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Maria Ubiali University of Cambridge
08th April 2019 Grad Days 2019
PAST PRESENT AND FUTURE CHALLENGES IN THE DETERMINATION OF THE STRUCTURE OF THE PROTON
LECTURE I
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Scope of the lectures➡ Give an overview on our understanding on the structure of the proton: from Feynman parton model to modern QCD picture
➡ Introduce basic concepts and techniques behind the determination of the structure of the proton from experimental data
➡ Wealth of ingredients involved: perturbative QCD, experimental measurements, statistical and mathematical problems, higher order predictions, phenomenology tools, machine learning.
➡ Discuss PDF-related phenomenology at the Large Hadron Collider and beyond
➡ Discuss current frontiers and challenges
Disclaimer: these lectures are far from providing a complete picture of the topic. You can find complementary information in excellent lectures on PDFs from W. Giele, G. Salam, A. Martin, P. Nadolsky, S. Forte, D. Stump, W. Melnitchouk, D. Stump, A. Guffanti, J. Rojo ... at recent graduate schools
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References• G. Ridolfi “Notes on deep-inelastic scattering and the Parton model” • S. Forte lectures • Ellis, Stirling and Webber “QCD and collider physics” • G. Dissertori, I. Knowles, M. Schmelling “Quantum Chromo Dynamics” • J. Gao, L. Harland-Lang, J. Rojo - Phys.Rept. 742 (2018) 1-121 • S. Forte, G. Watt - Ann.Rev.Nucl.Part.Sci. 63 (2013) • S. Forte, Acta Phys.Polon. B41 (2010) 2859 • E. Perez, E. Rizvi, Rep.Prog.Phys. 76 (2013) 046201. • A. Accardi, et al., Eur. Phys. J. C76 (8) (2016) 471 • A. De Roeck, R. S. Thorne, Prog.Part.Nucl.Phys. 66 (2011) 727 • http://pdg.lbl.gov/2017/reviews/rpp2017-rev-structure-functions.pdf
List of references complemented by specific references during the lectures
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Outline
• First lecture (Today)
• Second lecture (Tuesday)
• Experimental Data
• Disentangling proton’s components
• Statistics and Methodology
• Third lecture (Wednesday)
• Fits and methodology
• The NNPDF approach
• Fourth lecture (Thursday)
• New frontiers and challenges
• Motivation: the big picture
• Parton Model and QCD
• Collinear Factorisation
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Standard Model of particle physics• Standard Model (SM) of particle physics one of the greatest triumph of Quantum
Field Theories in the past century • SM remarkably successful theory: no convincing deviations so far from its predictions
SU(3)c ⇥ SU(2)L ⇥ U(1)Y
SU(3)c ⇥ U(1)e.m.
Spontaneous EW Symmetry breaking
Quantum Chromo Dynamics
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Some compelling questions
Higgs Boson
Hierarchy problem: Huge gap between EW scale (102 GeV) and Gravitational scale (1019 GeV)
Elementary or composite? Additional Higgs bosons?
Is the vacuum of the universe stable?
Degrassi et al, 2012
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Dark Matter
Weakly-interacting massive particle?Sterile neutrino?Extremely light particle (axion)?Alternative explanations?
Interaction with SM?Self-interacting?
Degrassi et al, 2012
Some compelling questions
Higgs Boson
Hierarchy problem: Huge gap between EW scale (102 GeV) and Gravitational scale (1019 GeV)
Elementary or composite? Additional Higgs bosons?
Is the vacuum of the universe stable?
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Why 3 families? Can we explain mass & mixings?
Origin of matter-antimatter asymmetry in the Universe?
Are neutrinos Majorana or Dirac fermions?
Quarks and leptons
Super-Kamiokande observation of neutrino oscillations, 2004
Dark Matter
Weakly-interacting massive particle?Sterile neutrino?Extremely light particle (axion)?Alternative explanations?
Interaction with SM?Self-interacting?
Higgs Boson
Hierarchy problem: Huge gap between EW scale (102 GeV) and Gravitational scale (1019 GeV)
Elementary or composite? Additional Higgs bosons?
Is the vacuum of the universe stable?
Some compelling questions
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• The Large Hadron Collider at CERN most powerful accelerator ever built • Extremely successful Run I (7-8 TeV) and great performance at Run II (13-14 TeV) • As luminosity increases, stronger probe on known processes (Higgs, Flavour
anomalies…) & larger mass reach
Higgs rediscovery at Run II
2027 +
2017
With LHC upgrade in ten yearsmass reach increase by ~2
A unique opportunity
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Higgs rediscovery at Run II
2027 +
LHC at the forefront of the exploration of the highenergy regime and key to plan future colliders Precise predictions are the key not to miss this
unique opportunity!
With LHC upgrade in ten yearsmass reach increase by ~2
2017
• The Large Hadron Collider at CERN most powerful accelerator ever built • Extremely successful Run I (7-8 TeV) and great performance at Run II (13-14 TeV) • As luminosity increases, stronger probe on known processes (Higgs, Flavour
anomalies…) & larger mass reach
A unique opportunity
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A new precision era in particle physics
102 : EW SCALE
1019 : PLANK SCALEGeV
LHC
Direct detection:precision required to characterise NP
𝜦102 : EW SCALE
1019 : PLANK SCALEGeV
LHC
Indirect detection: precision essential to spot deviations from SMpredictions
𝜦
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A new precision era in particle physics• Is precision physics really possible/necessary at hadron colliders? At the LHC a paradigm shift took place: discovery ➜ discovery through precision •Theoretical predictions to catch up with precision of experimental data
ATLAS SM summary plot (2018)
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A new precision era in particle physics• Is precision physics really possible/necessary at hadron colliders? At the LHC a paradigm shift took place: discovery ➜ discovery through precision •Theoretical predictions to catch up with precision of experimental data
ATLAS SM summary plot (2018)
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• Hard scattering of partons or Partonic cross section (Perturbative QCD+EW)
• Parton Distribution Functions
• Parton Showering and Hadronization
• Multiple Parton Interaction, Underlying Events
The precision ingredients
�th = �̂[O(1) +O(↵s) +O(↵2s) + ...]⌦ f1 ⌦ f2 +O
✓⇤2
Q2
◆
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Partonic cross sections
Gavin Salam lectures, Quy Nhon Vietnam 2018
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Gavin Salam lectures, Quy Nhon Vietnam 2018
Partonic cross sections
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Partonic cross sectionsSlide from Gavin Salam lectures Quy Nhon Vietnam 2018
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Partonic cross sections• On previous page, we wrote the series in terms of powers of 𝛼S(MH/2) • But we are free to rewrite it in terms of 𝛼S(𝝻) for any choice of renormalisation scale 𝝻
Slide from Gavin Salam lectures Quy Nhon Vietnam 2018
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Partonic cross sections• On previous page, we wrote the series in terms of powers of 𝛼S(MH/2) • But we are free to rewrite it in terms of 𝛼S(𝝻) for any choice of renormalisation scale 𝝻
Slide from Gavin Salam lectures Quy Nhon Vietnam 2018
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Partonic cross sections• On previous page, we wrote the series in terms of powers of 𝛼S(MH/2) • But we are free to rewrite it in terms of 𝛼S(𝝻) for any choice of renormalisation scale 𝝻
Slide from Gavin Salam lectures Quy Nhon Vietnam 2018
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Partonic cross sections• On previous page, we wrote the series in terms of powers of 𝛼S(MH/2) • But we are free to rewrite it in terms of 𝛼S(𝝻) for any choice of renormalisation scale 𝝻
Slide from Gavin Salam lectures Quy Nhon Vietnam 2018
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Partonic cross sections Slide from Gavin Salam lectures Quy Nhon Vietnam 2018
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Partonic cross sections
Scale dependence as the theory uncertainty or Missing Higher Order Uncertainty (MHOU)
Slide from Gavin Salam lectures Quy Nhon Vietnam 2018
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• LO: almost all processes • NLO: most processes (automated calculations) • NNLO: all 2 → 1, most 2→2 (explosion of calculations in the past few years) • N3LO: Higgs gluon fusion and Higgs via vector boson fusion
Partonic cross sections
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• Hard scattering of partons or Partonic cross section (Perturbative QCD+EW)
• Parton Distribution Functions
• Parton Showering and Hadronization
• Multiple Parton Interaction, Underlying Events
The precision ingredients
�th = �̂[O(1) +O(↵s) +O(↵2s) + ...]⌦ f1 ⌦ f2 +O
✓⇤2
Q2
◆
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43.9 pb
3.75 pb
1.38 pb
0.87 pb
0.51 pb
ggF (N2LO+N2LL)
VBF (N2LO)
WH (N2LO)
ZH (N2LO)
ttH(N1LO)
0 5 10 15 20
PDF+as
Scale
PDF uncertainties limiting factor in the accuracy of theoretical predictions
Yellow Report 3 (2013)
Higgs Production Channel % theo. uncertainty σ@13 TeV
PDF uncertainties
Higgs physics
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ggF (N3LO)
VBF (N2LO)
WH (N2LO)
ZH (N2LO)
ttH (N1LO)
0 5 10 15 20
PDF+as
Scale
Higgs Production Channel % theo. uncertainty
Reduced (still often dominant) PDF uncertainties
σ@13 TeV
48.5 pb
3.78 pb
1.37 pb
0.88 pb
0.51 pb
Yellow Report 4 (2016)
PDF uncertainties
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Determination of SM parameters
ATLAS collaboration, EPJC 78 (2018) 110
PDF uncertainties
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New Physics
Beenakker et al. EPJC76 (2016)2, 53
PDF uncertainties are a limiting factor in the accuracy of theoretical predictions, both within SM and beyond
PDF uncertainties
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Discrepancy between QCD calculations and CDF jet data (1995)
At that time there was no information on PDF uncertainties and the theoretical prediction strongly depends on gluon shape at x>0.1
Historia magistra vitae est
PDF uncertainties
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Discrepancy between QCD calculations and CDF jet data (1995)
At that time there was no information on PDF uncertainties and the theoretical prediction strongly depends on gluon shape at x>0.1
Historia magistra vitae est
CTEQ re-performed the parton fit by including the jet data and the discrepancy was removed.
PDF uncertainties
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Discrepancy between QCD calculations and CDF jet data (1995)
At that time there was no information on PDF uncertainties and the theoretical prediction strongly depends on gluon shape at x>0.1
Historia magistra vitae est
CTEQ re-performed the parton fit by including the jet data and the discrepancy was removed.
PDFs and new physics are very much related with each other (much more on part IV)
PDF uncertainties
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The parton model and QCD
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Historic overview• 1955: Hofstadter et al observed first deviations in scattering of electron off proton
from simple point-like Mott scattering ➜ Finite radius of proton ~ 0.7 fm
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Historic overview• 1964: Zweig and Gell-Mann independently postulated existence of three aces
(Zweig) or quarks (Gell-Mann) with fractional electric charge and spin–1/2 to explain proliferation of mesons and baryons in nucleon collision experiments. More of a mathematical model rather than particles! How could such objects be bound so tightly together?
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Historic overview• 1967: First deep-inelastic scattering experiments at SLAC 20 GeV linear
accelerator gave first evidence of point-like elementary constituents which were later identified as quarks (Bjorken scaling)
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Deep Inelastic Scattering
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Deep Inelastic Scattering
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Deep Inelastic Scattering
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Deep Inelastic Scattering
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Deep Inelastic Scattering
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Deep Inelastic Scattering
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Deep Inelastic Scattering
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Deep Inelastic Scattering
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Deep Inelastic ScatteringThe surprising results at SLAC was that F1,2 did not vanish as Q2 increased, rather they remained finite and constant and depended only on xB - Bjorken scaling (1969)
Such scaling demonstrated that the exchanged vector boson (photon) scatters off point-like objects that have no mass or scale associated. The lepton scatters off charged spin 1/2 constituents (partons) that carry a fraction x of proton momentum
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The Parton Model
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The Parton Model
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The Parton Model
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The Parton Model
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The Parton Model
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Exercise I: Z contribution
F
�,Z3 (x) =
nfX
i=1
di[qi(x)� q̄i(x)]<latexit sha1_base64="PdoVdRm/hP+NEJxQeUo98h65UPI=">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</latexit>
• Show that, in the Parton model, considering also the contribution of a virtual Z boson and its interference with the photon one obtains:
F
�,Z2 (x) = x
nfX
i=1
ci[qi(x) + q̄i(x)]<latexit sha1_base64="j3tBct/hV1M6l6pbbjaKTd/UkQw=">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</latexit>
ci = e2i � 2eiVeZViZPZ + (V 2eZ +A2
eZ)(V2iZ +A2
iZ)P2Z
<latexit sha1_base64="CEeaJYPREtxG851qiPWaWSg91q8=">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</latexit>
di = �2eiAeZAiZPZ + 4VeZAeZViZAiZP2Z
<latexit sha1_base64="LLNHtAKl9EP3T9ra/eOnYKW6d+c=">AAACIHicbVDLSsNAFJ3UV62vqks3wSIIYklqoW6EqhuXFeyDtjFMJjft0MmDmYlQQj/Fjb/ixoUiutOvcdpG0dYDczmccy937nEiRoU0jA8ts7C4tLySXc2trW9sbuW3dxoijDmBOglZyFsOFsBoAHVJJYNWxAH7DoOmM7gc+8074IKGwY0cRmD5uBdQjxIslWTnK65Nz45LYNNzO4H2SFXaHtXs9lG58S2o2pjIP+Ztyc4XjKIxgT5PzJQUUIqanX/vuiGJfQgkYViIjmlE0kowl5QwGOW6sYAIkwHuQUfRAPsgrGRy4Eg/UIqreyFXL5D6RP09kWBfiKHvqE4fy76Y9cbif14nlt6pldAgiiUEZLrIi5kuQ32clu5SDkSyoSKYcKr+qpM+5phIlWlOhWDOnjxPGqWieVI0rsuF6kUaRxbtoX10iExUQVV0hWqojgi6R4/oGb1oD9qT9qq9TVszWjqzi/5A+/wCPQ+jCQ==</latexit>
PZ =Q2
(Q2 +M2Z)(4s
2wc
2w)
<latexit sha1_base64="IfboP2lfOAEVPh+L6j9JSQcMBl0=">AAACEXicbVDLSsNAFJ3UV62vqEs3wSKkCCWJBd0IRTduhBbsg7ZpmEwn7dDJg5mJUkJ/wY2/4saFIm7dufNvnLRZaOuBuRzOuZc797gRJVwYxreSW1ldW9/Ibxa2tnd299T9gyYPY4ZwA4U0ZG0XckxJgBuCCIrbEcPQdyluuePr1G/dY8ZJGNyJSYRtHw4D4hEEhZQcVa85ncuexyBK6n1rmuiynt46nb5V0ivceehbKC2lqaMWjbIxg7ZMzIwUQYaao371BiGKfRwIRCHnXdOIhJ1AJgiieFroxRxHEI3hEHclDaCPuZ3MLppqJ1IZaF7I5AuENlN/TyTQ53ziu7LTh2LEF71U/M/rxsK7sBMSRLHAAZov8mKqiVBL49EGhGEk6EQSiBiRf9XQCMp4hAyxIEMwF09eJk2rbJ6VjXqlWL3K4siDI3AMdGCCc1AFN6AGGgCBR/AMXsGb8qS8KO/Kx7w1p2Qzh+APlM8fSe+bZg==</latexit>
Where
cw = cos ✓w
sw = sin ✓w<latexit sha1_base64="vQbk/Nd0HUQsY/kbSNTV2nxDKkA=">AAACEnicbZDLSsNAFIYn9VbrrerSzWBRdFMSFXQjFN24rGAv0IQwmU7boZNJmDmxlNBncOOruHGhiFtX7nwbp20Ebf1h4Oc753Dm/EEsuAbb/rJyC4tLyyv51cLa+sbmVnF7p66jRFFWo5GIVDMgmgkuWQ04CNaMFSNhIFgj6F+P6417pjSP5B0MY+aFpCt5h1MCBvnFY+oP8OEldmmkXegxIP7AdQs6o5rLH+oXS3bZngjPGyczJZSp6hc/3XZEk5BJoIJo3XLsGLyUKOBUsFHBTTSLCe2TLmsZK0nItJdOThrhA0PauBMp8yTgCf09kZJQ62EYmM6QQE/P1sbwv1orgc6Fl3IZJ8AknS7qJAJDhMf54DZXjIIYGkOo4uavmPaIIhRMigUTgjN78rypn5Sd07J9e1aqXGVx5NEe2kdHyEHnqIJuUBXVEEUP6Am9oFfr0Xq23qz3aWvOymZ20R9ZH99X55yo</latexit>
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Exercise II: Paschos-Wolfenstein relation
R =�NC(⌫)� �NC(⌫̄)
�CC(⌫)� �CC(⌫̄)<latexit sha1_base64="ocRFikyeWlzkd3nUY07Kr1G8YSs=">AAACUnicbVLNS8MwHM3m15xTqx69BIewHRytCnoRhrt4kinuA9Yy0izdwpK0JKkwSv9GQbz4h3jxoGZbD+7jQeDx3u+R5CV+xKjStv2Zy29sbm3vFHaLe6X9g0Pr6Litwlhi0sIhC2XXR4owKkhLU81IN5IEcZ+Rjj9uTP3OK5GKhuJFTyLicTQUNKAYaSP1Lfp85wYS4cRVdMhRP3Elh4+NtOKKuHqxIvpIJsZJq+lCoLEu0FgM9K2yXbNngKvEyUgZZGj2rXd3EOKYE6ExQ0r1HDvSXoKkppiRtOjGikQIj9GQ9AwViBPlJbNKUnhulAEMQmmW0HCm/k8kiCs14b6Z5EiP1LI3Fdd5vVgHt15CRRRrIvB8oyBmUIdw2i8cUEmwZhNDEJbUnBXiETINa/MKRVOCs3zlVdK+rDlXNfvpuly/z+oogFNwBirAATegDh5AE7QABm/gC/yA39xH7jtvfsl8NJ/LMidgAfnSH0shtJc=</latexit>
R =1
2
✓1
2� sin ✓2w
◆
<latexit sha1_base64="N/POhavrC2OaHehfe/YYG8R50eo=">AAACHXicbVA9SwNBEN2LXzF+RS1tDoMQC8NdFLQRgjaWUUwi5GLY28wli3t7x+6cEo78ERv/io2FIhY24r9x81Fo4oOBx3szzMzzY8E1Os63lZmbX1hcyi7nVlbX1jfym1t1HSWKQY1FIlI3PtUguIQachRwEyugoS+g4d+dD/3GPSjNI3mN/RhaIe1KHnBG0Ujt/NHVqRcoylJ3kJYHnoAAi7+EA09z6WEPkLYfbsue4t0e7rfzBafkjGDPEndCCmSCajv/6XUiloQgkQmqddN1YmylVCFnAgY5L9EQU3ZHu9A0VNIQdCsdfTew94zSsYNImZJoj9TfEykNte6HvukMKfb0tDcU//OaCQYnrZTLOEGQbLwoSISNkT2Myu5wBQxF3xDKFDe32qxHTTZoAs2ZENzpl2dJvVxyD0vO5VGhcjaJI0t2yC4pEpcckwq5IFVSI4w8kmfySt6sJ+vFerc+xq0ZazKzTf7A+voBx0WiVw==</latexit>
• Show that, in the Parton model, considering a (anti)neutrino-initiated DIS process on a deuteron target — assuming SU(2) isospin symmetry un(x)=dp(x) and dn(x) = up(x) — the ratio R
NC (mediated by Z) and CC (mediated by W+/-), assuming strange and anti-strange to be equal in the target, is independent of Parton Distribution Functions and can be used to determined the Weinberg angle 𝜃W
You may use (without deriving it) the result (and set c, cbar = 0)
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Wrap-up
➡The structure of the proton has been a crucial ingredient to test and verify perturbative QCD and it is now key to the precision challenge that we are facing at the LHC
➡Today’s lecture
✓ Parametrisation of the proton in terms of structure functions
✓ Parton model picture
✓ (QCD - Improved parton model)
✓ (DGLAP evolution equations)
✓ (Collinear Factorisation Theorem)
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Extra material
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Deep Inelastic ScatteringSlide from F Olness lectures CTEQ school 2017
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Partonic cross sections Slide from Gavin Salam lectures Quy Nhon Vietnam 2018