Precise theoretical predictions for Large Hadron Collider ...repodip.fisica.unimi.it/cdip17/talks/1_2_GFerrera-compressed.pdf · The Large Hadron Collider (LHC) at CERN is the world’s

Precise theoretical predictionsfor Large Hadron Collider physics

Giancarlo Ferrera

Milan University & INFN, Milan

Milan – June 28th 2017

TIF LAB: particle physicsphenomenology group

Members:S. Forte (Head) G. Sborlini (Postdoc)A. Vicini Z. Kassabov (PhD)G. Ferrera C. Muselli (PhD)

Strong connections with scientific activities at CERN.

Interactions with the local particle physics experimentalgroups (in particular ATLAS and LHCb).

Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 1/20

High Energy Physics and the LHC

Explore elementary constituents of matter and energy,their interactions.

The Standard Model (SM) of elementaryparticles describes strong (QCD) andelectroweak (EW) interactions.

The Large Hadron Collider (LHC) at CERN is the world’slargest particle accelerator (2009-2035). It explores theunknown region of the TeV energy frontier (i.e. 10−18m).

The LHC is addressing many fundamental questions in High Energy Physics:

What is the origin of the masses of the elementary particles?What is the nature of “dark matter”?Why is there a large matter and anti-matter asymmetry in the Universe?Do extra spatial dimensions exist?What is the connection between Higgs field and cosmological inflation?


From Maxwell equations to Higgs boson

∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t

+j or ∂µFµν=jν (Fµν=∂µAν−∂νAµ, jν=(ρ,j))

L0=− 14FµνFµν QED (massless photons) local gauge invariant (Aµ→Aµ+∂µλ(x))

How to describe massive vector bosons (e.g. weak interactions)?

Lm=− 14FµνFµν+✘✘

✘✘❳❳❳❳

m2

2AµAµ forbidden by gauge invariance (cannot quantize the theory!)

How to add a mass term preserving gauge invariance? The Higgs mechanism (1964):

LH=− 14FµνFµν+|(∂µ+iqAµ)φ|2−V (φ) , φ complex scalar field (LH gauge inv. φ→eθ(x)φ)

V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ

LH=− 14FµνFµν+(∂µh)2−

q2α4β

AµAµ+2αh2+···

Gauge invariance preserved! (Gauge bosons acquire massthrough spontaneous symmetry breaking).

It may look like a kind of magic, however extra massive scalarparticle (h) appears: the Higgs boson! After a 50-year hunt. . .



∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t





✘✘❳❳❳❳

m2




V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ


q2α4β

AµAµ+2αh2+···





∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t





✘✘❳❳❳❳

m2




V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ


q2α4β

AµAµ+2αh2+···





∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t





✘✘❳❳❳❳

m2




V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ


q2α4β

AµAµ+2αh2+···





∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t





✘✘❳❳❳❳

m2




V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ


q2α4β

AµAµ+2αh2+···





∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t





✘✘❳❳❳❳

m2




V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ


q2α4β

AµAµ+2αh2+···





∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t





✘✘❳❳❳❳

m2




V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ


q2α4β

AµAµ+2αh2+···





∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t





✘✘❳❳❳❳

m2




V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ


q2α4β

AµAµ+2αh2+···





∇·E=ρ, ∇·B=0, ∇×E=− ∂B∂t

, ∇×B= ∂E∂t





✘✘❳❳❳❳

m2




V (φ)=α|φ|2+β|φ|4, α<0, β>0, φ0=√

−α2β

, φ=φ0+h+iπ


q2α4β

AµAµ+2αh2+···




The Higgs boson discovery (→ see M. Fanti talk)

[ATLAS and CMS Coll. PLB716 (’12)]

On July 2012 the discovery of theHiggs boson at CERN: mostimportant breakthrough in particlephysics of the last 30 years.

Understanding the electroweaksymmetry breaking and the origin ofthe masses of the elementary particles.

Next LHC goal: detailedmeasurement of the Higgs bosonproperties. Key to unravel deviationfrom Standard Model predictions.

Besides Higgs boson discovery manyoutstanding results obtained by theLHC, and new discoveries are withinthe LHC reach in the next years.


LHC key results: Higgs boson and much more

pp

total (x2)

inelastic

JetsR=0.4

nj ≥ 10.1< pT < 2 TeV

nj ≥ 20.3<mjj < 5 TeV

γ

fid.

pT > 25 GeV

pT > 100 GeV

W

fid.

nj ≥ 0

nj ≥ 1

nj ≥ 2

nj ≥ 3

nj ≥ 4

nj ≥ 5

nj ≥ 6

nj ≥ 7

Z

fid.

nj ≥ 0

nj ≥ 1

nj ≥ 2

nj ≥ 3

nj ≥ 4

nj ≥ 5

nj ≥ 6

nj ≥ 7

nj ≥ 0

nj ≥ 1

nj ≥ 2

nj ≥ 3

nj ≥ 4

nj ≥ 5

nj ≥ 6

nj ≥ 7

t̄t

fid.

total

nj ≥ 4

nj ≥ 5

nj ≥ 6

nj ≥ 7

nj ≥ 8

t

tot.

s-chan

t-chan

Wt

VV

tot.

ZZ

WZ

WW

ZZ

WZ

WW

ZZ

WZ

WW

γγ

fid.

H

fid.

H→γγ

VBFH→WW

ggFH→WW

H→ZZ→4ℓ

H→ττ

total

Vγ

fid.

Zγ

Zγ

Wγ

t̄tWtot.

t̄tZtot.

t̄tγ

fid.

ZjjEWK

fid.

WWExcl.

tot.

Zγγ

fid.

Wγγ

fid.

VVjjEWKfid.

W ±W ±

WZ

σ[p

b]

10−3

10−2

10−1

1

101

102

103

104

105

106

1011

Theory

LHC pp√

s = 7 TeV

Data 4.5 − 4.9 fb−1

LHC pp√

s = 8 TeV

Data 20.3 fb−1

LHC pp√

s = 13 TeV

Data 0.08 − 14.8 fb−1

Standard Model Production Cross Section Measurements Status: August 2016

ATLAS Preliminary

Run 1,2√s = 7, 8, 13 TeV

Very good agreement between experimental results and SM theoreticalpredictions of the high-Q2 processes


How to increase the discovery power of the LHC?

The LHC is a hadron collidermachine: all the interesting reactionsinitiate by QCD hard scattering ofpartons: a good control of the QCDprocesses is necessary.

To fully exploit the information contained in the LHC experimentaldata, precise theoretical predictions of the Standard Model cross

sections are needed.


Theoretical predictions at the LHC

F (Q)

Parton densities(PDFs)

Partonic hardcross section

Parton Shower Jets(of hadrons)



F (Q)






>>>>..

>>>>

h1 + h2 → F (Q) + X

..

σ̂ab

F (Q)a(x1p1)

b(x2p2)

fa/h1(x1,µ

2F )

fb/h2(x2,µ

2F )

X

h1(p1)

h2(p2)

..

The asymptotically free QCD coupling αS (Q)

The framework: QCD factorization formula

σFh1h2(p1, p2) =

∑

a,b

∫ 1

0

dx1

∫ 1

0

dx2 fa/h1(x1, µ2F ) fb/h2(x2, µ

2F ) σ̂

Fab(x1p1, x2p2;µ

2F )+O

(ΛQCD

Q

)p

fa/h(x , µ2F ): Non perturbative universal parton densities (PDFs), µF ∼ Q.

σ̂ab: Hard scattering cross section. Process dependent, calculable with a perturbative expansion inthe strong coupling αS (Q) (Q ≫ ΛQCD ∼ 1GeV ).(

ΛQCD

Q

)p(with p ≥ 1): Non perturbative power-corrections.

Precise predictions for σ depend on good knowledge of both σ̂ab and fa/h(x , µ2F )


PDFs





Fit of PDFs

Method: typical parametrization of parton densities fa(x , µ20) at input

scale µ20 ∼ 1÷ 4 GeV 2. Parameters constrained by imposing momentum sum

rules:∑

a

∫ 1

0dx x fa(x , µ

20) = 1, then adjust parameters to fit data.

Typical constraining process:

DIS (fixed target exp. and HERA): sensitive to quark densities.Jet data (HERA and Tevatron): sensitive to high-x gluon density.Drell-Yan (low energy and Tevatron data): sensitive to (anti-)quark densities.

Evolution µ0 → µ using DGLAP equations:

∂fa(x , µ2)

∂ lnµ2=

αS(µ2)

2π

∫ 1

x

dξ

ξPab(x/ξ)fb(ξ, µ

2)

AP kernels calculable in pQCD

Pab(z) = P(0)ab (z) + αSP

(1)ab (z) + α2

SP(2)ab (z) + · · ·


Fit of PDFs

Method: typical parametrization of parton densities fa(x , µ20) at input

scale µ20 ∼ 1÷ 4 GeV 2. Parameters constrained by imposing momentum sum

rules:∑

a

∫ 1

0dx x fa(x , µ

20) = 1, then adjust parameters to fit data.

Typical constraining process:

DIS (fixed target exp. and HERA): sensitive to quark densities.Jet data (HERA and Tevatron): sensitive to high-x gluon density.Drell-Yan (low energy and Tevatron data): sensitive to (anti-)quark densities.

Evolution µ0 → µ using DGLAP equations:

∂fa(x , µ2)

∂ lnµ2=

αS(µ2)

2π

∫ 1

x

dξ

ξPab(x/ξ)fb(ξ, µ

2)

AP kernels calculable in pQCD

Pab(z) = P(0)ab (z) + αSP

(1)ab (z) + α2

SP(2)ab (z) + · · ·


Recent results on PDFs

x-510 -410 -310 -210 -110 1

)2(x

,Qγx

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

2 GeV4Photon PDF comparison at 10

MRST2004QEDNNPDF2.3QED averageNNPDF2.3QED replicas

σNNPDF 1NNPDF 68% c.l.

Some recent developments:

inclusion of LHC experimental data (W ,Z/γ∗ (at low/high invariant mass),isolated γ, jets, tt̄ production). andinclusion of QED corrections andextraction of photon PDF (withuncertainty) from data NNPDF Coll.

[Forte,Kassabov et al.

(’13,’14,’17)] (N3PDF ERC project).

Photon PDF has to be consistentlycombined with the Altarelli-Parisisplitting functions with mixed QCD-QEDcorrections [de Florian,Rodrigo,

Sborlini(’16)].


Recent results on PDFs

x-510 -410 -310 -210 -110 1

)2(x

,Qγx

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

2 GeV4Photon PDF comparison at 10

MRST2004QEDNNPDF2.3QED averageNNPDF2.3QED replicas

σNNPDF 1NNPDF 68% c.l.

!"#$

!%#$

!&#$

Some recent developments:

inclusion of LHC experimental data (W ,Z/γ∗ (at low/high invariant mass),isolated γ, jets, tt̄ production). andinclusion of QED corrections andextraction of photon PDF (withuncertainty) from data NNPDF Coll.

[Forte,Kassabov et al.

(’13,’14,’17)] (N3PDF ERC project).

Photon PDF has to be consistentlycombined with the Altarelli-Parisisplitting functions with mixed QCD-QEDcorrections [de Florian,Rodrigo,

Sborlini(’16)].


Partonic Hard Cross Section

F (Q)





Higher-order calculations

F

X


Partonic crosssection σ̂

Factorization theorem

σ=∑

a,b

fa(M2) ⊗ fb(M

2)⊗σ̂ab(αS) + O

( Λ

M

)

Perturbation theory at leading order (LO):

σ̂(αS) = σ̂(0) + αS σ̂(1) + α2

S σ̂(2) + O(α3

S)

LO result: only order of magnitude estimate.NLO: first reliable estimate.NNLO: precise prediction & robust uncertainty.

Higher-order calculations not an easy taskdue to infrared (IR) singularities:impossible direct use of numerical techniques.(alternatives to standard techniques beingexplored [Rodrigo, Sborlini et al. (’15,’16,’17)])



F

X




σ=∑

a,b

fa(M2) ⊗ fb(M


( Λ

M

)

Perturbation theory at next order (NLO):

σ̂(αS) = σ̂(0) + αS σ̂(1) + α2

S σ̂(2) + O(α3

S)





F

X




σ=∑

a,b

fa(M2) ⊗ fb(M


( Λ

M

)

Perturbation theory at NNLO:

σ̂(αS) = σ̂(0) + αS σ̂(1) + α2

S σ̂(2) + O(α3

S)





F

X




σ=∑

a,b

fa(M2) ⊗ fb(M


( Λ

M

)

Perturbation theory at NNLO:

σ̂(αS) = σ̂(0) + αS σ̂(1) + α2

S σ̂(2) + O(α3

S)



Drell-Yanprocess

LODrell,Yan(1974)

NLOAltarelli,Ellis,GrecoMartinelli,(1980-84)

NNLOCatani,Cieri,deFlorian,G.F.,Grazzini (2009)


NNLO QCD predictions compared with LHC datapp → W + X → lνl + X

|l

η|0 0.5 1 1.5 2 2.5

lA

0.1

0.15

0.2

0.25

0.3

0.35 = 7 TeV)sData 2010 (

MSTW08HERAPDF1.5ABKM09JR09

-1 L dt = 33-36 pb∫

Stat. uncertainty

Total uncertainty

ATLAS

Lepton charge asymmetry. Comparison betweenexperimental data and NNLO predictions (DYNNLO[Catani,Cieri,de Florian, G.F.,Grazzini(’09),(’10)]) using various PDFs (from [ATLASColl.(’12)]).

pp → γγ + X

[pb/

rad]

γγφ∆/dσd

1

10

210-1Ldt = 4.9 fb ∫ Data 2011,

DIPHOX+GAMMA2MC (CT10)

NNLO (MSTW2008)γ2

ATLAS

= 7 TeVs

data

/DIP

HO

X

00.5

11.5

22.5

3

[rad]γγ

φ∆0 0.5 1 1.5 2 2.5 3

NN

LOγ

data

/2

00.5

11.5

22.5

3

Azimuthal diphoton separation. Comparison betweenexp. data, NLO and NNLO predictions(2γNNLO[Catani,Cieri,de Florian,G.F.,Grazzini (’12)]) (from [ATLAS Coll.(’13)]).


NNLO QCD predictions at the LHC

pp → W+H + X → l+νbb̄ + X

d /dpTbb [fb/GeV]

µR = µF = MWH

µr = mH

pp W+H+X l bb_ +X

s=13 TeV, mH=125 GeV

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035d /dpT

bb [fb/GeV]

µR = µF = MWH

µr = mH

pp W+H+X l bb_ +X

s=13 TeV, mH=125 GeV

full NNLO

NNLO(prod)+NLO(dec)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

pTbb[GeV]

(full NNLO)/(NNLO(prod)+NLO(dec))

0.8

0.9

1

1.1

50 100 150 200 250 300

pTbb[GeV]

0.8

0.9

1

1.1

50 100 150 200 250 300

pTbb[GeV]

(full NNLO)/(NNLO(prod)+NLO(dec))

0.8

0.9

1

1.1

50 100 150 200 250 300

Left panel: transverse momentum of the Higgs bosonin production in NNLO (HVNNLO [G.F.,Grazzini,Tramontano (’11),(’14),(’15),(’17)]).

pp → t̄t + X

0

50

100

150

200

250

300

350

0.1 0.2 0.3 0.5 1 2 3 5

�

(pb

)µR/m

Renormalization Scale Variation: LHC 8 TeV

LO

NLO

NNLO

NNNLO

NNLO+NNLL

Right panel: Total cross section for (dependence onunphysical renormalization scale)[Muselli,Bonvini,Forte,Marzani,Ridolfi (’15)].


Parton Shower and Hadronization





Parton Shower and Hadronization

Complete description of a hadron scattering event.

QCD parton shower (PS): Starting from LOQCD, inclusion of dominant collinear andsoft-gluon emissions to all order in a approximateway as a Markov process (probabilistic picture).

No analytic solution but simple iterative structureof coherent parton branching.

Implemented in numerical Monte Carlo programs.

QCD parton cascade matched with hadronizationmodel for conversion of partons into hadrons(and model for resonance decay) ⇒ QCD eventgenerators.

Scheme of QCD Parton Shower andhadronization in hadron collisions.


Parton shower at NLO

pp → W + X → lν + X

0

50

100

150

200

d

�✴

dM

✦✭ W

✮

(pb/GeV)

-17

-14

-11

-8

-5

-2

1

50 60 70 80 90 100

2d

�

1

✧

d

�

2

d

�

1

✰

d

�

2

✭

%

✮

M✁✂W✄ (GeV)

PWG EW w PYTHIA+PHOTOSPWG w PYTHIAEW NLOBORN

1. PWG EW w shower - 2. PWG w shower1. EW NLO - 2. BORN

pp → Z/γ∗ + X → l+l− + X

�✁

✂✁

✄✁

☎✁

✆✁

✝✁

✞✁

✟✁

✠✛✡✠♣❄❧✰☛☞✌✍✎✏✑✒

✓✔✕ ✖✔ ✗ ✓✘✙✚✜✢ ✗ ✓✚✣✙✣✤✓✔✕ ✗ ✓✘✙✚✜✢✓✔✕ ✖✔ ✥✦✣✧✣★✥

✩✟✩✝✩☎✩✂✁

✂

☎✝

✟�✁

✂✆ ✄✁ ✄✆ ☎✁ ☎✆ ✆✁ ✆✆ ✝✁

✪✫✬❂✭✬✮✯✱

✲✳✴✵ ✶✷✸✹✺

✻✼ ✓✔✕ ✖✔ ✗ ✓✚✣✙✣✤ ✗ ✓✘✙✚✜✢ ✽ ✾✼ ✓✔✕ ✗ ✓✘✙✚✜✢✻✼ ✖✔ ✥✦✣ ✽ ✾✼ ✧✣★✥

Transverse mass (left panel) and lepton transverse momentum (right panel) distribution in vectorboson production. Parton shower predictions at NLO QCD×EW accuracy. Relative size of EWand QCD×EW corrections (lower panels) [Vicini et al. (’12,’13,’17)].


Conclusions

The LHC is exploring the unknownregion of the TeV energy frontier,trying to address manyfundamental questions in HighEnergy Physics.

Main message: to increase the LHC discovery power,accurate theoretical predictions are necessary ⇒ preciseparton density (PDFs) determinations and higher-orderperturbative calculations in QCD (and EW theory).

The members (including the younger ones) of TIF Labobtained significant results relevant to the physics program ofthe LHC.


Documents

Precise theoretical predictions for Large Hadron Collider ...repodip.fisica.unimi.it/cdip17/talks/1_2_GFerrera-compressed.pdf · The Large Hadron Collider (LHC) at CERN is the world’s