lectures on the sm beyond lo and vbs/vbfrebuzzi/didattica_files/pellen... · theory" weinberg:...
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Lectures on the SM beyond LO and VBS/VBF
Mathieu PELLEN
Cavendish Laboratory,University of Cambridge
University of Pavia - Lectures
3rd and 4th of April 2019
References: Textbook
Bohm/Denner/Joos: “Gauge Theories of the Strong andElectroweak Interaction”
Collins: “Renormalization”
Itzykson/Zuber: “Quantum Field Theory”
Peskin/Schroeder: “An Introduction to Quantum FieldTheory”
Weinberg: “The Quantum Theory of Fields, Vol. 1:Foundations”;“The Quantum Theory of Fields, Vol. 2: ModernApplications”
Maggiore: “A Modern Introduction to Quantum Field Theory”
Aitchison/Hey: “Gauge Theories in Particle Physics” Vol. 1and 2
Schwartz: “Quantum Field Theory and the Standard Model”
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 2 / 51
References: Others
EWSB: Lecture of Riccardo Torre:https://indico.cern.ch/event/673580See references inside
Exercises (corrected) in my lecture:https://indico.cern.ch/event/673580
Review on VBS/VBF: Michael Rauch 1610.08420
+ many more on the Internet or libraries...
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 3 / 51
Part II: The Standard Modelbeyond leading order
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 4 / 51
Higgs coupling
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 5 / 51
General rule for QCD corrections
There is no rule...
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 6 / 51
QCD effects (1)
Example:NLO QCD corrections to pp→ t?t? → (W? → νµµ
−) (W? → νee+) bb
Mt [GeV]
176174172170168
10
0
−10
∆FwW [%]
Mt [GeV]
176174172170168
10
0
−10
pp → νee+µ−νµbb+X @
√s = 8 TeV
176174172170168
3
2
1
0
K pp → νee+µ−νµbb+X @
√s = 8 TeV
176174172170168
3
2
1
0
Mt [GeV]
176174172170168
100
10NLO
LON
dσ/dMt [fb/GeV]
Mt [GeV]
176174172170168
100
10
[Denner et al.; 1207.5018]
→ Same effect for QED corrections (kinematic effect)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 7 / 51
QCD effects (2)
Example:NNLO QCD corrections to pp→ Zj
[Gehrmann-De Ridder et al.; 1507.02850]
→ Sudakov shoulder due to non-local cancelation of IR divergences[Catani, Webber; hep-ph/9710333]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 8 / 51
General rule for EW corrections
Leading effects
EW = QED + Weak
QED effects: photon radiation→ kinematic effects in particular close to resonancesWeak effects: Sudakov logarithms→ in high-energy limit
→ NB: QED and Weak corrections cannot always be separated
Possible when no W-boson exchange at tree level→ [Collins; Renormalization] Chapter 12.9
→ Example: pp→ Z?Z? → 4` [Biedermann et al.; 1611.05338]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 9 / 51
QED effects (1)
Example:NLO EW corrections to pp→ t?t? → (W? → νµµ
−) (W? → νee+) bb
dσ dMt
[fb GeV
]
LONLO EW
101
102
103
δ[%
]
Mt [GeV]
NLO EWphoton
-5
0
5
10
15
20
168 170 172 174 176 178 180
[Denner, MP; 1607.05571]
→ M2t =
(pνµ + pµ− + pb
)2
→ In the real radiation, γ is carrying some energyif not reconstructed with final states, shift events below the peak
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 10 / 51
QED effects (2)
Example:NLO QCD to pp→ Z?Z? → 4`
[Biedermann et al.; 1611.05338]
→ Very different QED correctiondue to rich resonance structure
M4` = MZ ' 90 GeV→ single-resonant Z boson
M4` = MZ + 2pT,min ' 120 GeV→ kinematic cut
M4` = 2MZ ' 180 GeV→ double-resonant Z bosons
→Weak corrections small ...... in this energy range
2001801601401201008060
1.10
1.05
1.00
0.95
0.90
NLO: [2µ2e]/(2 · [4µ])LO: [2µ2e]/(2 · [4µ])
M4ℓ [GeV]
[2µ2e
]/(2
·[4µ
])
5
4
3
2
1
0
−1
δqγ [2µ2e]δγγ [2µ2e]
δqγ [4µ]
δγγ [4µ]
δ[%
]
40
30
20
10
0
−10
δEWqq [2µ2e]
δweakqq [2µ2e]δEWqq [4µ]
δweakqq [4µ]
δ[%
]
10−1
10−2
10−3
10−4
10−5
NLO EW [2µ2e]LO [2µ2e]
NLO EW [4µ]LO [4µ]
√s = 13 TeV
dσ
dM
4ℓ
[fb
GeV
]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 11 / 51
Weak corrections
Example:NLO QCD to pp→ Z?Z? → 4`
[Biedermann et al.; 1611.05338]
→ Weak corrections become nega-tively large in the high energy limitlog2
(M2
V /s), log
(M2
V /s)
→ High-energy limit:
high invariant mass, hightransverse momentum, etc.
when the typical energy (s) ofthe partonic-process is largeNB: Small difference betweenEW and weak at high energy
1000900800700600500400300200100
1.08
1.06
1.04
1.02
1
0.98
0.96
0.94
NLO: [2µ2e]/(2 · [4µ])LO: [2µ2e]/(2 · [4µ])
M4ℓ [GeV]
[2µ2e
]/(2
·[4µ
])
4
3
2
1
0
−1
δqγ [2µ2e]δγγ [2µ2e]
δqγ [4µ]δγγ [4µ]
δ[%
]
40
30
20
10
0
−10
−20
δEWqq [2µ2e]
δweakqq [2µ2e]δEWqq [4µ]
δweakqq [4µ]
δ[%
]
10−1
10−2
10−3
10−4
NLO EW [2µ2e]LO [2µ2e]
NLO EW [4µ]LO [4µ]
√s = 13 TeV
dσ
dM
4ℓ
[fb
GeV
]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 12 / 51
Principle of (N)LO calculation
σ =1
F
∫dPSP|ME |2
→What is needed to compute a cross section at the LHC?
Phase space
Matrix element
PDF factor
→ At LO and for low multiplicity processes:• Phase-space and Matrix element can be computed analytically• PDF factor has to be obtained numerically
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 13 / 51
Principle of (N)LO calculation
Beyond 2→ 3, analytic computations become difficult(even with computer algebra)
→ Numerical computations are more appropriate
Use of Monte Carlo integration→ Allow for large number of integration variables(high-multiplicity processes)
Arbitrary differential distributions
Simpler(provided you have matrix elements and phase-space generators)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 14 / 51
Principle of NLO calculation
LO cross section:
σLO =
∫dΦnM2
0,n
NLO corrections:
δσNLO = real + virtual
=
∫dΦn+1M2
0,n+1 + 2
∫dΦnRe
[M∗
1,nM0,n
]
→ Problem: these two terms are separately divergent
Analytically not a problem→With a regulator, these can be computed separately→ Adding them, the regulator dependence disappears
Numerically impossible to integrate (without regulator) ...... a divergent quantity(the two terms have different integration variables)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 15 / 51
Principle of NLO calculation
Two solutions:
Slicing method→ Use of a cut-off to integrate divergent part analytically→ Computationally intensive as
The cut-off should be small enough (to only cut the divergentpart)The final result should be independent of this cut-off
Subtraction method:
Catani-Seymour (CS) dipoleFrixione-Kunszt-Signer (FKS)
→ Local cancellation of divergences→ Very efficient numerically
→ More details in [Frederix’s lecture] and [Denner’s lecture]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 16 / 51
Brief state-of-the-art of higher-order computations
NLO QCD / EW
Automatised and available for all 2→ 4/5 processes→ MadGraph5 aMC@NLO or Sherpa
For 2→ 6/7: specific tools required
NNLO QCD
Almost all 2→ 2 processes known but not all availablepublicly
One 2→ 3: VBF in approximate way[Cacciari et al.; 1503.02660], [Cruz-Martinez et al.; 1802.02445]
N3LO QCD
gg→ H in infinite top mass limit [Anastasiou et al.; 1503.06056]
VBF in approximate way [Dreyer and Karlberg; 1811.07906]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 17 / 51
Part III: Vector-boson fusionand vector-boson scattering
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 18 / 51
Slide from Christopher Schwan
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 19 / 51
LO contributions at: O(α6)
and O(αs
2α4)
(EW contribution/signal and QCD contribution/background)
→ Example of W+W+:
(GeV)jjm100 200 300 400 500 600 700 800
| jjy∆|
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0
0.002
0.004
0.006
0.008
0.01
0.012
6α|): jj
y∆, |jj
(fb) per bin (mσ
(GeV)jjm100 200 300 400 500 600 700 800
| jjy∆|
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
4α2sα|):
jj y∆, |
jj (fb) per bin (mσ
[Ballestrero, MP et al.; 1803.07943]
The contributions have different kinematic
Need for exclusive cuts to enhance the EW contribution→ typical cuts are mjj and |∆yjj|.
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 20 / 51
→ LO cross sections in fiducial volume
for W+W+:
Order O(α6)
O(α2
sα4)
σLO [fb] 1.4178(2) 0.17229(5)
[Biedermann, Denner, MP; 1708.00268]
for W+Z:
Order O(α6)
O(α2
sα4)
σLO [fb] 0.25416(6) 0.9912(2)
[Andersen, MP et al.; 1803.07977 LH proceedings]
→ The relative size of the EW contribution is process dependent(87% for W+W+ vs. 20% for W+Z)→ Background can be overwhelming(80% e.g. for W+Z)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 21 / 51
→ Example of WZ:
10−5
10−4
10−3
10−2
10−1
100
020406080
100
2 3 4 5 6 7 8 9 10
dσd∆
Rj 1
j 2[f
b]
LO EWLO INTLO QCDSum
δ[%
]
∆Rj1j2
LO EW LO INT LO QCD
10−6
10−5
10−4
10−3
10−2
020406080
100
400 600 800 1000 1200 1400 1600 1800 2000
dσdM
j 1j 2
[fb GeV
]
LO EWLO INTLO QCDSum
δ[%
]
Mj1j2 [GeV]
LO EW LO INT LO QCD
[Andersen, MP et al.; 1803.07977 LH proceedings]
→ Phase-space regions where EW contribution is dominating:very low statistics→ Challenge for experimental collaborations
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 22 / 51
Quality of the VBS approximation (LO)
(GeV)2
j1
jm0 100 200 300 400 500 600 700 800
(fb
/GeV
)2j 1j
/ d
mσd
0.001−
0
0.001
0.002
0.003
0.004
0.005
0.0066α
5αsα4α2
sα 4α2
sα + 5αsα + 6α
(fb/GeV)2j
1j / dmσInclusive study at LO: d
| 2
j1
j y∆|
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
| (f
b)
2j 1j y∆
/ d
|σd
0
0.2
0.4
0.6
0.8
1
6α5αsα4α2
sα 4α2
sα + 5αsα + 6α
| (fb)2j
1j
y∆ / d|σInclusive study at LO: d
[Ballestrero, MP et al.; 1803.07943]
→ Using the full computation:Presence of a peak at the W-boson mass (s-channel contribution)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 23 / 51
Quality of the VBS approximation (LO)
(GeV)jjm200 300 400 500 600 700 800
| jjy∆|
0
0.5
1
1.5
2
2.5
3
3.5
4
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
) planejj
y∆, jj
in the (m [full]σ
]2+|u|2 [|t|σ : 6α
(GeV)jjm200 300 400 500 600 700 800
| jjy∆|
0
0.5
1
1.5
2
2.5
3
3.5
4
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
) planejj
y∆, jj
in the (m [full]σ
]2+|u|2+|t|2 [|s|σ : 6α
[Ballestrero, MP et al.; 1803.07943]
For low mjj and low ∆yjj, significant s-channelcontributions→ tri-boson contributions with resonant W-boson
Good approximation in fiducial region for W+W+
→ confirmed for W±Z [Andersen, MP et al.; 1803.07977]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 24 / 51
Quality of the VBS approximation (LO)
10-4
10-3LO
dσ/d
mj 1j
2 [fb/
GeV
]
BONSAY
MG5_aMC
MoCaNLO+Recola
PHANTOM
POWHEG
VBFNLO
WHIZARD
10-4
10-3
0.9
1
1.1
500 1000 1500 2000 2500 3000 3500 4000Ratio
/MoC
aNLO
+Rec
ola
mj1j2 [GeV]
0.9
1
1.1
500 1000 1500 2000 2500 3000 3500 4000
0
0.1
0.2
0.3
0.4
0.5LO
dσ/d
Δy j 1
j 2 [fb]
BONSAY
MG5_aMC
MoCaNLO+Recola
PHANTOM
POWHEG
VBFNLO
WHIZARD
0
0.1
0.2
0.3
0.4
0.5
0.9
1
1.1
3 4 5 6 7 8 9Ratio
/MoC
aNLO
+Rec
ola
Δyj1j2
0.9
1
1.1
3 4 5 6 7 8 9
[Ballestrero, MP et al.; 1803.07943]
→ In single-differential distributions in fiducial region at LO:hardly any differences especially compared to QCD-scale band
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 25 / 51
VBF at NNLO QCD - [Cacciari et al.; 1506.02660]
NNPDF30_nnlo_as_118
µ0(pt,H)/2 < µR = µF < 2 µ0(pt,H)
VBF CUTSLHC 13 TeV
dσ/dpt, j1 [pb/GeV]
LONLO
NNLOPOWHEG
10-4
10-3
10-2
With updated NLO VBF H+3-jet virtual corrections
pt, j1 [GeV]
0.8
0.9
1
1.1
50 100 150 200 250 300
NNPDF30_nnlo_as_118
µ0(pt,H)/2 < µR = µF < 2 µ0(pt,H)
VBF CUTSLHC 13 TeV
dσ/dpt, j2 [pb/GeV]
LONLO
NNLOPOWHEG
10-4
10-3
10-2
With updated NLO VBF H+3-jet virtual corrections
pt, j2 [GeV]
0.8
0.9
1
1.1
20 40 60 80 100 120 140 160
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 26 / 51
VBF at NNLO QCD - [Cacciari et al.; 1506.02660]
NNPDF30_nnlo_as_118
µ0(pt, H)/2 < µR = µF < 2 µ0(pt,H)
VBF CUTSLHC 13 TeV
dσ/dpt, H [pb/GeV]
LONLO
NNLOPOWHEG
10-3
10-2
With updated NLO VBF H+3-jet virtual corrections
pt,H [GeV]
0.8
0.9
1
1.1
0 50 100 150 200 250 300
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 27 / 51
Jet dependence VBF - [Rauch and Zeppenfeld; 1703.05676]
750
800
850
900
950
1000
1050
1100
σ [f
b]
LONLONNLO
0.900.951.001.051.101.151.20
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
σ/σ
NLO
R
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 28 / 51
Jet dependence VBF - [Rauch and Zeppenfeld; 1703.05676]
0
2
4
6
8
10
12R=0.4
dσ/d
p T,j1
[fb/
GeV
]
NNLONLO
0.85
0.90
0.95
1.00
1.05
1.10
20 50 100 150 200 250 300
σ/σ
NLO
anti-kTC/AkT
R=1.0
NNLONLONLO (R=0.4)
20 50 100 150 200 250 300
R=1.6
NNLONLONLO (R=0.4)
20 50 100 150 200 250 300pT,j1 [GeV]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 29 / 51
WZ analysis - [CMS; 1901.04060]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 30 / 51
NLO corrections - W+W+
Calculation of both NLO QCD and EW corrections topp→ µ+νµe+νejj
→ NLO fiducial cross sections: (normalised to σLO)
Order O(α7)
O(αsα
6)
O(α2
sα5)
O(α3
sα4)
Sum
δσNLO [fb] −0.2169(3) −0.0568(5) −0.00032(13) −0.0063(4) −0.2804(7)
δσNLO/σLO [%] −13.2 −3.5 0.0 −0.4 −17.1
[Biedermann, Denner, MP; 1708.00268]
→ Large EW corrections at O(α7)
→ Negative corrections at O(αsα
6):
→ Photon PDF contribution at NLO (not included in NLO definitions):+1.50% with LUXqed [Manohar et al.; 1607.04266]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 31 / 51
NLO corrections - W+W+ / Separated contributions
10−5
10−4
10−3
-30-25-20-15-10-505
10
-4-3-2-10123
600 800 1000 1200 1400 1600 1800 2000
dσdM
j 1j 2
[fb GeV
]
LO EWLO QCDLO INTNLO
δ[%
]
α7 αsα6 NLO
δ[%
]
Mj1j2 [GeV]
α2s α5 α3
s α4 photon α7
10−5
10−4
10−3
10−2
-40-30-20-10
0102030
-4-3-2-101234
0 100 200 300 400 500 600 700 800dσ
dpT,j 1
[fb GeV
]
LO EWLO QCDLO INTNLO
δ[%
] α7 αsα6 NLO
δ[%
]pT,j1 [GeV]
α2s α5 α3
s α4 photon α7
[Biedermann, Denner, MP; 1708.00268]
→ Clear hierarchy of LO contributions→ Different behaviour of the NLO corrections (normalised to the full LO)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 32 / 51
NLO corrections - W+W+ / Combined predictionsdσ
dMe+
µ+
[fb GeV
]
LONLO
10−4
10−3
10−2
δ[%
]
Me+µ+ [GeV]
-60-50-40-30-20-10
0102030
0 100 200 300 400 500 600 700 800
dσd∆
y e+µ−
[fb]
LONLO
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
δ[%
]
∆ye+µ−
-40-30-20-10
0102030
-4 -2 0 2 4
[Biedermann, Denner, MP; 1708.00268]
→ Large negative corrections for the full process→ Corrections dominated by EW correction to EW process
→ Bands do not overlap
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 33 / 51
NLO corrections
Commonfeatureof all VBSsignatures
EW corrections O(α7)large with respect to LO O
(α6)
Correction of O(αsα
6)
are expected to be of comparable size
Small but not negligible photon contribution
The size of O(α3
sα4)
depends strongly on the size of theQCD-induced process at LO
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 34 / 51
NLO EW corrections - W±W±
LO: O(α6)
NLO: O(α7) σLO [fb] σNLO
EW [fb] δEW [%]
1.5348(2) 1.2895(6) −16.0
dσdp
T,j 1
[fb GeV
]
LONLO EW
10−5
10−4
10−3
10−2
δ[%
]
pT,j1 [GeV]
NLO EW-40-35-30-25-20-15-10-50
0 100 200 300 400 500 600 700 800
[Biedermann, Denner, MP; 1611.02951]
→ Huge NLO electroweak correction (!)Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 35 / 51
NLO EW corrections - WZ
→ Cross section:
LO O(α6)
[fb] NLO EW O(α7)
[fb] Corrections [%]
0.255 0.214 −16.0
[Denner, Dittmaier, Maierhofer, MP, Schwan] Preliminary→ Differential distribution:
0.00
0.02
0.04
0.06
0.08
0.10
0.12
dσ/d
∆Rµ−µ
+[f
b]
LO
NLO QCD
NLO EW
NLO QCD+EW
0 1 2 3 4∆Rµ−µ+
−50
0
50
δ[%
]
[Denner, Dittmaier, Maierhofer, MP, Schwan] Preliminary→ Also large corrections!Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 36 / 51
Quality of the VBS approximation (LO)
(GeV)jjm200 300 400 500 600 700 800
| jjy∆|
0
0.5
1
1.5
2
2.5
3
3.5
4
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
) planejj
y∆, jj
in the (m [full]σ
]2+|u|2 [|t|σ : 6α
(GeV)jjm200 300 400 500 600 700 800
| jjy∆|
0
0.5
1
1.5
2
2.5
3
3.5
4
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
) planejj
y∆, jj
in the (m [full]σ
]2+|u|2+|t|2 [|s|σ : 6α
[Ballestrero, MP et al.; 1803.07943]
For low mjj and low ∆yjj, significant s-channelcontributions→ tri-boson contributions with resonant W-boson
Good approximation in fiducial region for W+W+
→ confirmed for W±Z [Andersen, MP et al.; 1803.07977]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 37 / 51
Quality of the VBS approximation (NLO)
(GeV)2
j1
jm200 300 400 500 600 700 800
|2j 1j
y∆|
2
2.5
3
3.5
4
4.5
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
) plane2j
1j
y∆, 2j
1j
in the (m[full]σ
]2+|u|2[|t|σ : 6αsα
(GeV)2
j1
jm200 300 400 500 600 700 800
|2j 1j
y∆|
2
2.5
3
3.5
4
4.5
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
) plane2j
1j
y∆, 2j
1j
in the (m[full]σ
]2+|u|2+|t|2[|s|σ : 6αsα
[Ballestrero, MP et al.; 1803.07943]
The approximations are in general worse at NLO
Approximation can fail by up to 20% even in fiducial region→ OK now for current experimental precision but might beimportant in the future
Similar behaviour expected for other signatures:→ but harder to predict→ full computation not available for other signatures (yet)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 38 / 51
Quality of the VBS approximation (NLO)
10-4
10-3NLO
dσ/d
mj 1j
2 [fb/
GeV
]
BONSAY
MG5_aMC
MoCaNLO+Recola
POWHEG
VBFNLO
10-4
10-3
0.9
1
1.1
500 1000 1500 2000 2500 3000 3500 4000Ratio
/MoC
aNLO
+Rec
ola
mj1j2 [GeV]
0.9
1
1.1
500 1000 1500 2000 2500 3000 3500 4000
0
0.1
0.2
0.3
0.4
0.5NLO
dσ/d
Δy j 1
j 2 [fb]
BONSAY
MG5_aMC
MoCaNLO+Recola
POWHEG
VBFNLO
0
0.1
0.2
0.3
0.4
0.5
0.9
1
1.1
3 4 5 6 7 8 9Ratio
/MoC
aNLO
+Rec
ola
Δyj1j2
0.9
1
1.1
3 4 5 6 7 8 9
[Ballestrero, MP et al.; 1803.07943]
Differences lie outside the band→ relevant for precision measurements
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 39 / 51
Beyond fixed order (1)
NLO (fixed order)MG5 aMC+H7-DefaultMG5 aMC+Py8PHANTOM+H7-DefaultPHANTOM+Py8VBFNLO 3+H7-DipoleWHIZARD+Py8
10−4
10−3
Dijet invariant mass (LO+PS)
dσ
pp→
e+ν
µ+
νjj
/d
mj 1
j 2[f
b/G
eV]
500 1.0 · 103 1.5 · 103 2.0 · 103 2.5 · 103 3.0 · 103 3.5 · 103 4.0 · 1030.50.60.70.80.9
11.11.21.31.4
mj1j2[GeV]
Rat
io
NLO (fixed order)MG5 aMC+H7-DefaultMG5 aMC+Py8Powheg+Py8Powheg-no showerVBFNLO 3+H7-DefaultVBFNLO 3+H7-Dipole
10−4
10−3
Dijet invariant mass (NLO+PS)
dσ
pp→
e+ν
µ+
νjj
/d
mj 1
j 2[f
b/G
eV]
500 1000 1500 2000 2500 3000 3500 40000.50.60.70.80.91.01.11.21.31.4
mj1j2[GeV]
Rat
io[Ballestrero, MP et al.; 1803.07943]
→ Reasonable agreement at both LO (left) and NLO (right)for observables defined at LO→ NB: input parameters (masses, widths, PDF, scales)all set to common values
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 40 / 51
Beyond fixed order (2)
NLO (fixed order)MG5 aMC+H7-DefaultMG5 aMC+Py8PHANTOM+H7-DefaultPHANTOM+Py8VBFNLO 3+H7-DipoleWHIZARD+Py8
0
0.2
0.4
0.6
0.8
1
1.2Normalised average rapidity of the third jet (LO+PS)
dσ
pp→
e+ν
µ+
νjj
/d
z j3
[fb]
0 0.2 0.4 0.6 0.8 1 1.2 1.40.50.60.70.80.9
11.11.21.31.4
zj3
Rat
io
NLO (fixed order)MG5 aMC+H7-DefaultMG5 aMC+Py8MG5 aMC+Py8, Qsh/2Powheg+Py8Powheg-no showerVBFNLO 3+H7-DefaultVBFNLO 3+H7-Dipole
0
0.2
0.4
0.6
0.8
1
1.2Normalised average rapidity of the third jet (NLO+PS)
dσ
pp→
e+ν
µ+
νjj
/d
z j3
[fb]
0 0.2 0.4 0.6 0.8 1 1.2 1.40.50.60.70.80.91.01.11.21.31.4
zj3
Rat
io[Ballestrero, MP et al.; 1803.07943]
→ Very large differences for observables related to the third jet(only defined at NLO)→ Different treatment of recoil in Pythia→ Triggered similar study in ATLAS with Sherpa[ATL-PHYS-PUB-2019-004]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 41 / 51
Beyond fixed order (3)
→ Also observed by CMS in VBF-Z production [CMS; 1712.09814]
(i.e. pp→ jjZ)
(GeV)T
Third jet p0 50 100 150 200 250 300
Gap
vet
o ef
ficie
ncy
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1CMSBDT > 0.92Dilepton
(13 TeV)-135.9 fb
Data
DY (MG5_aMC NLO + Pythia8)
DY + EWK Zjj (MG5_aMC LO + Pythia8)
DY + EWK Zjj (MG5_aMC LO + Herwig)
→ Processes with larger cross sections ...... but similar topologies ...... can help to improve on the predictions for VBSMathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 42 / 51
State-of-the-art VBF
Full NLO QCD [Figy, Oleari, Zeppenfeld; hep-ph/9206246]
NLO EW [Ciccolini, Denner, Dittmaier; 0707.0381, 0710.4749]
NLO QCD matched to parton shower in VBS approximation[Nason, Oleari; 0911.5299]
→ Available in VBFNLO, Powheg, MG5 aMC@NLO orSherpa
NNLO QCD in VBS approximation [Cacciari et al.; 1503.02660], [Cruz-Martinez
et al.; 1802.02445]
N3LO QCD in VBS approximation and for total cross sectiononly [Dreyer, Karlberg; 1606.00840] (using stucture function)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 43 / 51
State-of-the-art VBS
W±W±
NLO QCD to EW-induced process in VBS approximation[Jager, Oleari, Zeppenfeld; 0907.0580], [Denner, Hosekova, Kallweit; 1209.2389]
NLO QCD to QCD-induced process [Melia et al.; 1007.5313, 1104.2327],
[Campanario et al.; 1311.6738]
Matching to parton shower [Jager, Zanderighi; 1108.0864], [Melia et al.;
1102.4846]
→ Available in VBFNLO or Powheg-BoxFull NLO QCD and EW to EW- and QCD-induced process[Biedermann, Denner, MP; 1611.02951, 1708.00268]
W±ZNLO QCD to EW-induced process in VBS approximation[Bozzi et al.; hep-ph/0701105]
Matching to parton shower [Jager, Karlberg, Scheller; 1812.05118]
NLO QCD to QCD-induced process [Campanario et al.; 1305.1623]
→ Available in VBFNLO and Powheg-Box
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 44 / 51
State-of-the-art VBS
W+W−
NLO QCD to EW-induced process in VBS approximation[Jager, Oleari, Zeppenfeld; hep-ph/0603177]
NLO QCD to QCD-induced process [Melia et al.; 1104.2327], [Greiner et al.;
1202.6004]
Matching to parton shower [Jager, Zanderighi; 1301.1695], [Rauch, Platzer;
1605.07851]
→ Available in VBFNLO or Powheg-Box
ZZ
NLO QCD to EW-induced process in VBS approximation andmatching to parton shower [Jager, Karlberg, Zanderighi; 1312.3252]
NLO QCD to QCD-induced process [Campanario et al.; 1405.3972]
→ Available in VBFNLO or Powheg-Box
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 45 / 51
State-of-the-art VBS
→ All processes known at NLO QCD accuracy matched to PS
in VBS approximation
for both QCD-/EW-induced process
all available in VBFNLO (apart from QCD-induced W+W−)
all available in Powheg-Box
possible to generate in MG5 aMC@NLO or Sherpa
→ NLO EW corrections only known for W+W+ (WZ preliminary)→ Full NLO computation only known for W+W+
→ No NNLO computation known apart in VBF[Cacciari et al.; 1503.02660], [Cruz-Martinez et al.; 1802.02445]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 46 / 51
Higgs witdh determniation - [Campbell, Ellis, Williams; 1311.3589]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 47 / 51
[pb]
σP
rodu
ctio
n C
ross
Sec
tion,
4−10
3−10
2−10
1−10
1
10
210
310
410
510
CMS PreliminaryJuly 2018
All results at: http://cern.ch/go/pNj7
W
n jet(s)≥
Z
n jet(s)≥
γW γZ WW WZ ZZµll, l=e,→, Zνl→EW: W
qqWEW
qqZEW
WW→γγ
γqqWEW
ssWW EW
γqqZEW
qqWZEW
qqZZEW γWV γγZ γγW tt
=n jet(s)
t-cht tW s-cht γtt tZq ttZ γt ttW ttttσ∆ in exp. Hσ∆Th.
ggH qqHVBF VH WH ZH ttH tH HH
CMS 95%CL limits at 7, 8 and 13 TeV
)-1 5.0 fb≤7 TeV CMS measurement (L )-1 19.6 fb≤8 TeV CMS measurement (L )-1 35.9 fb≤13 TeV CMS measurement (L
Theory prediction
→ Limited experimental precision for VBS (for now)
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 48 / 51
Experimental status (1): Measured
→ Several VBS signatures according to the final state (VV ):
VV = W±W± (leptonic) → Golden channel
Low backgroundEvidence by ATLAS and CMS at Run-I [1405.6241, 1611.02428, 1410.6315]
Measurement by ATLAS and CMS at run-II[CMS-PAS-SMP-17-004; 1709.05822], [ATLAS-CONF-2018-030]
VV = WZ (leptonic)
Good rate but large backgroundObservation by ATLAS and CMS at Run-II[ATLAS-CONF-2018-033, 1812.09740], [CMS-PAS-SMP-18-001, 1901.04060 ]
VV = ZZ (leptonic)
Low cross section but good reconstructionEvidence by CMS at Run-II for ZZ [1708.02812]
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 49 / 51
Experimental status (2): Not (yet) measured
→ Several VBS signatures according to the final state (VV ):
VV = W+W− (leptonic)
VBF (pp→ jjH) + H→W+W− in a larger phase spaceVery large background from tt
VV (semi-leptonic: 4 jets in the final state)
Large cross section but very large backgroundUsed for BSM exlcusion only (for now) [ATLAS; 1609.05122, 1710.07235]
VV (fully-leptonic: 6 jets in the final state)
Very large cross section but gigantic background
Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 50 / 51
Slide from Jakob Salfeld-Nebgen (https://indico.cern.ch/event/711256/)
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Mathieu PELLEN Lectures on the SM beyond LO and VBS/VBF 51 / 51