lectures on the sm beyond lo and vbs/vbfrebuzzi/didattica_files/pellen... · theory" weinberg:...

$: Lectures on the SM beyond LO and VBS/VBFrebuzzi/Didattica_files/PELLEN... · Theory" Weinberg: \The Quantum Theory of Fields, Vol. 1: Foundations"; \The Quantum Theory of Fields,$
Lectures on the SM beyond LO and VBS/VBF

Mathieu PELLEN

Cavendish Laboratory,University of Cambridge

[email protected]

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...


Part II: The Standard Modelbeyond leading order


Higgs coupling


General rule for QCD corrections

There is no rule...


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)


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]


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]


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


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

]


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

]


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


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)


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)


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]


https://indico.hep.manchester.ac.uk/contributionDisplay.py?contribId=23&confId=4688

https://indico.cern.ch/event/49675/contributions/1175622/attachments/961511/1364963/EWRCLHC_1.pdf

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]


Part III: Vector-boson fusionand vector-boson scattering


Slide from Christopher Schwan


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|.


→ 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)


→ 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


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


→ Using the full computation:Presence of a peak at the W-boson mass (s-channel contribution)



(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


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]



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


→ In single-differential distributions in fiducial region at LO:hardly any differences especially compared to QCD-scale band


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


pt, j2 [GeV]

0.8

0.9

1

1.1

20 40 60 80 100 120 140 160


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


pt,H [GeV]

0.8

0.9

1

1.1

0 50 100 150 200 250 300


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


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]


WZ analysis - [CMS; 1901.04060]


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


→ 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]


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


→ Clear hierarchy of LO contributions→ Different behaviour of the NLO corrections (normalised to the full LO)


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


→ Large negative corrections for the full process→ Corrections dominated by EW correction to EW process

→ Bands do not overlap


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


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


→ 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


(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


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]


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


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)


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


Differences lie outside the band→ relevant for precision measurements


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



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]



→ 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)


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



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



→ 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]


Higgs witdh determniation - [Campbell, Ellis, Williams; 1311.3589]


[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)


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]


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


Slide from Jakob Salfeld-Nebgen (https://indico.cern.ch/event/711256/)

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