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Diffraction studies at LHeC and FCC-eh
Anna Staśto
Studies done by Wojciech Słomiński, Jagiellonian University, Kraków
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018 1
Outline
• Introduction: diffraction at HERA
• Phase space for inclusive diffraction at LHeC and FCC-eh
• Reduced cross section - pseudodata simulation
• Simulation of diffractive parton distribution functions
• Diffraction on nuclei
2Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
DiÄractive Selection
Proton Spectrometer• clean measurement - nodouble dissociativebackground
• low statistics
Large Rapidity Gap• high statistics• contains double dissociativebackground
FCAL BCAL RCAL
η=−0.75η=1.1
electron
scattered electron
proton
Grzegorz Gach Recent Results on Diffraction at HERA 12
IntroductionWhat is diffraction ?
• Diffractive processes are characterized by the rapidity gap: absence of any activity in part of the detector.
• Diffraction is interpreted as to be mediated by the exchange of an ‘object’ with vacuum quantum numbers - usually referred to as the Pomeron.
Diffractive event in ZEUS at HERA
At HERA in electron-proton collisions: about 10% events diffractive
3Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
4
Diffractive kinematics in DIS
� =Q2
Q2 + M2X � t
xBj = xIP �
momentum fraction of the Pomeron w.r.t hadron
momentum fraction of parton w.r.t Pomeron
t = (p� p0)2 4-momentum transfer squared
Two classes of diffractive events in DIS:photoproduction deep inelastic scatteringQ2 ⇠ 0 Q2 � 0
y =p · qp · k
W 2 = (q + p)2
s = (k + p)2
Q2 = �q2
x =�q2
2p · q
electron-proton cms energy squared:
Standard DIS variables:
photon-proton cms energy squared:
inelasticity
Bjorken x
(minus) photon virtuality
Diffractive DIS variables:
⇠ ⌘ xIP =Q2 +M2
X � t
Q2 +W 2
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
5
Diffractive structure functions
d3�D
dxIP dx dQ2=
2⇡↵2em
xQ4Y+ �D(3)
r (xIP , x,Q2)
Y+ = 1 + (1� y)2
�D(3)r = FD(3)
2 � y2
Y+FD(3)L
Reduced diffractive cross section depends on two structure functions
For y not to close to unity we have: �D(3)r ' FD(3)
2
FD(3)T,L (x,Q2, xIP ) =
Z 0
�1dtFD(4)
T,L (x,Q2, xIP , t)
Integrated vs unintegrated structure functions over t:
FD(4)2 = FD(4)
T + FD(4)L
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
6
Collinear factorization in diffraction
Collinear factorization in diffractive DIS
• Diffractive cross section can be factorized into the convolution of the perturbatively calculable partonic cross sections and diffractive parton distributions (DPDFs).
• Partonic cross sections are the same as for the inclusive DIS.
• The DPDFs represent the probability distributions for partons i in the proton under the constraint that the proton is scattered into the system Y with a specified 4-momentum.
• Factorization should be valid for sufficiently(?) large Q2 (and fixed t and xIP).
Collins
d�ep!eXY (x,Q2, xIP , t) =X
i
fDi ⌦ d�̂ei + O(⇤2/Q2)
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
7
DPDF parametrization
Regge factorization (additional assumption)
fDi (x,Q2, xIP , t) = fIP/p(xIP , t) fi(� = x/xIP , Q
2)
where k=g,d. Light quarks equal u=d=s.
fIP/p(xIP , t) = AIPeBIP t
x2↵IP (t)�1
Pomeron flux is parametrized as parton distributions in the Pomeron
fDi (x,Q2, xIP , t) = fIP/p(xIP , t) fi(�, Q
2) + nIRfIR/p(xIP , t) fIRi (�, Q2)
For good description of the data usually subleading Reggeons are included
↵IP (t) = ↵IP (0) + ↵0IP t
fk(z) = AkzBk(1� z)Ck
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
8
Diffractive fits⇠ = xIP
Comparison of H1-2006B and ZEUS-SJ fits to the H1-LRG 2012 dataZEUS-SJ fit seems to better describe the data in the low β region
Example of the DGLAP fit to the diffractive dataHERA models vs. recent HERA data
2017-11-15 Wojtek Slominski - PDFs and Low x at LHeC/FCC-he WG meeting 4
Compatible description ZEUS-SJ chosen for simulations
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
Phase space: HERA to LHeC to FCC-ehQ
2 [G
eV2 ]
x = βξ
θ > 1°θ = 10°ZEUS-LRGH1-LRGHERA-FLPS
10-2
10-1
100
101
102
103
104
105
106
107
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1
0.001 < y < 0.96β < 1ξ < 0.4
0.001 < y < 0.96β < 1ξ < 0.4
50 TeV60 GeV50 TeV60 GeV
1.3 GeV2
m2t
Q2
[GeV
2 ]
x = βξ
10-2
10-1
100
101
102
103
104
105
106
107
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1
0.001 < y < 0.96β < 1ξ < 0.4
0.001 < y < 0.96β < 1ξ < 0.4
7 TeV60 GeV7 TeV
60 GeV
1.3 GeV2
m2t
Q2
[GeV
2 ]
x = βξ
10-2
10-1
100
101
102
103
104
105
106
107
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1
0.001 < y < 0.96β < 1ξ < 0.4
0.001 < y < 0.96β < 1ξ < 0.4
HERAHERA
1.3 GeV2
m2t
Phase space ― HERA ! LHeC ! FCC-he
• CD = 7TeV vs. HERA– HIJK down by factor ~20
– -ILM0 up by factor ~100
• CD = 50TeV vs. 7TeV– HIJK down by factor ~10
– -ILM0 up by factor ~10
2017-11-15 Wojtek Slominski - PDFs and Low x at LHeC/FCC-he WG meeting 6
The grid shows suggested binning:4 bins per order of magnitude
for each of 3, -0, 5
CO = 60G1RCO = 60G1R
p, e energies
⇠ =
9Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
LHeC phase space: (β,Q2) fixed ξ
10Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
LHeC phase space ― Ep = 7 TeV
V W X. Z[# bins for V W X. Z[• no top
– 1589 for '( \ 1.3GeV(– 1229 for '( \ 5GeV(
• with top quark– 17 bins more
2017-11-15 Wojtek Slominski - PDFs and Low x at LHeC/FCC-he WG meeting 7
FCC-eh phase space: (β,Q2) fixed ξ
11Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
FCC-he phase space ― Ep = 50 TeV
2017-11-15 Wojtek Slominski - PDFs and Low x at LHeC/FCC-he WG meeting 8
V W X. Z[# bins for V W X. Z[• no top
– 2171 for '( \ 1.3GeV(– 1735 for '( \ 5GeV(
• with top quark– 275 (255) bins more
Data simulations
• Simulations based on extrapolation from ZEUS-SJ DPDFs
• VFNS scheme but no top at HERA so top contribution neglected in the simulation
• Errors simulated with 5% Gaussian noise
• Reggeon contribution is included but hard to constrain at HERA, could lead to large uncertainty in the extrapolation at ξ>0.01
• Binning to assume negligible statistical errors
12Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
Example of data: large ξ, LHeC
13Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
Simulated data ― an example
2017-11-15 Wojtek Slominski - PDFs and Low x at LHeC/FCC-he WG meeting 9
Extrapolationsand data
simulated with5% Gaussian noise
Example of data: large ξ, FCC-ehσred for Ep = 50 TeV, Ee = 60 GeV
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1×10-5 0.0001 0.001 0.01 0.1 1β
ξ = 0.018
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1×10-5 0.0001 0.001 0.01 0.1 1β
ξ = 0.032
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1×10-5 0.0001 0.001 0.01 0.1 1β
ξ = 0.056
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
1×10-5 0.0001 0.001 0.01 0.1 1β
ξ = 0.1
Q2 = 1.8Q2 = 3.2Q2 = 5.6Q2 = 10Q2 = 18Q2 = 32Q2 = 56
Q2 = 100Q2 = 180Q2 = 320Q2 = 560
Q2 = 1000Q2 = 1800Q2 = 3200Q2 = 5600
Q2 = 10000Q2 = 18000
14Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
DPDFs from simulations
15Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
DPDFs for LHeC
Krzysztof Golec-Biernat Di↵raction studies for future colliders 18 / 25
DPDFs error bands
16Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
DPDF accuracy improvement wrt. HERA
Krzysztof Golec-Biernat Di↵raction studies for future colliders 20 / 25
Luminosity studyGluon DPDF error bands from 5% simulations
Ep = 50 TeV, Q2min ≈ 5 GeV2, ξmax = 0.1
-0.04
-0.02
0
0.02
0.04
10-5 10-4 10-3 10-2 10-1
zg
z
Lumi = 2 fb-1
infinite Lumi
-0.04
-0.02
0
0.02
0.04
10-5 10-4 10-3 10-2 10-1
μ2 = 6 GeV2 -0.04
-0.02
0
0.02
0.04
10-5 10-4 10-3 10-2 10-1
z
-0.04
-0.02
0
0.02
0.04
10-5 10-4 10-3 10-2 10-1
μ2 = 20 GeV2
Quark DPDF error bands from 5% simulationsEp = 50 TeV, Q2
min ≈ 5 GeV2, ξmax = 0.1
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
10-5 10-4 10-3 10-2 10-1
zΣ
z
Lumi = 2 fb-1
infinite Lumi
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
10-5 10-4 10-3 10-2 10-1
μ2 = 6 GeV2
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
10-5 10-4 10-3 10-2 10-1
z
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
10-5 10-4 10-3 10-2 10-1
μ2 = 20 GeV2
Ee = 60 GeVEp = 50 TeV
Q2min ' 5 GeV2
Comparison of ‘infinite’ Lumi simulation and Lumi=2 fb-1
For this measurement there is negligible difference
17Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
Dependence on Qmin2 and EpGluon DPDF error bands from the 5% simulations
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
Ep = 7 TeV, #1229, Q2min = 4.2 GeV2
Ep = 50 TeV, #1735, Q2min = 4.2 GeV2
Ep = 7 TeV, #1589, Q2min = 1.3 GeV2
Ep = 50 TeV, #2171, Q2min = 1.3 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 6 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 20 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 60 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 200 GeV2
Gluon DPDF error bands from the 5% simulations
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
Ep = 7 TeV, #1229, Q2min = 4.2 GeV2
Ep = 50 TeV, #1735, Q2min = 4.2 GeV2
Ep = 7 TeV, #1589, Q2min = 1.3 GeV2
Ep = 50 TeV, #2171, Q2min = 1.3 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 6 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 20 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 60 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 200 GeV2
Gluon DPDF error bands from the 5% simulations
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
Ep = 7 TeV, #1229, Q2min = 4.2 GeV2
Ep = 50 TeV, #1735, Q2min = 4.2 GeV2
Ep = 7 TeV, #1589, Q2min = 1.3 GeV2
Ep = 50 TeV, #2171, Q2min = 1.3 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 6 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 20 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 60 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 200 GeV2
Improvement of accuracy of factor about 3 ÷ 5 for low Qmin2
Low Q2 region sensitive to higher twists, saturation etcespecially in diffraction. DGLAP fits may not work/be reliable in this region.
18
Quark DPDF error bands from the 5% simulations
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
zΣ
z
Ep = 7 TeV, #1229, Q2min = 4.2 GeV2
Ep = 50 TeV, #1735, Q2min = 4.2 GeV2
Ep = 7 TeV, #1589, Q2min = 1.3 GeV2
Ep = 50 TeV, #2171, Q2min = 1.3 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 6 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 20 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
zΣ
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 60 GeV2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 200 GeV2
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
19
DPDF accuracy: top contributionGluon DPDF error bands from the 5% simulations
Ep = 50 TeV
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
#1735, no top, Q2min = 4.2 GeV2
#1990, w. top, Q2min = 4.2 GeV2
#2171, no top, Q2min = 1.3 GeV2
#2446, w. top, Q2min = 1.3 GeV2
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 6 GeV2 -0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 20 GeV2
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 60 GeV2 -0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 200 GeV2
Quark DPDF error bands from the 5% simulationsEp = 50 TeV
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
zΣ
z
#1735, no top, Q2min = 4.2 GeV2
#1990, w. top, Q2min = 4.2 GeV2
#2171, no top, Q2min = 1.3 GeV2
#2446, w. top, Q2min = 1.3 GeV2
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 6 GeV2 -0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 20 GeV2
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
zΣ
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 60 GeV2 -0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 200 GeV2
Gluon DPDF error bands from the 5% simulationsEp = 50 TeV
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
#1735, no top, Q2min = 4.2 GeV2
#1990, w. top, Q2min = 4.2 GeV2
#2171, no top, Q2min = 1.3 GeV2
#2446, w. top, Q2min = 1.3 GeV2
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 6 GeV2 -0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 20 GeV2
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 60 GeV2 -0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 200 GeV2
Gluon DPDF error bands from the 5% simulationsEp = 50 TeV
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
zg
z
#1735, no top, Q2min = 4.2 GeV2
#1990, w. top, Q2min = 4.2 GeV2
#2171, no top, Q2min = 1.3 GeV2
#2446, w. top, Q2min = 1.3 GeV2
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 6 GeV2 -0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 20 GeV2
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
zgz
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 60 GeV2 -0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
z
-0.04
-0.02
0
0.02
0.04
10-6 10-5 10-4 10-3 10-2 10-1 100
μ2 = 200 GeV2
Top quark phase space region does not have big effect on
the DPDF extraction
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
20
Nuclear diffractive structure functionsPb208 FGS-2018 F2 sig NSuppr. at Q2 = 10, Ep = 7
0
0.2
0.4
0.6
0.8
1
10-4 10-3 10-2 10-1 100
RT ZM
ξ = 10-5
β
F2 FGS-L F2 FGS-H sig FGS-L sig FGS-H
0
0.2
0.4
0.6
0.8
1
10-4 10-3 10-2 10-1 100
RT ZM
ξ = 0.0001
β
0
0.2
0.4
0.6
0.8
1
10-4 10-3 10-2 10-1 100
RT ZM
ξ = 0.001
β
0
0.2
0.4
0.6
0.8
1
10-4 10-3 10-2 10-1 100
RT ZM
ξ = 0.01
β
0
0.2
0.4
0.6
0.8
1
10-4 10-3 10-2 10-1 100
RT ZM
ξ = 0.05
β
0
0.2
0.4
0.6
0.8
1
10-4 10-3 10-2 10-1 100
RT ZM
ξ = 0.1
β
• Model for nuclear shadowing: Frankfurt,Guzey,Strikman
• Two models: high and low shadowing
• Results for nuclear ratio:
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
21
Nuclear diffractive cross sections
ξσred for e-Pb at EPb/A = 19.7 TeV Ee = 60 GeV
0
0.02
0.04
0.06
0.01 0.1 1
ξ = 0.0001
ξσred
β
FGS18-LFGS18-H
0
0.02
0.04
0.06
0.08
0.01 0.1 1
ξσred
β
0.01 1
ξ = 0.001
β
0.1 1β
0
0.02
0.04
0.06
0.01 0.1 1
ξσred
β
0.01 1
ξ = 0.01
β
0.01 1β
0.1 1β
0
0.01
0.02
0.01 0.1 1
ξσred
β
0.0001 0.01 1
Q2
= 10
GeV
2
ξ = 0.1
β
0.01 1
Q2
= 10
0 G
eV2
β
0.01 1
Q2
= 10
3 G
eV2
β
0.1 1
Q2
= 10
4 G
eV2
β
ξσred for e-Pb at EPb/A = 2.76 TeV Ee = 60 GeV
0
0.01
0.02
0.03
0.04
0.05
0.01 0.1 1
ξ = 0.0001
ξσred
β
FGS18-LFGS18-H
0.1 1
ξ = 0.001
β
0
0.01
0.02
0.03
0.04
0.05
0.01 0.1 1
ξσred
β
0.01 1
ξ = 0.01
β
0.1 1β
0
0.01
0.02
0.03
0.01 0.1 1
ξσred
β
0.01 1
Q2
= 10
GeV
2
ξ = 0.1
β
0.01 1
Q2
= 10
0 G
eV2
β
0.1 1
Q2
= 10
3 G
eV2
β
0
0.005
0.01
0 0.2 0.4 0.6 0.8 1
Q2
= 10
4 G
eV2
ξσred
β
LHeC FCC-eh
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
Summary and Outlook
22
• New possibilities for studies of diffraction at LHeC and FCC-eh.
• DPDF accuracy increased by about factor 10 at LHeC and 20 at FCC-eh.
• It is possible to constrain gluon by inclusive data alone. Diffractive dijet production was necessary at HERA to constrain the gluon, such constraints could also be included at LHeC/FCC-eh further reducing accuracy.
• Possibility of producing diffractive top. DPDF determination does not seem to be affected much by the top though.
• Lowering initial Q2 increases the accuracy. This is the region that is expected to be very sensitive to higher twists in diffraction. Further analysis with better modeling of this region is necessary to estimate the impact of such correction.
• First analysis for diffraction in e-Pb at LHeC/FCC-eh.
Electrons for the LHC-LHeC/FCC-eh and Perle workshop, LAL-Orsay, June 28, 2018
