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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?
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 2/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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. . .
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 3/20
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.
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 4/20
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
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 5/20
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.
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 6/20
Theoretical predictions at the LHC
F (Q)
Parton densities(PDFs)
Partonic hardcross section
Parton Shower Jets(of hadrons)
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 7/20
Theoretical predictions at the LHC
F (Q)
Parton densities(PDFs)
Partonic hardcross section
Parton Shower Jets(of hadrons)
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 8/20
Theoretical predictions at the LHC
>>>>..
>>>>
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 )
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 9/20
PDFs
Parton densities(PDFs)
Partonic hardcross section
Parton Shower Jets(of hadrons)
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 10/20
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) + · · ·
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 11/20
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) + · · ·
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 11/20
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)].
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 12/20
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)].
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 12/20
Partonic Hard Cross Section
F (Q)
Parton densities(PDFs)
Partonic hardcross section
Parton Shower Jets(of hadrons)
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 13/20
Higher-order calculations
F
X
Parton densities(PDFs)
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)])
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 14/20
Higher-order calculations
F
X
Parton densities(PDFs)
Partonic crosssection σ̂
Factorization theorem
σ=∑
a,b
fa(M2) ⊗ fb(M
2)⊗σ̂ab(αS) + O
( Λ
M
)
Perturbation theory at next order (NLO):
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)])
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 14/20
Higher-order calculations
F
X
Parton densities(PDFs)
Partonic crosssection σ̂
Factorization theorem
σ=∑
a,b
fa(M2) ⊗ fb(M
2)⊗σ̂ab(αS) + O
( Λ
M
)
Perturbation theory at NNLO:
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)])
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 14/20
Higher-order calculations
F
X
Parton densities(PDFs)
Partonic crosssection σ̂
Factorization theorem
σ=∑
a,b
fa(M2) ⊗ fb(M
2)⊗σ̂ab(αS) + O
( Λ
M
)
Perturbation theory at NNLO:
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)])
Drell-Yanprocess
LODrell,Yan(1974)
NLOAltarelli,Ellis,GrecoMartinelli,(1980-84)
NNLOCatani,Cieri,deFlorian,G.F.,Grazzini (2009)
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 14/20
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)]).
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 15/20
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)].
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 16/20
Parton Shower and Hadronization
Parton densities(PDFs)
Partonic hardcross section
Parton Shower Jets(of hadrons)
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 17/20
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.
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 18/20
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)].
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 19/20
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.
Giancarlo Ferrera – Milan University & INFN Milan U. – 28/6/2017Precise theoretical predictions for LHC physics 20/20
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