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

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

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

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

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

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

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?

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

• 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

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

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

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)

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)

• 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

Gavin Salam lectures, Quy Nhon Vietnam 2018

Partonic cross sections

Partonic cross sectionsSlide from Gavin Salam lectures Quy Nhon Vietnam 2018

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

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

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

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

Partonic cross sections Slide from Gavin Salam lectures Quy Nhon Vietnam 2018

Partonic cross sections

Scale dependence as the theory uncertainty or Missing Higher Order Uncertainty (MHOU)

Slide from Gavin Salam lectures Quy Nhon Vietnam 2018

• 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

• 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

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

Determination of SM parameters

ATLAS collaboration, EPJC 78 (2018) 110

PDF uncertainties

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

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

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

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

The parton model and QCD

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

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?

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)

Deep Inelastic Scattering

Deep Inelastic Scattering

Deep Inelastic Scattering

Deep Inelastic Scattering

Deep Inelastic Scattering

Deep Inelastic Scattering

Deep Inelastic Scattering

Deep Inelastic Scattering

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

The Parton Model

The Parton Model

The Parton Model

The Parton Model

The Parton Model

Exercise I: Z contribution

F

�,Z3 (x) =

nfX

i=1

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• 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

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ci = e2i � 2eiVeZViZPZ + (V 2eZ +A2

eZ)(V2iZ +A2

iZ)P2Z

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di = �2eiAeZAiZPZ + 4VeZAeZViZAiZP2Z

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PZ =Q2

(Q2 +M2Z)(4s

2wc

2w)

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Where

cw = cos ✓w

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Exercise II: Paschos-Wolfenstein relation

R =�NC(⌫)� �NC(⌫̄)

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R =1

2

✓1

2� sin ✓2w

◆

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• 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)

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)

Extra material

Deep Inelastic ScatteringSlide from F Olness lectures CTEQ school 2017

Partonic cross sections Slide from Gavin Salam lectures Quy Nhon Vietnam 2018