Color Glass Condensate and the relation to HERA …...Ringberg Workshop New Trends in HERA Physics...
Transcript of Color Glass Condensate and the relation to HERA …...Ringberg Workshop New Trends in HERA Physics...
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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
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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 !
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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
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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 !
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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
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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.
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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
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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
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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
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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
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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 !
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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’)
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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 !
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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
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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 ))
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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
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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 !
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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)
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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
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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]
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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
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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 )
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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
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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)
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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
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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]
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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
)
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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
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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’)
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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)
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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)
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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)
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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
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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
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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
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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 !
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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)
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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�
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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
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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 ! ”
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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 !
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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
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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)
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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 !
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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’
![Page 46: Color Glass Condensate and the relation to HERA …...Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA](https://reader033.fdocuments.us/reader033/viewer/2022042916/5f5579f21e28eb6c9627d0bb/html5/thumbnails/46.jpg)
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 !
![Page 47: Color Glass Condensate and the relation to HERA …...Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA](https://reader033.fdocuments.us/reader033/viewer/2022042916/5f5579f21e28eb6c9627d0bb/html5/thumbnails/47.jpg)
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)
![Page 48: Color Glass Condensate and the relation to HERA …...Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA](https://reader033.fdocuments.us/reader033/viewer/2022042916/5f5579f21e28eb6c9627d0bb/html5/thumbnails/48.jpg)
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”)
![Page 49: Color Glass Condensate and the relation to HERA …...Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA](https://reader033.fdocuments.us/reader033/viewer/2022042916/5f5579f21e28eb6c9627d0bb/html5/thumbnails/49.jpg)
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