s. ostapchenko- pomeron calculus: x-sections, diffraction & mc
TRANSCRIPT
Pomeron Calculus: X-sections, Diraction & MC
S. Ostapchenko
NTNU (Trondheim)
ECT∗ Trento, December 3, 2010
arXive: 1003.0196 [hep-ph], hep-ph/0612175, 0602139, 0505259
Outline
I Optical theorem, unitarity & AGK cuts
I Enhanced Pomeron graphs: resummation
I Phenomenological approach - 2 Pomeron poles:
total, elastic & diractive x-sections
I 'Semihard Pomeron'
I MC approach (QGSJET II)
Outline
I Optical theorem, unitarity & AGK cuts
I Enhanced Pomeron graphs: resummation
I Phenomenological approach - 2 Pomeron poles:
total, elastic & diractive x-sections
I 'Semihard Pomeron'
I MC approach (QGSJET II)
Outline
I Optical theorem, unitarity & AGK cuts
I Enhanced Pomeron graphs: resummation
I Phenomenological approach - 2 Pomeron poles:
total, elastic & diractive x-sections
I 'Semihard Pomeron'
I MC approach (QGSJET II)
Outline
I Optical theorem, unitarity & AGK cuts
I Enhanced Pomeron graphs: resummation
I Phenomenological approach - 2 Pomeron poles:
total, elastic & diractive x-sections
I 'Semihard Pomeron'
I MC approach (QGSJET II)
Outline
I Optical theorem, unitarity & AGK cuts
I Enhanced Pomeron graphs: resummation
I Phenomenological approach - 2 Pomeron poles:
total, elastic & diractive x-sections
I 'Semihard Pomeron'
I MC approach (QGSJET II)
'Elementary' processes:
non-dir. production virtual rescattering diraction
I elastic scattering - coherence of the parton cascade preservedby the scattering process
I 'elementary' inel. process - coherence broken ⇒ hadronization
I general interaction - multiple scattering:
......σtot = Im = ∑
Optical theorem + AGK rules⇒ relation between elastic amplitude & inelastic nal states
+ +
2
+
= + + +
I AGK rules: no interference between dierent topologies ofnal states
I ⇒ all possible nal states - obtained via AGK-cuts of elasticscattering diagrams
I partial cross sections - expressed via amplitudes for'elementary' scattering
Optical theorem + AGK rules⇒ relation between elastic amplitude & inelastic nal states
+ +
2
+
= + + +
I AGK rules: no interference between dierent topologies ofnal states
I ⇒ all possible nal states - obtained via AGK-cuts of elasticscattering diagrams
I partial cross sections - expressed via amplitudes for'elementary' scattering
Optical theorem + AGK rules⇒ relation between elastic amplitude & inelastic nal states
+ +
2
+
= + + +
I AGK rules: no interference between dierent topologies ofnal states
I ⇒ all possible nal states - obtained via AGK-cuts of elasticscattering diagrams
I partial cross sections - expressed via amplitudes for'elementary' scattering
Optical theorem + AGK rules⇒ relation between elastic amplitude & inelastic nal states
+ +
2
+
= + + +
I AGK rules: no interference between dierent topologies ofnal states
I ⇒ all possible nal states - obtained via AGK-cuts of elasticscattering diagrams
I partial cross sections - expressed via amplitudes for'elementary' scattering
Schematic (elementary parton cascades ≡ Pomerons):
a
d
... ...1 2 m 1 n
......
a
d
I Pomeron amplitudes - various approaches possible(purely phenomenological, BFKL, ...)
Intermediate states between Pomeron exchanges include inelasticexcitations: ∑i |Xi 〉〈Xi |= |p〉〈p|+∑i 6=p |Xi 〉〈Xi |
I Good-Walker-like scheme - use elastic scattering eigenstates:
|Xi 〉 →∑j
√Cj/Xi
|j〉
Schematic (elementary parton cascades ≡ Pomerons):
a
d
... ...1 2 m 1 n
......
a
d
I Pomeron amplitudes - various approaches possible(purely phenomenological, BFKL, ...)
Intermediate states between Pomeron exchanges include inelasticexcitations: ∑i |Xi 〉〈Xi |= |p〉〈p|+∑i 6=p |Xi 〉〈Xi |
I Good-Walker-like scheme - use elastic scattering eigenstates:
|Xi 〉 →∑j
√Cj/Xi
|j〉
Schematic (elementary parton cascades ≡ Pomerons):
a
d
... ...1 2 m 1 n
......
a
d
I Pomeron amplitudes - various approaches possible(purely phenomenological, BFKL, ...)
Intermediate states between Pomeron exchanges include inelasticexcitations: ∑i |Xi 〉〈Xi |= |p〉〈p|+∑i 6=p |Xi 〉〈Xi |
I Good-Walker-like scheme - use elastic scattering eigenstates:
|Xi 〉 →∑j
√Cj/Xi
|j〉
E.g., using eikonal vertices for Pomeron emission:
fpp(s,b) = i∑j ,k
Cj/pCk/p
[1− e−χP
jk (s,b)]
χPjk = Imf P
jk - eikonal for Pomeron exchange between |j〉 and |k〉I ⇒ allows to calculate X-sections for various nal states:
σ(n)ad
(s) = ∑j ,k
Cj/pCk/p
∫d2b
[2χPjk(s,b)]
n
n!e−2χP
jk (s,b)
σdiffr−projad
(s) = ∑j ,k,l ,m
(Cj/pδjl −Cj/pCl/p
)Ck/pCm/p
×∫d2b
[1− e−χP
jk (s,b)][1− e−χP
lm(s,b)]
I partial x-sections are obtained after resummation of all virtual(elastic) rescatterings
I if the decomposition in eigenstates is energy-independent:low mass diraction (M2
X s) only
E.g., using eikonal vertices for Pomeron emission:
fpp(s,b) = i∑j ,k
Cj/pCk/p
[1− e−χP
jk (s,b)]
χPjk = Imf P
jk - eikonal for Pomeron exchange between |j〉 and |k〉I ⇒ allows to calculate X-sections for various nal states:
σ(n)ad
(s) = ∑j ,k
Cj/pCk/p
∫d2b
[2χPjk(s,b)]
n
n!e−2χP
jk (s,b)
σdiffr−projad
(s) = ∑j ,k,l ,m
(Cj/pδjl −Cj/pCl/p
)Ck/pCm/p
×∫d2b
[1− e−χP
jk (s,b)][1− e−χP
lm(s,b)]
I partial x-sections are obtained after resummation of all virtual(elastic) rescatterings
I if the decomposition in eigenstates is energy-independent:low mass diraction (M2
X s) only
E.g., using eikonal vertices for Pomeron emission:
fpp(s,b) = i∑j ,k
Cj/pCk/p
[1− e−χP
jk (s,b)]
χPjk = Imf P
jk - eikonal for Pomeron exchange between |j〉 and |k〉I ⇒ allows to calculate X-sections for various nal states:
σ(n)ad
(s) = ∑j ,k
Cj/pCk/p
∫d2b
[2χPjk(s,b)]
n
n!e−2χP
jk (s,b)
σdiffr−projad
(s) = ∑j ,k,l ,m
(Cj/pδjl −Cj/pCl/p
)Ck/pCm/p
×∫d2b
[1− e−χP
jk (s,b)][1− e−χP
lm(s,b)]
I partial x-sections are obtained after resummation of all virtual(elastic) rescatterings
I if the decomposition in eigenstates is energy-independent:low mass diraction (M2
X s) only
E.g., using eikonal vertices for Pomeron emission:
fpp(s,b) = i∑j ,k
Cj/pCk/p
[1− e−χP
jk (s,b)]
χPjk = Imf P
jk - eikonal for Pomeron exchange between |j〉 and |k〉I ⇒ allows to calculate X-sections for various nal states:
σ(n)ad
(s) = ∑j ,k
Cj/pCk/p
∫d2b
[2χPjk(s,b)]
n
n!e−2χP
jk (s,b)
σdiffr−projad
(s) = ∑j ,k,l ,m
(Cj/pδjl −Cj/pCl/p
)Ck/pCm/p
×∫d2b
[1− e−χP
jk (s,b)][1− e−χP
lm(s,b)]
I partial x-sections are obtained after resummation of all virtual(elastic) rescatterings
I if the decomposition in eigenstates is energy-independent:low mass diraction (M2
X s) only
Higher diraction = more asymmeric eigenstates
smaller σtot (σinel) - inelastic screening
bigger uctuations of multiplicity / of Npart in pA (AA)
Non-linear eects
Pomeron-Pomeron interactions ⇒ rich physics
I e.g. nal states with jets:...
...
...
...
'fan' diagrams - low-x PDFs as 'seen' in DIS & inclusivecross sections
'net fans' - 'reaction-dependent PDFs' (depend onrescattering on the partner hadron) )
p p
p...
(x, Q )2 (x, Q )2
High mass diraction from enhanced diagrams:
I sign-indenite contributions
I higher orders - increasingly important with energy
I ⇒ all order resummation needed
I same applies to other nal states
General solution to the problem (e.g. MC implementation) requires:
I knowledge of the Pomeron amplitude
I knowledge of multi-Pomeron vertices
I complete resummation of enhanced diagrams:for elastic scattering amplitude & for particular nal states
High mass diraction from enhanced diagrams:
I sign-indenite contributions
I higher orders - increasingly important with energy
I ⇒ all order resummation needed
I same applies to other nal states
General solution to the problem (e.g. MC implementation) requires:
I knowledge of the Pomeron amplitude
I knowledge of multi-Pomeron vertices
I complete resummation of enhanced diagrams:for elastic scattering amplitude & for particular nal states
High mass diraction from enhanced diagrams:
I sign-indenite contributions
I higher orders - increasingly important with energy
I ⇒ all order resummation needed
I same applies to other nal states
General solution to the problem (e.g. MC implementation) requires:
I knowledge of the Pomeron amplitude
I knowledge of multi-Pomeron vertices
I complete resummation of enhanced diagrams:for elastic scattering amplitude & for particular nal states
High mass diraction from enhanced diagrams:
I sign-indenite contributions
I higher orders - increasingly important with energy
I ⇒ all order resummation needed
I same applies to other nal states
General solution to the problem (e.g. MC implementation) requires:
I knowledge of the Pomeron amplitude
I knowledge of multi-Pomeron vertices
I complete resummation of enhanced diagrams:for elastic scattering amplitude & for particular nal states
High mass diraction from enhanced diagrams:
I sign-indenite contributions
I higher orders - increasingly important with energy
I ⇒ all order resummation needed
I same applies to other nal states
General solution to the problem (e.g. MC implementation) requires:
I knowledge of the Pomeron amplitude
I knowledge of multi-Pomeron vertices
I complete resummation of enhanced diagrams:for elastic scattering amplitude & for particular nal states
High mass diraction from enhanced diagrams:
I sign-indenite contributions
I higher orders - increasingly important with energy
I ⇒ all order resummation needed
I same applies to other nal states
General solution to the problem (e.g. MC implementation) requires:
I knowledge of the Pomeron amplitude
I knowledge of multi-Pomeron vertices
I complete resummation of enhanced diagrams:for elastic scattering amplitude & for particular nal states
High mass diraction from enhanced diagrams:
I sign-indenite contributions
I higher orders - increasingly important with energy
I ⇒ all order resummation needed
I same applies to other nal states
General solution to the problem (e.g. MC implementation) requires:
I knowledge of the Pomeron amplitude
I knowledge of multi-Pomeron vertices
I complete resummation of enhanced diagrams:for elastic scattering amplitude & for particular nal states
High mass diraction from enhanced diagrams:
I sign-indenite contributions
I higher orders - increasingly important with energy
I ⇒ all order resummation needed
I same applies to other nal states
General solution to the problem (e.g. MC implementation) requires:
I knowledge of the Pomeron amplitude
I knowledge of multi-Pomeron vertices
I complete resummation of enhanced diagrams:for elastic scattering amplitude & for particular nal states
Diagrammatic resummation
Without Pomeron 'loops' one would have 'net'-like graphs:
1
1 2
33
4
y ,b
y ,b
y ,b
y ,b y ,b
y ,b
y ,b
y ,b3
y ,b3
1
y ,b4
y ,b3
2
1
5
3
1 1
2 2
22
5
(a) (b) (c)
In reality, any 'intermediate' Pomeron may be replaced by 'loops':
...
Introduce 'net fan' contributions via Schwinger-Dyson equation:
y ,b22
net
...n2
y ,b1 1
y ,b
net net
11y ,b1 1
+...m
Σm +n >2
/
2
...l>1/
=2
2 2
2
/
m >1, n >0/
I correspond to arbitrary Pomeron 'nets' coupled to given vertex(for simplicity, loops not shown)
y ,b1 1
y ,b1 1
y ,b22
y ,b1 1
y ,b22
y ,b22
y ,b1 1y ,b
net
11
= + +
a
d
a
d
a
d
+y ,b
33
a
d
+ ...
I have the meaning of 'reaction-dependent PDFs'
Introduce 'net fan' contributions via Schwinger-Dyson equation:
y ,b22
net
...n2
y ,b1 1
y ,b
net net
11y ,b1 1
+...m
Σm +n >2
/
2
...l>1/
=2
2 2
2
/
m >1, n >0/
I correspond to arbitrary Pomeron 'nets' coupled to given vertex(for simplicity, loops not shown)
y ,b1 1
y ,b1 1
y ,b22
y ,b1 1
y ,b22
y ,b22
y ,b1 1y ,b
net
11
= + +
a
d
a
d
a
d
+y ,b
33
a
d
+ ...
I have the meaning of 'reaction-dependent PDFs'
Sum of (almost) all irredicible contributions to elastic amplitude(Ωpp(jk)(s,b)):
n1
−Σm
1
net
net
net
net
netnet y ,b
2
m...
...n2
...1n
mΣ−
m +n >2
...
...... +
1
1
1
ii
2 1
21m ,n >1m +n >3/
y ,b1 1
1 /
1
y ,b1
y ,b1 11
y ,b1 1
2
2m ,n >1/m ,n >0/
/
...
examples of graphs which are not included in this scheme:
p
p
p
p p p
pp
(a) (b) (c) (d)
Knowing the amplitude one can calculate σtot, dσel/dt, etc.
However, to describe the structure of nal states one needs thecomplete set of partial cross sections
I one assumes the validity of AGK cutting rules
I one starts from 'building blocks': AGK-cuts of 'net fans'- dened by Schwinger-Dyson equations
y ,b2 2
y ,b1 1
y ,b1 1
y ,b22
y ,b11
m>0/y ,b22
y ,b11
m>0/y ,b22
y ,b11
y ,b22
y ,b11
n>0/
m>2/
y ,b11y ,b1 1
y ,b22
y ,b22
y ,b11y ,b1 1
y ,b22
y ,b22
y ,b11
n>0/
m>2/
−
y ,b
= +−
1y ,b1 1
m=1_
y ,b1 1
+ −−
−= + + −/...
m>1/_
m>0
n>0/
net
net
......
net /
_/
net...
n>0...
...
net /
m>1_
/
net...
n>0...
...
...
net
netnet
.../
...
m>1/_
m>0
n>0/
net
net
......
m=1_
y ,b22
/...
m>1/_
m>0
n>0/
net
net
......
1
m=1_
m>1
...
net
netnet
...
One obtains the complete system of cuts:
...
1y ,b
1
_
net
/m>2/m>0
......
1y ,b
1
_
net
/m>2/m>0
net...
/n>2
net
...
/n>2_ n>0/
net...
/n>2
net
1y ,b
1
/m>0/m>2
_
...
net
...
n>0/1y ,b
1
_n=1
net
...n>0/1
y ,b1
_n=1
net
...
/m>0/m>2
_
/n>2_ n>0/
... net
...
/m>2
1y ,b
1
...netnet
/m>2
1y ,b
1−...
netnet
(2)/m>2
1y ,b
1
net
...n>0/
n=1_
net
...n>0/
n=1_
+ +
/m>0/m>2
_
...
net
...
1y ,b
1 1y ,b
1
n>1/ net
...
/m>0/m>2
_
+
/m>2
1y ,b
1
...netnet
1y ,b
1 n>0/
/n>2_
/m>1
...
net
net
......
(1)
1y ,b
1
/n>2_ n>0/
... net
...
/n>2_ n>0/
1y ,b
1
net
.../m>0
/m>2
...
_
net
......
/n>2_
...n>0/
net
... −−
1y ,b
1
/n>2_ n>0/
... net
...
/n>2_ n>0/
/m>2
net...
net/m>0
_m=1
...1
y ,b1 1
y ,b1
/n>2_
...n>0/
net
... +
net...
/n>2
1y ,b
1
net...
/n>2
1y ,b
1
...net
/m>0
_m=1
...
net...
/n>2
1y ,b
1
net/m>0
_m=1
/m>0
_m=1
net
+
(8)
+
+
(9)
net/m>0
_m=1
n>0/
/m>0
net
1y ,b
1
...
_m=1
_n=1
1y ,b
1
...
_m=1
_n=1
n>0/
/m>0
_m=1
1y ,b
1
_m=1
_n=1
1y ,b
1
_n=1
+ 1y ,b
1
_n=1
+
_n=1
1y ,b
1
_
net
/m>2
...
/m>0
net
−++ ......
... ......
_
net
/m>2/m>0
(3)
− ...
net
...
−...
netnet
−
_ne
t
...n>0/
n=1
...
net
...
(4)
+
(5) (6) (7)
−−
net
......
net
...net
(10)
netnet
−... ......
(11)
...... ...
−...net
... −...net
...
net
......
− +
Obtained contributions satisfy s-channel unitarity (completness):
11
∑i=1
Ω(i)pp(jk)(s,b) = Ωpp(jk)(s,b)
I allow to derive x-sections for various topologies of nal states
I e.g., diractive cuts:p
p
A B
C
E
p
p
E
C
D A B
C
CD
p
p
ED
A B
A B
(a) (b) (c)
I can be applied for a MC generation
I for all that one ONLY (?!) needs to know the Pomeronamplitude & multi-Pomeron vertices
Obtained contributions satisfy s-channel unitarity (completness):
11
∑i=1
Ω(i)pp(jk)(s,b) = Ωpp(jk)(s,b)
I allow to derive x-sections for various topologies of nal states
I e.g., diractive cuts:p
p
A B
C
E
p
p
E
C
D A B
C
CD
p
p
ED
A B
A B
(a) (b) (c)
I can be applied for a MC generation
I for all that one ONLY (?!) needs to know the Pomeronamplitude & multi-Pomeron vertices
Obtained contributions satisfy s-channel unitarity (completness):
11
∑i=1
Ω(i)pp(jk)(s,b) = Ωpp(jk)(s,b)
I allow to derive x-sections for various topologies of nal states
I e.g., diractive cuts:p
p
A B
C
E
p
p
E
C
D A B
C
CD
p
p
ED
A B
A B
(a) (b) (c)
I can be applied for a MC generation
I for all that one ONLY (?!) needs to know the Pomeronamplitude & multi-Pomeron vertices
Particular (simple) model
Let us assume eikonal multi-P vertices: G (m,n) = r3P γm+n−3P
I 2-component ('soft' +'hard') Pomeron:
DP(s, t) = 8π i[sαP(s) e
α ′P(s) lns t + rh/s sαP(h) e
α ′P(h) lns t]
I dipole form factor for proton elastic eigenstates |j〉:
FPj (t) =
γj
(1−Λj t)2; γj = γ (1±κ), j = 1,2
I Pomeron eikonal:χPjk(s,b) = 1
8π2is
∫d2q e−i~q
~b FPj (q2)FP
k (q2)DP(s,q2)
I P exchange between a proton and a multi-P vertex (y ,~b):
χPj (y ,b) =
γP8π2iey
∫d2q e−i~q
~b FPj (q2)DP(ey ,q2)
Particular (simple) model
Let us assume eikonal multi-P vertices: G (m,n) = r3P γm+n−3P
I 2-component ('soft' +'hard') Pomeron:
DP(s, t) = 8π i[sαP(s) e
α ′P(s) lns t + rh/s sαP(h) e
α ′P(h) lns t]
I dipole form factor for proton elastic eigenstates |j〉:
FPj (t) =
γj
(1−Λj t)2; γj = γ (1±κ), j = 1,2
I Pomeron eikonal:χPjk(s,b) = 1
8π2is
∫d2q e−i~q
~b FPj (q2)FP
k (q2)DP(s,q2)
I P exchange between a proton and a multi-P vertex (y ,~b):
χPj (y ,b) =
γP8π2iey
∫d2q e−i~q
~b FPj (q2)DP(ey ,q2)
Particular (simple) model
Let us assume eikonal multi-P vertices: G (m,n) = r3P γm+n−3P
I 2-component ('soft' +'hard') Pomeron:
DP(s, t) = 8π i[sαP(s) e
α ′P(s) lns t + rh/s sαP(h) e
α ′P(h) lns t]
I dipole form factor for proton elastic eigenstates |j〉:
FPj (t) =
γj
(1−Λj t)2; γj = γ (1±κ), j = 1,2
I Pomeron eikonal:χPjk(s,b) = 1
8π2is
∫d2q e−i~q
~b FPj (q2)FP
k (q2)DP(s,q2)
I P exchange between a proton and a multi-P vertex (y ,~b):
χPj (y ,b) =
γP8π2iey
∫d2q e−i~q
~b FPj (q2)DP(ey ,q2)
Particular (simple) model
Let us assume eikonal multi-P vertices: G (m,n) = r3P γm+n−3P
I 2-component ('soft' +'hard') Pomeron:
DP(s, t) = 8π i[sαP(s) e
α ′P(s) lns t + rh/s sαP(h) e
α ′P(h) lns t]
I dipole form factor for proton elastic eigenstates |j〉:
FPj (t) =
γj
(1−Λj t)2; γj = γ (1±κ), j = 1,2
I Pomeron eikonal:χPjk(s,b) = 1
8π2is
∫d2q e−i~q
~b FPj (q2)FP
k (q2)DP(s,q2)
I P exchange between a proton and a multi-P vertex (y ,~b):
χPj (y ,b) =
γP8π2iey
∫d2q e−i~q
~b FPj (q2)DP(ey ,q2)
Few parameter sets dier by the t to CDF/E710 at√s=1800 GeV
and by the P mass cuto (ξ = lnM2min
): ξ = 2 - A, C; ξ = 1.5 - B
αP(s) αP(h) α ′P(s),
GeV−2α ′P(h),
GeV−2γ,
GeV−1η rh/s Λ1 ,
GeV−2Λ2 ,
GeV−2r3P ,
GeV−1γP ,
GeV−1
(A) 1.145 1.35 0.13 0.075 1.65 0.6 0.06 1.06 0.3 0.14 0.5
(B) 1.15 1.35 0.165 0.08 1.75 0.6 0.065 1.03 0.3 0.15 0.5
(C) 1.14 1.31 0.14 0.085 1.6 0.5 0.09 1.1 0.4 0.14 0.5
I total / elastic cross sections and elastic slope
0
50
100
150
200
102
103
104
105
c.m. energy (GeV)
cro
ss s
ecti
on (
mb)
σtot
σel
10
15
20
25
30
102
103
104
105
c.m. energy (GeV)
slo
pe (
GeV
-2)
Using only 'net'-like (blue) / 'loop'-like (green) enhanced graphs:
0
50
100
150
200
102
103
104
105
c.m. energy (GeV)
cro
ss s
ecti
on (
mb) σtot
σel
0
50
100
150
200
102
103
104
105
c.m. energy (GeV) c
ross
sec
tion
(m
b)
σtot
σel
I ⇒ none of the two classes can be neglected
I P-loops only - far insicient for cross section calculations
I relative importance of P-loops - higher for smaller P-slope andfor non-eikonal multi-P vertices (e.g. in QCD)
Using only 'net'-like (blue) / 'loop'-like (green) enhanced graphs:
0
50
100
150
200
102
103
104
105
c.m. energy (GeV)
cro
ss s
ecti
on (
mb) σtot
σel
0
50
100
150
200
102
103
104
105
c.m. energy (GeV) c
ross
sec
tion
(m
b)
σtot
σel
I ⇒ none of the two classes can be neglected
I P-loops only - far insicient for cross section calculations
I relative importance of P-loops - higher for smaller P-slope andfor non-eikonal multi-P vertices (e.g. in QCD)
Using only 'net'-like (blue) / 'loop'-like (green) enhanced graphs:
0
50
100
150
200
102
103
104
105
c.m. energy (GeV)
cro
ss s
ecti
on (
mb) σtot
σel
0
50
100
150
200
102
103
104
105
c.m. energy (GeV) c
ross
sec
tion
(m
b)
σtot
σel
I ⇒ none of the two classes can be neglected
I P-loops only - far insicient for cross section calculations
I relative importance of P-loops - higher for smaller P-slope andfor non-eikonal multi-P vertices (e.g. in QCD)
Using only 'net'-like (blue) / 'loop'-like (green) enhanced graphs:
0
50
100
150
200
102
103
104
105
c.m. energy (GeV)
cro
ss s
ecti
on (
mb) σtot
σel
0
50
100
150
200
102
103
104
105
c.m. energy (GeV) c
ross
sec
tion
(m
b)
σtot
σel
I ⇒ none of the two classes can be neglected
I P-loops only - far insicient for cross section calculations
I relative importance of P-loops - higher for smaller P-slope andfor non-eikonal multi-P vertices (e.g. in QCD)
Dierential elastic cross section
10-5
10-4
10-3
10-2
10-1
1
10
10 2
10 3
10 4
10 5
10 6
0 0.1 0.2 0.3 0.4 0.5 |t| (GeV2)
dσ el
/dt
(mb/
GeV
2 )
546 (x101)
1800 (x100)
62.5 (x102)
53 (x103)
31 (x104)
14000 (x10-1)
Diractive cross sections
Single (M2
X/s < 0.15) and double (y(0)gap ≥ 3) diraction x-sections
1
10
102
103
104
105
c.m. energy (GeV)
cro
ss s
ectio
n (m
b)
σSD
σDD
1
10
102
103
104
105
c.m. energy (GeV) c
ross
sec
tion
(mb)
σSD
σDD
I high mass diraction - decreases with energy
I suppression of diraction - by eikonal RGS factors and byabsorptive corrections from higher order cut enhanced graphs
Diractive cross sections
Single (M2
X/s < 0.15) and double (y(0)gap ≥ 3) diraction x-sections
1
10
102
103
104
105
c.m. energy (GeV)
cro
ss s
ectio
n (m
b)
σSD
σDD
1
10
102
103
104
105
c.m. energy (GeV) c
ross
sec
tion
(mb)
σSD
σDD
I high mass diraction - decreases with energy
I suppression of diraction - by eikonal RGS factors and byabsorptive corrections from higher order cut enhanced graphs
Diractive cross sections
Single (M2
X/s < 0.15) and double (y(0)gap ≥ 3) diraction x-sections
1
10
102
103
104
105
c.m. energy (GeV)
cro
ss s
ectio
n (m
b)
σSD
σDD
1
10
102
103
104
105
c.m. energy (GeV) c
ross
sec
tion
(mb)
σSD
σDD
I high mass diraction - decreases with energy
I suppression of diraction - by eikonal RGS factors and byabsorptive corrections from higher order cut enhanced graphs
Examples - partiall resummations of higher order graphs
I dominant contributions to σSD:
/m>2
n>0/
/m>2
n>0/
n>1/_
n>1/_
/m>2
1y ,b
1 1y ,b
1 1y ,b
1
n>0/n>1/_ n>0/
m>2/_
/m>0
n>1/_
1y ,b
1
n>0/
m>2/_
/m>01y ,b
1
n>1/_
n>0/
m>2/_
n>1/_
/m>01y ,b
1
m>2/_
/m>01y ,b
1
net...
...
net...
/n>2
net...
/n>2
m>2/_
/m>01y ,b
1
net...
...
net...
/n>2
m>2/_
/m>01
y ,b1
n>0/
m>2/_
n>1/_
/m>01y ,b
1
n>0/
m>2/_
/m>01y ,b
11
y ,b1
net... n>0/
−...
netnet
...ne
t
...
net ...netnet
net
+
net
......
+...
netnet
−
net... ...
−
net
net
......
...
...
+
net
net
net
......
... net
...
net
net...
......
...
+
net
+ − ...... n
et
net
net...
......
...
+
netnet ne
t... ...
...
n>1/
net
...
_/n>2
/m>1...
+
net
...
(a) (b) (c) (d) (e) (f)
(g) (h) (i) (j) (k) (l)
I lowest order contribution only: p
p
n >1/1−
y ,b1 1
1m >1/
n >1/1− /1
n >0
22y ,b
y ,b1 1
m >12/ 1
m >1/
n >1/1−
k>1/
p
p
/1n >0
22y ,b
/2n >0
k>1/
p
p /1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
/2n >1
2/m >0...
......
...
...
...
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
p
p2
n =1
k=1
......
...
/k>2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
2/m >0
−n >1/2p
....../2n >0
...
......
p
(f)
...
...
/k>2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
2/m >0
/2n >2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
2/m >0
/k>0
k>1/−
/2n >2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
/k>12/m >1
/2n >2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
−n >1/2p
....../2n >0
/k>12/m >1
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
2/m >0
−n >1/2p
....../2n >0
/k>0
k>1/−...
...
......
...p
...
(g)
/1n >0
1/m >2
y ,b1 1
22y ,b
p
p2
n =1−
−n >1/1
k=1−
......
...
(h)
−
1/m >2
y ,b1 1
k=1−
2n =1−
22y ,b
1/m >2
y ,b1 1
2/m >0
22y ,b
/n >01
n >1/2−/n >0
2
1/m >2
y ,b1 1
22y ,b
n >1/2−/n >0
2
1/m >2
y ,b1 1
2/m >0
22y ,b
k>1/− /k>0
/n >01
n >1/2−/n >0
2
1/m >2
/1n >0
...
......
−
...
......
2m =1
k=1
p
p
......
......
...
...
(a) (b) (c)
−
(d) (e)
...
...
...
......
p
p...
...
...
......
...p
...
p...
...
...
...
......
p
p...
...
...
...
......
p
(i) (j) (k) (l)
−
...
.../n >0
1
...
p
p
...
... ......
... /k>2
...
p
p
...
... ......
.../k>1
...
...
p
p
...
...
...
......
2/m >1
/1n >1
(m) (n) (o) (p)
I triple-Pomeron graph only
I in all the cases - full re-summation of uncut enhanced graphs
Examples - partiall resummations of higher order graphs
I dominant contributions to σSD:
/m>2
n>0/
/m>2
n>0/
n>1/_
n>1/_
/m>2
1y ,b
1 1y ,b
1 1y ,b
1
n>0/n>1/_ n>0/
m>2/_
/m>0
n>1/_
1y ,b
1
n>0/
m>2/_
/m>01y ,b
1
n>1/_
n>0/
m>2/_
n>1/_
/m>01y ,b
1
m>2/_
/m>01y ,b
1
net...
...
net...
/n>2
net...
/n>2
m>2/_
/m>01y ,b
1
net...
...
net...
/n>2
m>2/_
/m>01
y ,b1
n>0/
m>2/_
n>1/_
/m>01y ,b
1
n>0/
m>2/_
/m>01y ,b
11
y ,b1
net... n>0/
−...
netnet
...ne
t
...
net ...netnet
net
+
net
......
+...
netnet
−
net... ...
−
net
net
......
...
...
+
net
net
net
......
... net
...
net
net...
......
...
+
net
+ − ...... n
et
net
net...
......
...
+
netnet ne
t... ...
...
n>1/
net
...
_/n>2
/m>1...
+
net
...
(a) (b) (c) (d) (e) (f)
(g) (h) (i) (j) (k) (l)
I lowest order contribution only: p
p
n >1/1−
y ,b1 1
1m >1/
n >1/1− /1
n >0
22y ,b
y ,b1 1
m >12/ 1
m >1/
n >1/1−
k>1/
p
p
/1n >0
22y ,b
/2n >0
k>1/
p
p /1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
/2n >1
2/m >0...
......
...
...
...
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
p
p2
n =1
k=1
......
...
/k>2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
2/m >0
−n >1/2p
....../2n >0
...
......
p
(f)
...
...
/k>2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
2/m >0
/2n >2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
2/m >0
/k>0
k>1/−
/2n >2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
/k>12/m >1
/2n >2
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
−n >1/2p
....../2n >0
/k>12/m >1
/1n >0n >1/1
−
1/m >2
y ,b1 1
22y ,b
2/m >0
−n >1/2p
....../2n >0
/k>0
k>1/−...
...
......
...p
...
(g)
/1n >0
1/m >2
y ,b1 1
22y ,b
p
p2
n =1−
−n >1/1
k=1−
......
...
(h)
−
1/m >2
y ,b1 1
k=1−
2n =1−
22y ,b
1/m >2
y ,b1 1
2/m >0
22y ,b
/n >01
n >1/2−/n >0
2
1/m >2
y ,b1 1
22y ,b
n >1/2−/n >0
2
1/m >2
y ,b1 1
2/m >0
22y ,b
k>1/− /k>0
/n >01
n >1/2−/n >0
2
1/m >2
/1n >0
...
......
−
...
......
2m =1
k=1
p
p
......
......
...
...
(a) (b) (c)
−
(d) (e)
...
...
...
......
p
p...
...
...
......
...p
...
p...
...
...
...
......
p
p...
...
...
...
......
p
(i) (j) (k) (l)
−
...
.../n >0
1
...
p
p
...
... ......
... /k>2
...
p
p
...
... ......
.../k>1
...
...
p
p
...
...
...
......
2/m >1
/1n >1
(m) (n) (o) (p)
I triple-Pomeron graph only
I in all the cases - full re-summation of uncut enhanced graphs
Impact on high mass part of σSD and diraction prole (at 14 TeV):
10-1
1
10
10 2
102
103
104
105
c.m. energy (GeV)
σSD
(HM
) (m
b)
10-3
10-2
10-1
1
0 1 2 3 b (fm)
σSD
(HM
)(b)
I using dominant contributions only - coincides with the fullre-summation within 5%
I lowest order contribution - order of magnitude dierence
I triple-P contribution only - violates unitarity:σSD > σtot, σSD(s,b) 1 at b ∼ 0
Impact on high mass part of σSD and diraction prole (at 14 TeV):
10-1
1
10
10 2
102
103
104
105
c.m. energy (GeV)
σSD
(HM
) (m
b)
10-3
10-2
10-1
1
0 1 2 3 b (fm)
σSD
(HM
)(b)
I using dominant contributions only - coincides with the fullre-summation within 5%
I lowest order contribution - order of magnitude dierence
I triple-P contribution only - violates unitarity:σSD > σtot, σSD(s,b) 1 at b ∼ 0
Impact on high mass part of σSD and diraction prole (at 14 TeV):
10-1
1
10
10 2
102
103
104
105
c.m. energy (GeV)
σSD
(HM
) (m
b)
10-3
10-2
10-1
1
0 1 2 3 b (fm)
σSD
(HM
)(b)
I using dominant contributions only - coincides with the fullre-summation within 5%
I lowest order contribution - order of magnitude dierence
I triple-P contribution only - violates unitarity:σSD > σtot, σSD(s,b) 1 at b ∼ 0
Impact on high mass part of σSD and diraction prole (at 14 TeV):
10-1
1
10
10 2
102
103
104
105
c.m. energy (GeV)
σSD
(HM
) (m
b)
10-3
10-2
10-1
1
0 1 2 3 b (fm)
σSD
(HM
)(b)
I using dominant contributions only - coincides with the fullre-summation within 5%
I lowest order contribution - order of magnitude dierence
I triple-P contribution only - violates unitarity:σSD > σtot, σSD(s,b) 1 at b ∼ 0
From the Tevatron to the LHC
1.8 TeV σ tot σ el σSD σDD σSDHM σDD
HM σDDLHM σDPE
Set (A) 79.3 19.3 9.62 3.62 4.52 1.95 1.20 (1.17) 0.19
Set (B) 80.5 19.9 9.84 4.06 4.78 2.37 1.24 (1.20) 0.23
Set (C) 72.8 16.4 10.5 3.84 5.74 2.01 1.42 (1.36) 0.28
KMR 73.7 16.4 13.8 9.7
GLM 73.3 16.3 9.76 5.36 1.2
14 TeV σ tot σ el σSD σDD σSDHM σDD
HM σDDLHM σDPE
Set (A) 128 37.5 12.1 4.61 3.62 2.06 1.40 (1.37) 0.10
Set (B) 126 37.3 12.4 5.18 4.24 2.50 1.60 (1.56) 0.14
Set (C) 108 29.7 12.3 5.36 5.06 2.81 1.72 (1.68) 0.20
KMR 91.7 21.5 19.0 14.1
GLM 92.1 20.9 11.8 6.08 1.28
I main dierence to KMR & GLM - faster rise of σtot
From the Tevatron to the LHC
1.8 TeV σ tot σ el σSD σDD σSDHM σDD
HM σDDLHM σDPE
Set (A) 79.3 19.3 9.62 3.62 4.52 1.95 1.20 (1.17) 0.19
Set (B) 80.5 19.9 9.84 4.06 4.78 2.37 1.24 (1.20) 0.23
Set (C) 72.8 16.4 10.5 3.84 5.74 2.01 1.42 (1.36) 0.28
KMR 73.7 16.4 13.8 9.7
GLM 73.3 16.3 9.76 5.36 1.2
14 TeV σ tot σ el σSD σDD σSDHM σDD
HM σDDLHM σDPE
Set (A) 128 37.5 12.1 4.61 3.62 2.06 1.40 (1.37) 0.10
Set (B) 126 37.3 12.4 5.18 4.24 2.50 1.60 (1.56) 0.14
Set (C) 108 29.7 12.3 5.36 5.06 2.81 1.72 (1.68) 0.20
KMR 91.7 21.5 19.0 14.1
GLM 92.1 20.9 11.8 6.08 1.28
I main dierence to KMR & GLM - faster rise of σtot
'Semihard Pomeron'
Parton cascades start at low virtualities ⇒I Q2
0- cuto between 'soft' and perturbative physics
I 'Soft' interactions (all |q2| - small ⇒ αs(q2) > 1):- pQCD is inapplicable ⇒'soft' Pomeron amplitude
I 'Semihard' processes (|q2|> Q20⇒ αs(q2) 1)
- 'soft' Pomeron for∣∣p2t ∣∣ < Q2
0
- DGLAP ladder for∣∣p2t ∣∣ > Q2
0
I general interaction ⇒ 'general Pomeron':
I
= +
soft Pomeron
QCD ladder
soft Pomeron
I same multi-P vertices: G (m,n) = r3P γm+n−3P
(couple soft Ps & soft 'ends' of semihard Ps)
'Semihard Pomeron'
Parton cascades start at low virtualities ⇒I Q2
0- cuto between 'soft' and perturbative physics
I 'Soft' interactions (all |q2| - small ⇒ αs(q2) > 1):- pQCD is inapplicable ⇒'soft' Pomeron amplitude
I 'Semihard' processes (|q2|> Q20⇒ αs(q2) 1)
- 'soft' Pomeron for∣∣p2t ∣∣ < Q2
0
- DGLAP ladder for∣∣p2t ∣∣ > Q2
0
I general interaction ⇒ 'general Pomeron':
I
= +
soft Pomeron
QCD ladder
soft Pomeron
I same multi-P vertices: G (m,n) = r3P γm+n−3P
(couple soft Ps & soft 'ends' of semihard Ps)
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Monte Carlo approach (QGSJET-II)
MC procedure:
I choose between low mass diraction or multiple productionI sample impact parameter & elastic scattering eigenstatesI sample a particular 'macro-conguration' of the interactionI for each cut 'net-fan': generate (recursively) all cut Pomerons
& rapidity gapsI perform energy partition between all cut PomeronsI for each cut 'semihard Pomeron': reconstruct the perturbative
'piece' (hard process, ISR, FSR)I for each cut Pomeron: string formation & hadronization
Like in the linear (quasi-eikonal) scheme
I interaction congurations are dened by Regge cuts of elasticdiagrams
I the procedure generalizes to hA (AA) in a parameter-free way
Main dierences of the latest version (QGSJET-II-04)compared to QGSJET-II-03 (released in 2005):
I Pomeron loops included (only net-like graphs in II-03)
⇒ twice smaller triple-P coupling: r3P ' 0.1 GeV
I PP-coupling xed by H1 LPS diractive data
(in II-03 - by FD(3)2
from ZEUS rap-gap data)
I parameter t included data on dσ elpp/dt, dσ el
πp/dt, dσ elKp/dt
I higher soft/hard cuto: Q20
= 3 GeV2 (Q20
= 2.5 GeV2 in II-03)
corresponds to pmin
⊥,hard = 2Q0 ' 3.4 GeV for the chosen
factorization scale in the model: M2F = p2⊥/4
Dierences between the two versions for particle production:at ne-tuning level (no drastic modications induced by LHC)
Main dierences of the latest version (QGSJET-II-04)compared to QGSJET-II-03 (released in 2005):
I Pomeron loops included (only net-like graphs in II-03)
⇒ twice smaller triple-P coupling: r3P ' 0.1 GeV
I PP-coupling xed by H1 LPS diractive data
(in II-03 - by FD(3)2
from ZEUS rap-gap data)
I parameter t included data on dσ elpp/dt, dσ el
πp/dt, dσ elKp/dt
I higher soft/hard cuto: Q20
= 3 GeV2 (Q20
= 2.5 GeV2 in II-03)
corresponds to pmin
⊥,hard = 2Q0 ' 3.4 GeV for the chosen
factorization scale in the model: M2F = p2⊥/4
Dierences between the two versions for particle production:at ne-tuning level (no drastic modications induced by LHC)
Main dierences of the latest version (QGSJET-II-04)compared to QGSJET-II-03 (released in 2005):
I Pomeron loops included (only net-like graphs in II-03)
⇒ twice smaller triple-P coupling: r3P ' 0.1 GeV
I PP-coupling xed by H1 LPS diractive data
(in II-03 - by FD(3)2
from ZEUS rap-gap data)
I parameter t included data on dσ elpp/dt, dσ el
πp/dt, dσ elKp/dt
I higher soft/hard cuto: Q20
= 3 GeV2 (Q20
= 2.5 GeV2 in II-03)
corresponds to pmin
⊥,hard = 2Q0 ' 3.4 GeV for the chosen
factorization scale in the model: M2F = p2⊥/4
Dierences between the two versions for particle production:at ne-tuning level (no drastic modications induced by LHC)
Main dierences of the latest version (QGSJET-II-04)compared to QGSJET-II-03 (released in 2005):
I Pomeron loops included (only net-like graphs in II-03)
⇒ twice smaller triple-P coupling: r3P ' 0.1 GeV
I PP-coupling xed by H1 LPS diractive data
(in II-03 - by FD(3)2
from ZEUS rap-gap data)
I parameter t included data on dσ elpp/dt, dσ el
πp/dt, dσ elKp/dt
I higher soft/hard cuto: Q20
= 3 GeV2 (Q20
= 2.5 GeV2 in II-03)
corresponds to pmin
⊥,hard = 2Q0 ' 3.4 GeV for the chosen
factorization scale in the model: M2F = p2⊥/4
Dierences between the two versions for particle production:at ne-tuning level (no drastic modications induced by LHC)
Main dierences of the latest version (QGSJET-II-04)compared to QGSJET-II-03 (released in 2005):
I Pomeron loops included (only net-like graphs in II-03)
⇒ twice smaller triple-P coupling: r3P ' 0.1 GeV
I PP-coupling xed by H1 LPS diractive data
(in II-03 - by FD(3)2
from ZEUS rap-gap data)
I parameter t included data on dσ elpp/dt, dσ el
πp/dt, dσ elKp/dt
I higher soft/hard cuto: Q20
= 3 GeV2 (Q20
= 2.5 GeV2 in II-03)
corresponds to pmin
⊥,hard = 2Q0 ' 3.4 GeV for the chosen
factorization scale in the model: M2F = p2⊥/4
Dierences between the two versions for particle production:at ne-tuning level (no drastic modications induced by LHC)
Main dierences of the latest version (QGSJET-II-04)compared to QGSJET-II-03 (released in 2005):
I Pomeron loops included (only net-like graphs in II-03)
⇒ twice smaller triple-P coupling: r3P ' 0.1 GeV
I PP-coupling xed by H1 LPS diractive data
(in II-03 - by FD(3)2
from ZEUS rap-gap data)
I parameter t included data on dσ elpp/dt, dσ el
πp/dt, dσ elKp/dt
I higher soft/hard cuto: Q20
= 3 GeV2 (Q20
= 2.5 GeV2 in II-03)
corresponds to pmin
⊥,hard = 2Q0 ' 3.4 GeV for the chosen
factorization scale in the model: M2F = p2⊥/4
Dierences between the two versions for particle production:at ne-tuning level (no drastic modications induced by LHC)
Total, elastic & diractive X-sections / slope
0
25
50
75
100
125
102
103
104
c.m. energy (GeV)
cro
ss s
ectio
n (m
b)
h+p QGSJET II-04
σtot
σel
10
15
20
102
103
104
c.m. energy (GeV)
slo
pe (G
eV-2
)
p+p QGSJET II-04
1
10
102
103
104
c.m. energy (GeV)
cro
ss se
ctio
n (m
b)
QGSJET II-04
σSD
σDD
dσ elhp/dt - only for small |t| (Gaussian form-factor used)
1
10
10 2
10 3
0 0.1 0.2 0.3 |t| (GeV2)
dσ el
/dt
(m
b/G
eV2 )
1800
62.5 (x10)
31 (x100)
1
10
10 2
10 3
0 0.1 0.2 0.3 |t| (GeV2)
dσ el
/dt
(m
b/G
eV2 )
Kp (x10)
πp
F2,FD(3)2
0
1
2
10-4
10-1
x
F2(x
,Q2 )
Q2=3.5 GeV2
10-4
10-1
x
Q2=4.5 GeV2
10-4
10-1
x
Q2=6.5 GeV2
10-4
10-1
x
Q2=8.5 GeV2
10-4
10-1
x
Q2=10.0 GeV2
FD(3)2
- upper limit on r3P (RRP & qq contributions neglected)
0
0.02
0.04 xP F
2D(3
)
Q2=3.9 GeV2
β=0.011Q2=3.9 GeV2
β=0.031Q2=7.1 GeV2
β=0.019Q2=7.1 GeV2
β=0.055
0
0.02
0.04
10-3
10-1
xP
xP F
2D(3
)
Q2=5.3 GeV2
β=0.02
10-3
10-1
xP
Q2=5.3 GeV2
β=0.06
10-3
10-1
xP
Q2=10.7 GeV2
β=0.02
10-3
10-1
xP
Q2=10.7 GeV2
β=0.06
Some results at xed target energies
10-1
1
0.2 0.4 0.6 0.8 1 x
xE d
n/dx
p+p → p
100 GeV/c
QGSJET II-04
1
10
0.8 0.85 0.9 0.95 1 x
xE d
n/dx
p+p → p QGSJET II-04
100 GeV/c
200 GeV/c (x 3)
10-4
10-3
10-2
10-1
1
10
10 2
0 0.2 0.4 0.6 0.8 1 x
dn/
dx
p+p → π+/π- QGSJET II-04
0
0.2
0.4
0.6
0.8
0 1 2 3 4 5 y
dn/
dy
p+p → π+/π- QGSJET II-04
Versions II-04 (solid) / II-03 (dashed) at√s = 0.2÷7 TeV
0
2
4
6
-5 -2.5 0 2.5 5 η
dN
ch/d
η NSD
1800
200
0
2
4
6
8
-5 -2.5 0 2.5 5 η
dN
ch/d
η
NSD
7000
900
2360
10-7
10-5
10-3
10-1
10
0 2 4 6 8 pt (GeV/c)
dn/
dyd2 p t (c
2 /GeV
2 )
NSD
200 (| η| < 2.5)
1800 (| η| < 1.0)
10-5
10-3
10-1
10
10 3
0 2 4 6 pt (GeV/c)
dn/
dηd2 p t (c
2 /GeV
2 )
NSD
| η| < 2.4
900 (x 0.1)
2360
7000 (x 10)
But: the inuence of detector eects unclear in CMS resultsE.g., contradiction with ALICE 'inel>0' selection:
0
2
4
6
8
-5 -2.5 0 2.5 5 η
dN
ch/d
η INEL+ QGSJET II-04
7000
900
2360
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Outlook
QGSJET-II is based on
I optical theorem & s-channel unitarityI all-order resummation of enhanced Pomeron graphsI complete set of partial x-sections (for all possible nal states)I self-consistent MC implementationI 'semihard Pomeron' scheme for hard processesI phenomenological soft Pomeron (⇒ strings) for soft processesI phenomenological vertices for Pomeron-Pomeron interactions
Main drawbacks:
I neglects energy-momentum correlations (at amplitude level) inmultiple scattering
I neglects 'hard' (|q2|> Q20) Pomeron-Pomeron coupling
⇒ no evolution of saturation scale above Q20
= 3 GeV2
(treatment currently in progress (higher twist resummation))
Backup
Procedure for a 'cut net-fan' reconstruction(for simplicity, illustrated without Pomeron loops)
1 1y ,b
1 1y ,b
n’>0/
1 1y ,b
m’>2/_
/m’>0
1 1y ,b
n’>0/= ...y’,b’+ ...
net
......
net
+...
netnet
/m’>2
...y’,b’
net......
net
I at each step, one checks if the remaining piece is just a singlecut Pomeron (with all the absorptive eects included):
...
= + ...+
a
d
y ,b1 1
+ + +
I or a diractive cut (last graph in the rhs)I or a splitting into 2 or more cut net-fans (2nd graph in the rhs)
Backup
Procedure for a 'cut net-fan' reconstruction(for simplicity, illustrated without Pomeron loops)
1 1y ,b
1 1y ,b
n’>0/
1 1y ,b
m’>2/_
/m’>0
1 1y ,b
n’>0/= ...y’,b’+ ...
net
......
net
+...
netnet
/m’>2
...y’,b’
net......
net
I at each step, one checks if the remaining piece is just a singlecut Pomeron (with all the absorptive eects included):
...
= + ...+
a
d
y ,b1 1
+ + +
I or a diractive cut (last graph in the rhs)I or a splitting into 2 or more cut net-fans (2nd graph in the rhs)
Backup
Procedure for a 'cut net-fan' reconstruction(for simplicity, illustrated without Pomeron loops)
1 1y ,b
1 1y ,b
n’>0/
1 1y ,b
m’>2/_
/m’>0
1 1y ,b
n’>0/= ...y’,b’+ ...
net
......
net
+...
netnet
/m’>2
...y’,b’
net......
net
I at each step, one checks if the remaining piece is just a singlecut Pomeron (with all the absorptive eects included):
...
= + ...+
a
d
y ,b1 1
+ + +
I or a diractive cut (last graph in the rhs)I or a splitting into 2 or more cut net-fans (2nd graph in the rhs)
Fixed target pC-collision
10-3
10-2
10-1
1
10
10 2
0 0.25 0.5 0.75 1 x
dn/
dx
p+C → π+/π- QGSJET II-04
0
0.25
0.5
0.75
1
-4 -2 0 2 4 y
dn/
dy
p+C → π+/π- QGSJET II-04
Interferention between double diraction and double singlediraction
Example: double high mass diraction at the lowest order
+
2
= + +
Comparison with heavy ions (QGSJET-II-03 - previousversion)
0
200
400
600
800
-5 -2.5 0 2.5 5pseudorapidity eta
dn/d
eta Au+Au 130 GeV → C
0-5%
5-10%
10-20%
20-30%
30-40%
40-50%0
200
400
600
800
-5 -2.5 0 2.5 5pseudorapidity eta
dn/d
eta Au+Au 200 GeV → C
0-5%
5-10%
10-20%
20-30%
30-40%40-50%