QCD and the LHC - CERN · 2011. 2. 15. · The use of Quantum Chromodynamics, i.e. the theory that governs the behaviour of quarks and gluons G. Salam (CERN/Princeton/LPTHE) QCD and

QCD and the LHC

Gavin Salam

CERN, Princeton & LPTHE/CNRS (Paris)

Rutgers University, February 15 2011

The scales at play[Introduction]


tµ τneutrinos e

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1 century

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neutrinoexperiments

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neutrinoexperiments

LHC

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happens here...get clues as to what

The hope:

matter−antimatter asymmetry+ other questions, e.g.

nature of dark matter/energy

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neutrinoexperiments

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cosmic rays, astrophysics, cosmologyg−2, dark matter searches, proton decay, ...


The hope:



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LHC

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cosmic rays, astrophysics, cosmologyg−2, dark matter searches, proton decay, ...


The hope:



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LHC

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The Large Hadron Collider[Introduction]

The world’s largest fundamentalphysics endeavour

Designed to be 7× more powerfulthan its predecessor, Tevatron

Involving O (10 000) scientistsFrom about 60 countries

At a cost of several billion US$

This talk is about one of the facets of discovery at the LHC:

The use of Quantum Chromodynamics, i.e. the theory that governsthe behaviour of quarks and gluons

G. Salam (CERN/Princeton/LPTHE) QCD and the LHC 3 / 36

What does discovery look like?


What kinds of searches?[Introduction]

mass peak

dσ

/ dm

[log

sca

le]

mass

Signal

QCDprediction

New resonance (e.g. Z ′) where you see alldecay products and reconstruct an invari-ant mass

pp Z’

Sufficiently large, sharp signal emerges in-dependently of any knowledge of back-grounds.



New resonance (e.g. Z ′) where you see alldecay products and reconstruct an invari-ant mass

pp

µ+

µ−

Z’

Sufficiently large, sharp signal emerges in-dependently of any knowledge of back-grounds.



high−mass excess

dσ

/ dm

[log

sca

le]

mass

Signal

QCDprediction

UnreconstructedSUSY cascade.Study effective mass(sum of all transversemomenta).

~g

~g~g

~q

~q

χ0

χ0

g

q

q

q

q

g

Broad excess at high mass scales.

Knowledge of backgrounds is crucial isdeclaring discovery.



[GeV]effm

0 200 400 600 800 1000 1200 1400

En

trie

s / 1

00

Ge

V

-110

1

10

210

310 = 7 TeV)sData 2010 (Standard ModelmultijetsW+jetsZ+jetstt

single topDibosons

=2801/2=360 m0MSUGRA mµ1 lepton: e,

-1L dt ~ 35 pb∫

ATLAS

UnreconstructedSUSY cascade.Study effective mass(sum of all transversemomenta).

~g

~g~g

~q

~q

χ0

χ0

g

q

q

q

q

g

Broad excess at high mass scales.

Knowledge of backgrounds is crucial isdeclaring discovery.


dσ

/ dm

[log

sca

le]

mass

Signal ?

CONTINUEHERE

dσ

/ dm

[log

sca

le]

mass

Signal ?

STARTHERE


How do you predict a background?

The LHC collides protons — made of quarks and gluons.

The theory that governs the behaviour of quarks andgluons is Quantum Chromodynamics (QCD)


QCD[QCD]

QCD, an SU(3) Yang-Mills theory, gives the rules for the interaction ofquark fields (ψ) with gluon fields (A), and gluon fields with themselves.Most simply expressed in terms of the Lagrangian

L = ψ̄a(iγµ∂µδab − gsγµtCabACµ −m)ψb −1

4FµνA F

Aµν

FAµν

= ∂µAAν − ∂νAAν − gs fABCABµACν [tA, tB ] = ifABC tC


The QCD coupling[QCD]

One key parameter: the strength ofthe interaction, i.e. the strongcoupling ‘constant’ αs = g

2s /4παs = g2s /4παs = g2s /4π

αs(Q) ≃1

b0 lnQ2/Λ2

Nobel: Gross, Politzer & Wilczek

◮ strong interactions at proton (GeV) scale

◮ weak interactions at LHC (TeV)scales:

αs(1 TeV) ≃ 0.09

QCD α (Μ ) = 0.1184 ± 0.0007s Z

0.1

0.2

0.3

0.4

0.5

αs (Q)

1 10 100Q [GeV]

Heavy Quarkoniae+e– AnnihilationDeep Inelastic Scattering

July 2009

Bethke ’09


QCD predictions[QCD]

Given small coupling, the most widespread approach to

making QCD predictions is perturbation theory.E.g. using Feynman diagrams; basic rules for QCD known for ∼40 years

recursive techniques for trees (late 80’s); unitarity for loops (90’s and 00’s)

A cross section σ is written as a series in powers of αs:

σ =︷︸︸︷

σ2 α2s︸︷︷︸

leading order (LO)

+ σ3 α3s + σ4 α

4s

︸︷︷︸

NNLO

+ · · ·


QCD predictions[QCD]

Given small coupling, the most widespread approach to

making QCD predictions is perturbation theory.E.g. using Feynman diagrams; basic rules for QCD known for ∼40 years

recursive techniques for trees (late 80’s); unitarity for loops (90’s and 00’s)

A cross section σ is written as a series in powers of αs:

σ =

next-to-leading order(NLO)︷︸︸︷

σ2 α2s︸︷︷︸

leading order (LO)

+ σ3 α3s + σ4 α

4s

︸︷︷︸

NNLO

+ · · ·


Controlling QCD for discovery[QCD]

We can only approximate QCD (e.g. LO, NLO, etc.).

Discovery comes if you have an excess with respect to a QCDprediction accounting for its uncertainties.

Standard Model

0.01

0.1

1

10

100

1000

200 400 600 800 1000

dσ/d

p t [p

b/G

eV]

pt [GeV]

QCD predictionand uncertainty





New Physics

0.01

0.1

1

10

100

1000

200 400 600 800 1000

dσ/d

p t [p

b/G

eV]

pt [GeV]


data





New Physics

0.01

0.1

1

10

100

1000

200 400 600 800 1000

dσ/d

p t [p

b/G

eV]

pt [GeV]


data

New Physics?

0.01

0.1

1

10

100

1000

200 400 600 800 1000

dσ/d

p t [p

b/G

eV]

pt [GeV]


data





New Physics

0.01

0.1

1

10

100

1000

200 400 600 800 1000

dσ/d

p t [p

b/G

eV]

pt [GeV]


data

New Physics?

0.01

0.1

1

10

100

1000

200 400 600 800 1000

dσ/d

p t [p

b/G

eV]

pt [GeV]


data


A non-issue?

Even for a basic leading-order approximation, with αs ≃ 0.1,expect ∼ 10% uncertainty from missing NLO(?)

How well does QCD perturbative series converge?[QCD]

Consider LO, NLO and their ratio K =NLO

LO

0.001

0.01

0.1

1

10

100

1000

200 400 600 800 1000 1200 1400

dσ/d

p t [p

b/G

eV]

pt [GeV]

pp, 14 TeVFastNLO, kt R=0.7

LO

NLO

K ≃ 1.2

gluon

proton proton

quark




LO

0.001

0.01

0.1

1

10

100

1000

200 400 600 800 1000 1200 1400

dσ/d

p t [p

b/G

eV]

pt [GeV]


LO

NLO

K ≃ 1.2

Look at p t ofquark or gluon (jets)

gluon

proton proton

quark




LO

0.001

0.01

0.1

1

10

100

1000

200 400 600 800 1000 1200 1400

dσ/d

p t [p

b/G

eV]

pt [GeV]


LO

NLO

K ≃ 1.2

Look at p t ofquark or gluon (jets)

gluon

proton proton

quark

K of 1.2 is compatible with being 1 +O (αs)




LO

10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400

dσ/d

p t,Z

[fb

/ 100

GeV

]

pt,Z [GeV]

pp, 14 TeV

LO

NLO

K ≃ 1.5

MCFM

Look at p t ofZ−boson Z−boson

proton proton

quark




LO

10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400

dσ/d

p t,Z

[fb

/ 100

GeV

]

pt,Z [GeV]

pp, 14 TeV

LO

NLO

K ≃ 1.5

MCFM

Look at p t ofZ−boson Z−boson

proton proton

quark

K of 1.5 is compatible with being 1 + C × αs, with quite large C

To date, no generalised understanding of size of C when in range 5− 10




LO

10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400

dσ/d

p t,j1

[fb

/ 100

GeV

]

pt,j1 [GeV]

pp, 14 TeV

LO

NLO

K ≃ 5

MCFM

Look at p t ofquark (jet) Z−boson

proton proton

quark




LO

10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400

dσ/d

p t,j1

[fb

/ 100

GeV

]

pt,j1 [GeV]

pp, 14 TeV

LO

NLO

K ≃ 5

MCFM

Look at p t ofquark (jet) Z−boson

proton proton

quark

K of 5?!!! Found by several groups.Butterworth, Davison, Rubin & GPS ’08

Bauer & Lange ’09; Denner et al ’09




LO

10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400

dσ/d

HT

,jets

[fb

/ 100

GeV

]

HT,jets [GeV]

pp, 14 TeV

LO

NLO

K ≃ 100

MCFM

Look at sum of p t ofquarks and gluons (jets)

Z−boson

proton proton

quark

Rubin, GPS & Sapeta ’10




LO

10-2

10-1

1

101

102

103

104

200 400 600 800 1000 1200 1400

dσ/d

HT

,jets

[fb

/ 100

GeV

]

HT,jets [GeV]

pp, 14 TeV

LO

NLO

K ≃ 100

MCFM

Look at sum of p t ofquarks and gluons (jets)

Z−boson

proton proton

quark

Rubin, GPS & Sapeta ’10

What can it possibly mean to do perturbation theory if the “O (αs)”NLO correction is so much larger than LO?


So what happens at the next order, NNLO?[QCD]

The last examples are somewhat extreme. In such cases, it’s fair toask the question:

What happens at the next order? Does QCD converge?

Despite over 10 years’ work by many people, not a single NNLOcalculation exists for a hadron-collider process with coloured particlesin the final state.

Several groups working on NNLO for this and related processes; maybeZ+jet jet process will be completed in a year or two or . . . ?

Gehrmann family, Glover, Heinrich & al

Weinzierl

Somogyi, Trocsanyi, Del Duca, et al.

Czakon, Mitov, et al.

etc.


Why the large K -factor from LO to NLO?[QCD]

Leading Order

αsαEW

Next-to-Leading Order

α2sαEW

LHC probes scales well above EW scale,√s ≫ MZ .

EW bosons are light.New (logarithmically enhanced) topologies appear.


In absence of a full calculation atNNLO, try to gain physical insight


Leading Order

αsαEW


α2sαEW





Leading Order

αsαEW


α2sαEW ln2 ptMZ




Physical understanding → better predictions[QCD]

Since dominant contribution comes from Z+2partons, try combining NLOZ+parton with NLO Z+2partons. LoopSim: Rubin, GPS & Sapeta ’10

ptptpt of jet 1

0

2

4

6

8

10

250 500 750 1000 1250

K-f

acto

r w

rt L

O

pt,j1 (GeV)

MCFM 5.7, CTEQ6Mpp, 14 TeV

anti-kt, R=0.7pt,j1 > 200 GeV

LONLO–nNLO (µ dep)–nNLO (RLS dep)

Never achieved previously

We call this n̄NLO

Not quite full NNLO

But has many of its qualities

◮ ptj distribution seems toconverge at n̄NLO

◮ scale uncertainties reduced by∼ factor 2


Physical understanding → better predictions[QCD]

Since dominant contribution comes from Z+2partons, try combining NLOZ+parton with NLO Z+2partons. LoopSim: Rubin, GPS & Sapeta ’10

HT, jets =∑

jets pt,jHT, jets =∑

jets pt,jHT, jets =∑

jets pt,j

1

10

100

1000

500 1000 1500 2000 2500

K-f

acto

r w

rt L

O

HT,jets (GeV)

MCFM 5.7, CTEQ6Mpp, 14 TeVanti-kt, R=0.7pt,j1 > 200 GeV

LONLO

–nNLO (µ dep)–nNLO (RLS dep)

Never achieved previously

We call this n̄NLO

Not quite full NNLO

But has many of its qualities

◮ Signficiant furtherenhancement for HT ,jets

◮ n̄NLO brings clear message:

HT ,jetsHT ,jetsHT ,jets is not a goodobservable!


0.01

0.1

1

10

100

1000

200 400 600 800 1000

dσ/d

p t [p

b/G

eV]

pt [GeV]


data

Really New Physics?

What went into the QCDprediction?


As if “giant” K -factors weren’t bad enough. . .

How about infinite K -factors?


Quarks & gluons? You never see them[Jets]

q

q

Start off with quark and anti-quark, qq̄



In perturbative quantum chromody-namics (QCD), probability that aquark or gluon emits a gluon:

∼ dEE

dθ

θ

Diverges for small gluon energies E

Diverges for small angles θ

θ

q

q

A quark never survives unchangedit always emits a gluon (usually low-energy, at small angles)




∼ dEE

dθ

θ



q

q

Each gluon radiates a further gluon




∼ dEE

dθ

θ



q

q

And so forth




∼ dEE

dθ

θ



q

q

Meanwhile the same happens on other side of event




∼ dEE

dθ

θ



q

q

And then a non-perturbative transition occurs



q

q

π, K, p, ...

Giving a pattern of hadrons that “remembers” the gluon branchingHadrons mostly produced at small angle wrt qq̄ directions or with low energy



jet

jet

q

q

π, K, p, ...




jet

jet

q

q

π, K, p, ...



Instead of quarks and gluons, one sees “jets” of hadrons.

How can you compare a calculation of quarks and gluonsto a measurement of hadrons?

What happens to the divergences that arise inperturbative QCD beyond leading order?

Jets made systematic: jet definitions[Jets]

jet 1 jet 2

LO partons

Jet Def n

jet 1 jet 2

Jet Def n

NLO partons

jet 1 jet 2

Jet Def n

parton shower

jet 1 jet 2

Jet Def n

hadron level

π π

K

p φ

LHC events may be discussed in terms of quarks, quarks+gluon, or hadrons

A jet definition provides common representation of different “levels” ofevent complexity.


QCD jets flowchart[Jets]

Jet (definitions) provide central link between expt., “theory” and theory

And jets are an input to almost all analyses


A $100 000 000, 20-year old problem[Jets]

A significant community of QCD theorists has spent the past ten yearsmaking accurate calculations of signals and backgrounds at the LHC (withremarkable advances in field theory on the way)

O (100) people × 10 years ≃ $100 000 000

Problem 1: the jet definitions previously used by LHC experiments werenot compatible with these calculations — they “leaked” infinities:

σ = c1 αs + c2 α2s +∞∞∞α3s + · · ·

Problem 2: the jet definitions advocated by theorists since 1990’s hadbeen mostly shunned by proton-collider experiments

a) bad response to experimental noiseb) severe computational issues (1 minute/event ×1010 recorded events)


Solving the jets problem[Jets]

Discovered a link between QCD jet-finding and problems

of 2D computational geometryCacciari & GPS ’05

Many techniques could be carried over from comp. geom field

Developed a theory of the interplay between jet-finding,QCD radiation and experimental noise

Cacciari, GPS & Soyez ’08

A crucial element was linearity of response

Proposed a new jet-definition based on what we’d learnt

anti-ktCacciari, GPS & Soyez ’08


[Jets]

How anti-kt works:

◮ Define pairwise i–j distances

dij = min

(

1

p2ti,1

p2tj

)

∆R2ij

◮ Define single-particle distances

diB =1

p2ti

◮ If smallest is dij merge iand j

◮ If smallest is diB call i a jet

A non-intuitive successor to

kt alg of Catani et al. ’91

You can cluster anything[Jets]

Island Beach State Park

How anti-kt works:


dij = min

(

1

p2ti,1

p2tj

)

∆R2ij


diB =1

p2ti



