153=0.0291
0.02
0.04
0.06=0.0196
=0.0338 =0.0632
ZEUS FPC FS04 sat b = 6.8 GeV-2
FS04 no sat b = 8 GeV-2
CGC b = 6.8 GeV-2
=0.1209
0.02
0.04
0.06=0.062 =0.1037 =0.1824 =0.3125
0.02
0.04
0.06=0.1818 =0.28 =0.4286 =0.6044
0.02
0.04
0.06=0.4706 =0.6087 =0.75 =0.8594
10-4 10-3 10-2
0.02
0.04
0.06=0.8475
10-4 10-3 10-2
=0.9067
10-4 10-3 10-2
=0.9494
10-4 10-3 10-2 10-1
=0.9745
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 33
Saturation vs. Regge fits for F2
Forshaw and Shaw (04) Relatively low Q2
10-6 10-5 10-4 10-3 10-2 10-1
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
F 2
x
Q2=15 GeV2
Q2=0.25 GeV2
Q2=2.7 GeV2
10-6 10-5 10-4 10-3 10-2 10-1
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
F 2
x
Q2=15 GeV2
Q2=0.25 GeV2
Q2=2.7 GeV2
■ Left: Regge fits (a sum of ‘soft’ + ‘hard’ Pomerons)
■ Right: 2 saturation fits (FS04 and CGC)
■ Data appear to prefer saturation !
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 34
DIS Diffraction
Ygap
Q2}
MX
rQ2 }
M2X∼ Q2
■ An ideal laboratory to study saturation/unitarity effects
◆ sensitive to relatively large dipole sizes
◆ sensitive to theoretical models (or prejudices)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 34
DIS Diffraction
Ygap
Q2}
MX
rQ2 }
M2X∼ Q2
■ An ideal laboratory to study saturation/unitarity effects
◆ sensitive to relatively large dipole sizes
◆ sensitive to theoretical models (or prejudices)
■ Original prejudice: “Even for large Q2, diffraction is soft”
σdiff ∝ x−2(αP−1) and henceσdiff
σtot∼ x−(αP−1) at small x X�
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 35
Diffractive over inclusive ratio at HERAGolec-Biernat, Wusthoff (99) ; Bartels, Golec-Biernat & Kowalski (02)
σdiff/σ
tot
ZEUSQ2 = 8 GeV2
Q2 = 14 GeV2Q2 = 27 GeV2
Q2 = 60 GeV2
Satur. Mod. with evol MX < 3 GeV
3 < MX < 7.5 GeV
W(GeV)
7.5 < MX < 15 GeV
0
0.02
0.04
0.06
0
0.02
0.04
0.06
0
0.02
0.04
0.06
40 60 80 100 120 140 160 180 200 220
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 36
Diffractive dissociation of the virtual photon
dσdiff
d2b=
∫
dz d2r |Ψγ(z, r;Q)|2
(
T (r, Y ))2
■ The photon wavefunction favors small dipoles (r ∼ 1/Q)
dσdiff
d2b∼ 1
Q2
∞∫
1/Q2
dr2
r4
(
T (r, Y ))2
■ The dipole amplitude favors relatively large dipoles :
T (r) ∝ r2 (single scattering)
■ “The integral is dominated by large, non–perturbative,
dipoles with size r ∼ 1/ΛQCD, hence the soft pomeron ! ”
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
● Saturation models
● GBW
● CGC fit to F2
● F2c
● F2D3
● F2D3
● F2 Regge vs Sat
● DIS Diffraction
● Soft diffraction (?)
● Semi-Hard diffraction
Backup
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 37
Hardening the diffraction
■ At sufficiently high energy, gluon saturation cuts off the
large dipoles already on the ‘semi–hard’ scale 1/Qs !
dσdiff
d2b∼ 1
Q2
1/Q2
s∫
1/Q2
dr2
r4
(
r2Q2s(x)
)2
∼ Q2s(x)
Q2∝ x−λ
◆ σdiff is dominated by dipole sizes r ∼ 1/Qs(x) !
◆ σdiff ∝ x−λ : single, hard pomeron increase with 1/x
(instead of double soft !)
◆ σdiff/σtot ≈ constant ! X
■ ‘Semi–hard diffraction’ ... at intermediate energies !
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
● Fluctuations
● Pomeron loops
● Front diffusion
● Dispersion: FC
● Dispersion: RC
● Single scattering
● Multiple scattering
● No Jets
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 38
Stochastic aspects of high–energy QCD
■ Classical fields (JIMWLK) : no gluon–number fluctuations
■ Gluons in the same cascade are correlated with each other
■ Saturation & multiple scattering could probe the correlations
■ ‘Reaction–diffusion’ A ⇋ 2A Munier, Peschanski (03)
∂tn(x, t) = ∂2x n(x, t)
︸ ︷︷ ︸
diffusion
+ αn(x, t)︸ ︷︷ ︸
growth
−β n2(x, t)︸ ︷︷ ︸
recombination
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
● Fluctuations
● Pomeron loops
● Front diffusion
● Dispersion: FC
● Dispersion: RC
● Single scattering
● Multiple scattering
● No Jets
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 39
DIS with Pomeron loops
■ Statistical physics: The effects of fluctuations are dramatic !(The front is pulled by the dynamics in its dilute tail)
■ Important consequences for high–energy QCD(Mueller, Shoshi; E.I., Mueller, Munier; E.I., D. Triantafyllopoulos, 2004)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
● Fluctuations
● Pomeron loops
● Front diffusion
● Dispersion: FC
● Dispersion: RC
● Single scattering
● Multiple scattering
● No Jets
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 40
Front diffusion through fluctuations
■ The stochastic evolution generates un ensemble of frontswhich differ by their saturation momentum ρs ≡ lnQ2
s
〈ρs(Y )〉 = λY, 〈ρ2s〉 − 〈ρs〉2 = DY, D ∼ 1
ln3(1/αs)
log(r20/r
2)
T
2520151050-5
1
0.8
0.6
0.4
0.2
0
■ With increasing energy, the fronts spread from each other
=⇒ geometric scaling is progressively washed out !
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
● Fluctuations
● Pomeron loops
● Front diffusion
● Dispersion: FC
● Dispersion: RC
● Single scattering
● Multiple scattering
● No Jets
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 41
Dispersion: Fixed coupling
■ σ2(Y ) ≃ DαsY with D ∼ O(1)
0
5
10
15
20
25
0 10 20 30 40 50
σ2
Y
αs=0.2αs=0.5
■ Fluctuations effects are clearly important ...
αs = 0.5 =⇒ σ2(Y ) ≃ 10 for Y = 10
■ σ2(Y ) >∼ 1 =⇒ a totally new picture : ‘diffusive scaling’
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
● Fluctuations
● Pomeron loops
● Front diffusion
● Dispersion: FC
● Dispersion: RC
● Single scattering
● Multiple scattering
● No Jets
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 42
Dispersion: Running coupling
■ The dispersion keeps rising with Y ...
0
1
2
3
4
5
0 10 20 30 40 50
σ2
Y
FC: αs=0.2FC: αs=0.5RC: β=0.72RC: β=0.50
■ ... but now it is tremendously smaller ! (by a factor ∼ 100)
■ No physical effect up to unrealistically large Y !
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
● Fluctuations
● Pomeron loops
● Front diffusion
● Dispersion: FC
● Dispersion: RC
● Single scattering
● Multiple scattering
● No Jets
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 43
Single scattering: 2–gluon exchange
■ The dipole scatters off the gluon field in the target
V (r) ≃ gtar · Ea =⇒ T (x, r, b) ∝ g2r2〈Ea · Ea〉x
T (x, r, b) ≃ αs r2 xG(x, 1/r2)
πR2≡ αs n(x,Q2 ∼ 1/r2)
Weak scattering (T ≪ 1) ⇐⇒ Low gluon occupation (n≪ 1/αs)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
● Fluctuations
● Pomeron loops
● Front diffusion
● Dispersion: FC
● Dispersion: RC
● Single scattering
● Multiple scattering
● No Jets
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 44
Multiple scattering: Unitarization
■ When decreasing x at fixed r : xG(x, 1/r2) ∼ 1/xλ
=⇒ Unitarity is eventually violated ! (T >∼ 1)
■ Multiple scattering becomes important and restores unitarity
■ Eikonal approximation + Incoherent scattering =⇒
T (x, r) ≃ 1 − exp
{
−αs r2 xG(x, 1/r2)
πR2
}
(“Glauber–Mueller”)
Introduction
Motivation
Gluon evolution at small x
AdS/CFT
CGC & Geometric scaling
Some consequences for HERA
Backup
● Fluctuations
● Pomeron loops
● Front diffusion
● Dispersion: FC
● Dispersion: RC
● Single scattering
● Multiple scattering
● No Jets
Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 45
No forward jets !
■ No large–x partons =⇒ no forward/backward jets in a
hadron–hadron collision at strong coupling
t < 0
min
■ ‘The Nightmare of CMS’
|η| . ηmax(Q) = ln
√s
Q− ln
1
xs(Q), xs(Q) ∼ Λ2
Q2N2c
≪ 1
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