◦ Precision measurements at the Z pole

Teilchenphysik 2 — W/Z/Higgs an Collidern

Sommersemester 2019

Matthias Schr¨oder und Roger Wolf

|

INSTITUT FUR¨ EXPERIMENTELLETEILCHENPHYSIK(ETP)

KIT – Die Forschungsuniversit¨at in der Helmholtz-Gemeinschaft www.kit.edu

4. Physics of the W and Z Bosons

4.1 Determination of SM parameters

◦ Precision measurements at the Z pole

◦ W production at colliders

◦ Global electroweak fits 4.2 W/Z physics at the LHC

◦ Single W/Z boson production

◦ W / Z + jets production

◦ Vector boson pair-production

◦ Vector boson scattering

◦ Anomalous couplings

◦ Exotic resonances

4.1.1. Precision measurements at the Z pole

Asymmetries

◦ Generic definition of asymmetry: split dataset into 2 parts X , Y :

A = ^X − ^Y X + Y

◦ Measure/predict asymmetry = ratio, not absolute rate

◦ If backgrounds or systematic uncertainties identical or similar in numerator/denominator → uncertainties reduced by cancellation

◦ Improved sensitivity to small differences

Differential e ⁺ e ⁻ → ff Cross-Section

◦ Angular dependence from particle spins:

◦ ^{For pure} QED process d σ

d cos θ = N

Q

πα

2s ( 1 + cos

θ)

→ symmetric in scattering angle

Differential e ⁺ e ⁻ → ff Cross-Section

◦ Angular dependence from particle spins:

◦ ^{For pure Z exchange}

d σ

d cos θ = ³

8 σ

h

( 1 + cos

θ) + ( 2A

A

cos θ) i

symmetric in cos θ symmetric in cos θ with “asymmetry parameter”

A

= ^{2 g}

Vf

/ g

1 + ( g

/ g

)

≡ ( g

)

− ( g

)

( g

)

+ ( g

)

, g

= g

∓ ^g

→ asymmetric in scattering angle?

Forward-Backward Asymmetry

◦ Cross-sections depending on scattering angle of final-state fermion

Winter Semester 2017/2018 Particle Physics I (4022031) – Lecture #10

Forward-Backward Asymmetry

Definitions: forward and backward cross sections depending on scattering angle of final-state fermion


Forward-backward asymmetry:


From dσ/d(cos θ):

!397

F=Z⇡/2 0

d

d cos✓d✓, B=Z⇡

⇡/2

d d cos✓d✓

A

=

F

+

3.3 Kopplung desZ-Bosons an Fermionen 57

e^– e⁺

f

f

θ e^– e⁺

f

f θ

„Vorwärts” „Rückwärts”

e^– e⁺ e^– e⁺

„linkshändiges Elektron” „rechtshändiges Elektron”

e^– θ e⁺

„linkshändiges Tau”

e^– θ e⁺

„rechtshändiges Tau”

τ^– τ^–

τ⁺ τ⁺

Abbildung 3.15:Asymmetrien: Vorw¨arts- und R¨uckw¨artsstreuung (oben). Polarisation vont- Leptonen im Endzustand (Mitte). Streuung linksh¨andig und rechtsh¨andig po- larisierter Elektronen (unten).

Polarisation im Endzustand

Der Asymmetrieparameter im EndzustandAfkann separat gemessen werden, wenn man die Polarisation der Teilchen im Endzustand bestimmen kann. Aus Gleichungen (3.25)–(3.28) kann man die Anteile mit rechtsh¨andig polarisierten und linksh¨andig po- larisierten Teilchen im Endzustand vergleichen:

Pf(cosq):=sr sl

sr+sl= Af(1+cos²q) +2Aecosq

(1+cos²q) +2AfAecosq (3.33) mitsr:= dsRr

dcosq+ dsLr

dcosq, sl:= dsRl dcosq+ dsLl

dcosq.

Wenn man Z¨ahler und Nenner in (3.33) separat ¨uber den Winkelqintegriert, bleiben nur Terme ¨ubrig, die FB-symmetrisch sind, also⇠(1+cos²q). Man erh¨alt so die mittlere Polarisation im Endzustand

hPfi= Af. (3.34)

Eine Messung der Polarisation im Endzustand ist experimentell nur f¨urt-Leptonen m¨oglich, da man deren Spin aus der Winkelverteilung der Produkte vont-Zerf¨allen bestimmen kann. Die Lebensdauer vont-Leptonen betr¨agt ca. 0,3 ps, somit zerfal- len sie in unmittelbarer N¨ahe ihres Produktionspunkts. Besonders geeignet f¨ur die Polarisationsmessung sind Zerf¨alle in Hadronen, insbesondere die Zweik¨orperzerf¨alle t !p n+ h.c.,t !r n+ h.c. undt !a n + h.c. Rein leptonischet-Zerf¨alle

A

= 3 4 A

A

d σ / d cos θ[nb]

e⁺e⁻ → e⁺e⁻(γ)

peak−2 peak peak+2

0 0.5 1

-1 -0.5 0 0.5 1

L3

√s = mz

√s = mz + 2 GeV

√s = mz – 2 GeV

Phys. Rep. 427 (2006) 257

„Vorwärts”

„Rückwärts”

“Forward” “Backward”

σ

= Z

0

d σ

d cos θ ^d θ , σ

= Z

π/2

d σ d cos θ ^d θ

◦ Forward-backward asymmetry A

= σ

− σ

σ

+ σ

= . . . =

A

A

cos θ

d σ / d cos θ[nb]

e⁺e⁻ → e⁺e⁻(γ)

peak−2 peak peak+2

0 0.5 1

-1 -0.5 0 0.5 1

L3

Phys. Rep. 427 (2006) 257

“backward” “forward”

Matthias Schr¨oder – W/Z/Higgs an Collidern (Sommersemester 2019) Vorlesung 10 7/59

Forward-Backward Asymmetry: LEP Results

LEP average: A

for leptons

ALEPH DELPHI L3 OPAL LEP

0.0173±0.0016 0.0187±0.0019 0.0192±0.0024 0.0145±0.0017 0.0171±0.0010

common: 0.0003 χ

/DoF = 3.9/3

A

Phys. Rep. 427 (2006) 257

A

separately for e , µ, τ vs. R

0.01 0.014 0.018 0.022

20.6 20.7 20.8 20.9

R

=Γ

/Γ

A

68% CL

l⁺l⁻ e⁺e⁻ µ⁺µ⁻ τ⁺τ⁻

α_s mt

mH

∆α

→ test of lepton universality

Weak Mixing Angle

◦ Electroweak theory: (effective) weak mixing angle sin

θ

= ^I

2Q

1 − ^g

Vf

g

=

1 − ^m

2W

m

LEP, SLC, ν LEP, SLC, TeV, LHC

◦ Non-trivial dependence on radiative corrections absorbed in “effective” quantity

◦ LEP and SLC: sin

θ

from A

A

= ³

4 A

A

with A

= ^{2 g}

f V

/ g

1 + ( g

/ g

)

◦ ^{Leptons: A}

very sensitive to sin

θ

◦ Down-type quarks: only weak dependence of A

on sin

θ

◦ Experimentally: only down-type

quarks can be identified (b tagging)

Weak Mixing Angle

Elektroweak theory: (effective) weak mixing angle


Non-trivial: LH and RH side depend differently on radiative corrections LEP and SLC: sin

θ

from A

Leptons: 𝒜

very sensitive to sin

θ

Down-type quarks (d, s, b): only weak dependence of 𝒜

on sin

θ

Only down-type quark to be identified easily: b-quark tagging (→ later)

LEP, SLC, Neutrinos LEP, SLC, TeV, LHC

!400

0 0.2 0.4 0.6 0.8 1

-1 -0.5 0 0.5 1

A

A

A

sin² θ_W

A

= 3

4 A

A

sin

✓

= I

2Q

✓ 1 g

g

◆

= 1 m

m

with A

= 2 g

/g

1 + g

/g

Weak Mixing Angle: LEP/SLC Results

◦ Compare different channels

◦ Most precise: A

◦ ³ . 2 σ discrepancy between leptonic and hadronic final states!

◦ Additional 3 . 2 σ deviation:

neutrino-nucleon scattering (NuTeV) Unresolved. . .

10² 10³

0.23 0.232 0.234

sin

θ

m

[ GeV ]

χ²/d.o.f.: 11.8 / 5

A^0,l_fb 0.23099 ± 0.00053

A_l(P_τ) 0.23159 ± 0.00041

A_l(SLD) 0.23098 ± 0.00026

A^0,b_fb 0.23221 ± 0.00029

A^0,c_fb 0.23220 ± 0.00081

Q^had_fb 0.2324 ± 0.0012

Average 0.23153 ± 0.00016

∆α_had= 0.02758 ± 0.00035

∆α⁽⁵⁾ m_t= 178.0 ± 4.3 GeV

Phys. Rep. 427 (2006) 257

4.1.2. W production at colliders

W Boson production at LEP

◦ ^{W + W −} -pair production at e ⁺ e ⁻ colliders

e⁺ W⁺

νe

e⁻ W⁻

e⁺

e⁻ γ

W⁺

W⁻ e⁺

e⁻ Z

W⁺

W⁻

◦ ^{Kinematic production} threshold: √

s ≥ ^2m

◦ Pair production: cross section reaches plateau (no peak!)

◦ Threshold scan: scattering matrix only unitary if both ν exchange and triple-gauge-boson vertex

(ZWW) are considered ⁰

10 20 30

160 180 200

√ s (GeV) σ

(pb)

YFSWW/RacoonWW no ZWW vertex (Gentle) only ν_e exchange (Gentle)

LEP

Phys.Rept.532(2013)119

W Boson production at Hadron Colliders

◦ W ⁺ W ⁻ -pair production at hadron colliders

◦ LO: valence-quark annihilation

◦ pp: equal W

cross section

◦ ^{pp: uud} → ^W

more probable

Phys.Rev.D69(2004)094008

◦ Differential cross-section known at NNLO QCD (partially also EWK)

W Boson Decays

◦ Expectation: “democratic” distribution of branching fractions into 9 final states

◦ ^W → ^l ν : 3 lepton flavours

◦ ^W → ^qq

^{: q (=u,c)} × 3 colours = 6 final states

◦ Results from LEP:

W Hadronic Branching Ratio

ALEPH 67.13 ± 0.40

DELPHI 67.45 ± 0.48

L3 67.50 ± 0.52

OPAL 67.41 ± 0.44

LEP 67.41 ± 0.27

χ²/ndf = 15.4 / 11

66 68 70

Br(W→hadrons) [%]

W Leptonic Branching Ratios

ALEPH 10.78 ± 0.29

DELPHI 10.55 ± 0.34

L3 10.78 ± 0.32

OPAL 10.71 ± 0.27

LEP W→eν 10.71 ± 0.16

ALEPH 10.87 ± 0.26

DELPHI 10.65 ± 0.27

L3 10.03 ± 0.31

OPAL 10.78 ± 0.26

LEP W→µν 10.63 ± 0.15

ALEPH 11.25 ± 0.38

DELPHI 11.46 ± 0.43

L3 11.89 ± 0.45

OPAL 11.14 ± 0.31

LEP W→τν 11.38 ± 0.21

LEP W→lν 10.86 ± 0.09

χ²/ndf = 6.3 / 9

χ²/ndf = 15.4 / 11

10 11 12 Br(W→lν) [%]

Phys.Rept.532(2013)119

W Boson Mass

See Exercises No 5

4.1.3. Global electroweak fits

Global Electroweak Fits

◦ Free parameters of Standard Model Lagrangian

◦ Gauge couplings: 3 ( α

_, α

_, α

₎

◦ Higgs potential: 2

◦ Fermion masses/Yukawa couplings: 9 (neglect neutrino masses)

◦ Quark-mixing matrix: 4

◦ Neutrino-mixing matrix: 4

→ 14–22 free parameters

◦ But many more independent properties measured

→ constraints of SM parameters

(each property: different superposition of SM parameters)

◦ ^Allows prediction of unmeasured quantities,

e. g. top-quark mass before 1995, Higgs-boson mass before 2012

Reminder of Interdependencies

◦ Predictions of electroweak theory

◦ Interdependence of W and Z masses via weak mixing angle m

≡

^gv , m

≡

p

g

+ g

v → ρ = ^m

m

cos θ

= 1

◦ Interdependence with masses of top quark and Higgs boson via loop

corrections

Global Electroweak Fits: Typical Ingredients

Details: Phys. Rep. 427 (2006) 257

Fit of the Top-Quark Mass

◦ Existence of the top quark strongly assumed since discovery of the b quark (1977)

◦ Mass well-constrained due to quadratic contribution to W/Z mass

◦ Still, direct t-quark mass

measurement much more precise ( ≈ 500 MeV uncertainty)

cf. CMS (2016):

m

= 172 . 4 ± 0 . 5 GeV

Year M

[ GeV ]

SM constraint Tevatron

Direct search lower limit (95% CL) 68% CL

50 100 150 200

1990 1995 2000 2005

Phys.Rep.427(2006)257

Fit of the Higgs-Boson Mass

◦ Best-fit Higgs mass:

m

= 94 ⁺ ₋

GeV

◦ ^Light Higgs boson preferred

◦ Logarithmic dependence: m

only weakly constrained

“Blue Band Plot”: Higgs mass limits (before LHC)

0 1 2 3 4 5 6

100

30 300

m

[GeV]

∆χ

Excluded

∆α_had =

∆α⁽⁵⁾ 0.02750±0.00033 0.02749±0.00010 incl. low Q² data

Theory uncertainty

July 2011 m_Limit = 161 GeVLEPEWKWorkingGroup

Including the Higgs Boson

[GeV]

m

140 150 160 170 180 190

[GeV]

M

80.25 80.3 80.35 80.4 80.45 80.5

68% and 95% CL contours

measurements and mt

fit w/o MW

measurements and MH

, mt

fit w/o MW

measurements and mt

direct MW

σ

± 1 world comb.

MW

0.015 GeV

± = 80.385 MW

σ

± 1 world comb.

mt

= 173.34 GeV mt

= 0.76 GeV σ

GeV 0.50theo

= 0.76 ⊕ σ

= 125.14 GeV MH

= 50 GeV

MH _H = 300 GeV

M _H = 600 GeV

M

Eur.Phys.J.C74(2014)3046

4. Physics of the W and Z Bosons

4.1 Determination of SM parameters

◦ Z factories

◦ Precision measurements at the Z pole

◦ W production at colliders

◦ Global electroweak fits 4.2 W/Z physics at the LHC

◦ Single W/Z boson production

◦ W / Z + jets production

◦ Vector boson pair-production

◦ Vector boson scattering

◦ Anomalous couplings

◦ Exotic resonances

4.2 W/Z physics at the LHC

4.2.1. Single W/Z boson production

Inclusive W/Z Cross-Section

Center-of-mass energy [TeV]

B [pb]×σ

102

103

104

(13 TeV) CMS Preliminary, 43 pb-1

(8 TeV) CMS, 18 pb-1

(7 TeV) CMS, 36 pb-1 CDF Run II D0 Run I UA2 UA1

Theory: NNLO, FEWZ and NNPDF 3.0 PDFs

p p

pp

0.5 1 2 5 7 10 20

W₊ W_- W

Z

) [pb]

ν µ

→ xBR(W

W

σfid

8500 9000 9500

) [pb]µµ→xBR(ZZfidσ

620 640 660 680 700 720 740

(13 TeV) 43 pb-1 Preliminary

CMS

FEWZ NNLO Prediction

× Acc.

sys)

⊕ Data (stat

lumi)

⊕ sys

⊕ Data (stat CT14 NNPDF3.0 MMHT2014 ABM HERAPDF15

CMS-PAS-SMP-15-004

◦ Wide range of centre-of-mass energies probed from 0.6–13 TeV (SppS – Tevatron – LHC): very good agreement with NNLO prediction

◦ Correlation of W and Z cross-sections relatively well modelled

Comparing PDF Predictions

◦ ^Inclusive W/Z cross-section sensitive to differences in PDF sets

◦ For example:

W production

2) (MZ

αS

0.114 0.116 0.118 0.12 0.122 0.124

) (nb)ν± l→± B(W⋅±Wσ

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8

68% C.L. PDF MSTW08 CTEQ6.6 CT10 NNPDF2.1 HERAPDF1.0 ABKM09 GJR08

= 7 TeV) s at the LHC (

±ν l

±→ NLO W

S Outer: PDF+α Inner: PDF only Vertical error bars

2) (MZ

αS

0.114 0.116 0.118 0.12 0.122 0.124

) (nb)ν± l→± B(W⋅±Wσ

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8

Ratio W/Z

2) (MZ

αS

0.114 0.116 0.118 0.12 0.122 0.124

Zσ ⋅-l+l / BWσ ⋅νl B≡WZR

10.65 10.7 10.75 10.8 10.85 10.9 10.95 11 11.05

68% C.L. PDF MSTW08 CTEQ6.6 CT10 NNPDF2.1 HERAPDF1.0 ABKM09 GJR08

= 7 TeV) s NLO W/Z ratio at the LHC (

αS Outer: PDF+

Inner: PDF only Vertical error bars

2) (MZ

αS

0.114 0.116 0.118 0.12 0.122 0.124

Zσ ⋅-l+l / BWσ ⋅νl B≡WZR

10.65 10.7 10.75 10.8 10.85 10.9 10.95 11 11.05

JHEP1109(2011)069

Kinematic ( x , Q ² ) _Plane

10^-7 10^-6 10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10⁰

10¹ 10² 10³ 10⁴ 10⁵ 10⁶ 10⁷ 10⁸ 10⁹

fixed target HERA

x_1,2 = (M/13 TeV) exp(±y) Q = M

13 TeV LHC parton kinematics

M = 10 GeV M = 100 GeV

M = 1 TeV

M = 10 TeV

6 6

y = 4 2 0 2 4

Q2 (GeV2 )

x

WJS2013

W.J.Stirling,privatecommunication

W/Z as Probes to QCD

◦ Idea:

◦ Same initial-state momenta: Z at rest

◦ Deduce initial-state momenta from Z speed of flight

→ probes directly parton density

Y =

ln

E (µµ) + p

(µµ) E (µµ) − p

(µµ)

=

ln x

x

(see Exercises No 1)

◦ Double-differential cross-section d

σ( pp → µµ)

dm dY

◦ ^Di- µ mass m

◦ ^Di- µ rapidity Y

→ Compare to different PDFs

W/Z as Probes to QCD

◦ ^Idea:

◦ Same initial-state momenta: Z at rest

◦ Deduce initial-state momenta from Z speed of flight

→ probes directly parton density

Y =

ln

E (µµ) + p

(µµ) E (µµ) − p

(µµ)

=

ln x

x

(see Exercises No 1)

◦ Double-differential cross-section d

σ( pp → µµ)

dm dY

◦ ^Di- µ mass m

◦ ^Di- µ rapidity Y

→ Compare to different PDFs

/d|y|σ dZσ1/

0 0.01 0.02 0.03 0.04 0.05

0.06 ^CMS, ∫ Ldt = 4.5 fb^-1 at s = 7 TeV, 30 < m < 45 GeV

Data FEWZ+CT10 NNLO FEWZ+NNPDF2.1 NNLO FEWZ+MSTW2008 NNLO FEWZ+CT10W NNLO FEWZ+JR09 NNLO FEWZ+ABKM09 NNLO FEWZ+HERAPDF15 NNLO

Absolute dimuon rapidity, |y|

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Data/theory

0.7 0.8 0.9 1 1.1 1.2 1.3

= 7 TeV, 30 < m < 45 GeV s

at Ldt = 4.5 fb-1

∫

CMS,

/d|y|σ dZσ1/

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016

= 7 TeV, 200 < m < 1500 GeV s

at Ldt = 4.5 fb-1

∫

CMS,

Data FEWZ+CT10 NNLO FEWZ+NNPDF2.1 NNLO FEWZ+MSTW2008 NNLO FEWZ+CT10W NNLO FEWZ+JR09 NNLO FEWZ+ABKM09 NNLO FEWZ+HERAPDF15 NNLO

Absolute dimuon rapidity, |y|

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Data/theory

0.5 0.6 0.7 0.80.9 1 1.1 1.21.3 1.4 1.5

= 7 TeV, 200 < m < 1500 GeV s

at Ldt = 4.5 fb-1

∫

CMS,

JHEP1312(2013)030

W-Charge Asymmetry

◦ Event selection targeting W → µν

◦ ^{Muon with p}

> _{25 GeV}

◦ _E /

> _{25 GeV}

◦ ^m

> 40 GeV

◦ Measure charge asymmetry

A _µ = σ _η ⁺ − σ ⁻ _η σ η ⁺ + σ ⁻ η

with

σ

= ^d

d η σ( pp → ^W

→ µ

ν)

0 0.5 1 1.5 2

Charge asymmetry

0.1 0.15 0.2 0.25

NNLO FEWZ + NNLO PDF, 68% CL CT10

NNPDF30 MMHT2014 ABM12 HERAPDF15

> 25 GeV

µ

pT

Data = 8 TeV s

-1 at CMS, L = 18.8 fb

Eur.Phys.J.C76(2016)469

◦ Constrains ratio of u/d-quark PDFs for 10 ⁻

< x < 10 ⁻

W-Charge Asymmetry and LHCb

◦ LHCb: forward spectrometer

◦ Extends measurement to 2 . 5 < | η | < 4 . 0

 η



0 0.5 1 1.5 2 2.5 3 3.5 4

Lepton charge asymmetry

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

) 35 pb-1 ν

→ l ATLAS (extrapolated data, W

) 36 pb-1 ν µ

→ CMS (W

) 36 pb-1 ν µ

→ LHCb (W

MSTW08 prediction (MC@NLO, 90% C.L.) CTEQ66 prediction (MC@NLO, 90% C.L.) HERA1.0 prediction (MC@NLO, 90% C.L.)

ATLAS+CMS+LHCb Preliminary

=7 TeV s

> 20 GeV

l

pT

ATLAS-CONF-2011-129

Mod.Phys.Lett.A31(2016)1630044

4.2.2. W/Z+jets production

W / _Z + _Jets

◦ W/Z at the LHC: high probability for radiation of additional partons

◦ Important background for many high-p

analyses (Higgs, Top, Supersymmetry, . . . )

◦ Requires good theoretical understanding and precise simulation

◦ Cross section for W / Z + jets (V + jets)

◦ ^{Naive: factor} α

per additional parton

◦ More precise: inclusive cross-section scales geometrically → ^{ratio of n} /( n + 1 ) jets constant (“Berends–Giele scaling”)

σ( pp → ^W + ( n + 1 ) jets )

σ( pp → ^W + n jets ) = σ( pp → ^W + 2 jets )

σ( pp → ^W + 1 jets )

(except for n = 0 due to phase-space difference)

Radiative Corrections

◦ ^W / Z + jets prototype for processes with many particles in the final state (“2 → ⁿ process”)

◦ LO: solved for 2 → 10 processes

◦ Computation completely automated

◦ NLO: solved for 2 → 4 processes

◦ Higher multiplicities (2 → 6) depending on process

◦ Partially automated (NLO revolution)

◦ NNLO: up to now largely low multiplicity

State-of-the-Art Example: W + _{5 Jets @ NLO}

◦ ^W + jets production at the LHC

q W

g

g g g q^′ e ν

g

g g e W

ν q^′ q

Q¯₁ Q¯₁

g Q₂

Q¯₂ e W

ν q^′ q

Q¯₁ Q¯₁

g

g g

¯q^′ q

ν

¯ Q₂

¯ Q₁

Q₁ Q₂ W e

g q

g g

ν

g e

q^′ W

g g

◦ Computed for up to 5 additional jets at NLO precision (using the programmes BlackHat and Sherpa)

◦ Inclusive cross-section and per-jet p

distributions

◦ Ratios of inclusive cross-sections → extrapolation formula

to larger number of jets

W / _Z + Jets: Measurements

(W)σ n-jets)≥(W + σ

10-3

10-2

10-1

data energy scale unfolding MadGraph Z2 MadGraph D6T Pythia Z2

CMS = 7 TeV s at 36 pb-1

ν

→ e W

> 30 GeV

jet

ET

inclusive jet multiplicity, n (n-1)-jets)≥(W + σ n-jets)≥(W + σ 0

0.1 0.2

1 2 3 4

(Z)σ n-jets)≥(Z + σ

10-3

10-2

10-1

data energy scale unfolding MadGraph Z2 MadGraph D6T Pythia Z2

CMS = 7 TeV s at 36 pb-1

→ ee Z > 30 GeV

jet

ET

inclusive jet multiplicity, n (n-1)-jets)≥(Z + σ n-jets)≥(Z + σ 0

0.1 0.2 0.3

1 2 3 4

JHEP1201(2012)010

◦ Measured cross-section well-described by (most) MC simulations (ME+PS simulation)

◦ Berends–Giele scaling: decent description of data

W / _Z + Jets: Measurements

) [pb]jet N≥) + -l+ l→*(γ(Z/σ

10-3 10-2 10-1 1 10 102 103 104 105 106

= 7 TeV) s Data 2011 ( ALPGEN SHERPA MC@NLO

+ SHERPA HAT BLACK ATLAS Z/γ*(→ l⁺l^-)+jets (l=e,µ) L dt = 4.6 fb-1

∫

| < 4.4 > 30 GeV, |yjet jet pT

≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7

NLO / Data 0.6 0.8 1 1.2

1.4 _{BLACKHAT + SHERPA}

≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7

MC / Data

0.6 0.8 1 1.2

1.4 _ALPGEN

Njet

≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7

MC / Data

0.6 0.8 1 1.2

1.4 _SHERPA

)jet N≥)+-l+ l→*(γ(Z/σ+1)/jet N≥)+-l+ l→*(γ(Z/σ0.05

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

= 7 TeV) s Data 2011 ( ALPGEN SHERPA

+ SHERPA HAT BLACK ATLAS Z/γ*(→ l⁺l^-)+jets (l=e,µ) L dt = 4.6 fb-1

∫

| < 4.4 > 30 GeV, |yjet jet pT

≥-1

≥0/ ≥1/≥0 ≥2/≥1 ≥3/≥2 ≥4/≥3 ≥5/≥4 NLO / Data 0.6

0.8 1 1.2

1.4 _{BLACKHAT + SHERPA}

≥0

≥1/ ≥2/≥1 ≥3/≥2 ≥4/≥3 ≥5/≥4 ≥6/≥5

MC / Data

0.6 0.8 1 1.2

1.4 _ALPGEN

+1/Njet Njet

≥0

≥1/ ≥2/≥1 ≥3/≥2 ≥4/≥3 ≥5/≥4 ≥6/≥5

MC / Data

0.6 0.8 1 1.2

1.4 _SHERPA

JHEP1307(2013)032

◦ NLO calculation (BlackHat+Sherpa) : very good description of data

◦ ^MC simulations (N)LO ME plus PS

◦ PS simulates additional jets beyond 5, some significant deviations

4.2.3. Vector boson pair-production

Vector Boson Pair-Production at the LHC

◦ LO Feynman diagrams for diboson production

◦ Standard Model: V

V

= WW , WZ , ZZ , W γ, Z γ

◦ Diboson physics

◦ SM test and search for new physics, e. g. anomalous triple gauge couplings (aTGC)

◦ ^Background for other high-p

processes: Higgs boson, top quarks, . . .

WW Production

◦ Cleanest channel: WW → ^ll νν (e µ better than ee, µµ )

◦ Important background:

tt production

[GeV]

miss

ET

0 50 100 150 200

Events

0 50 100 150 200 250 300 350

400 WW Top-quark

Higgs VZ/VVV

γ

V Non-prompt

DY Data

Systematics

(13 TeV) L = 2.3 fb-1

CMS Preliminary

WW Top-quark

Higgs VZ/VVV

γ

V Non-prompt

DY Data

Systematics

CMS-PAS-SMP-16-006

ZZ Production

◦ Cleanest channel: ZZ → 4 l

◦ ≈ background free

◦ Low statistics

◦ Background for Higgs measurements

m4`(GeV)

10² 10³

Data/Theo.

0.5 1

1.5 MG5_aMC@NLO+MCFM+POWHEG+Pythia8

Data/Theo.

0.5 1 1.5

POWHEG+MCFM+Pythia8

1 σfiddσfid dm4`1 GeV

0 2 4 6 8 10 12 14 16 18

×10⁻³

Data + stat. unc.

Stat.⊕syst. unc.

MG5_aMC@NLO+MCFM+POWHEG+Pythia8 POWHEG+MCFM+Pythia8

35.9 fb⁻¹(13 TeV) CMS

Eur.Phys.J.C78(2018)165

ZZ Production

◦ Cleanest channel: ZZ → 4 l

◦ ≈ background free

◦ Low statistics

◦ Background for Higgs measurements

◦ Interpret also as aTGC

mZZ(TeV)

0.2 0.4 0.6 0.8 1 1.2

Events/0.05TeV

1 10 10² 10³

Data f^γ5=0.0019,f^Z5=0.0015 f^γ4=0.0019,f^Z4=0.0015 q¯q→ZZ (SHERPA) q¯q→ZZ, Zγ^∗ gg→ZZ, Zγ^∗ ZZ+2 jets EWK t¯tZ, WWZ Z+X

35.9 fb⁻¹(13 TeV) CMS

Eur.Phys.J.C78(2018)165

WZ Production

◦ WZ reconstruction

◦ Signature: 3 leptons (W → ^l ν , Z → ^ll)

◦ Main backgrounds: Z + jets, ZZ

◦ Search for new physics

◦ ^High-p

Z boson

◦ High invariant WZ mass

NEW 2019

(WZ) [GeV]

M

Events/bin

1 10 102

103

104

105 ^CombinedData

= -3 SM + AC cWWW

W = 4 SM + AC c

= -4 SM + AC cW

= 150 SM + AC cb WZ SM Nonprompt ZZ

γ X+

ttX VVV VH tZq Total bkg. unc.

(13 TeV) 35.9 fb-1

CMS

(WZ) [GeV]

M

0 100 200 300 400 500 600 700 800

Data/pred.

0 1 2 3

Stat. bkg. unc. Total bkg. unc.

JHEP1903(2019)026

Matthias Schr¨oder – W/Z/Higgs an Collidern (Sommersemester 2019) Vorlesung 10 44/59

Diboson Cross-Section

Diboson Cross-Section (Status 2019)

σ

/ σ Production Cross Section Ratio:

0.5 1 1.5 2

CMS Preliminary

March 2019

All results at:

http://cern.ch/go/pNj7

γ

γ 1.06 ± 0.01 ± 0.12 5.0 fb

(NLO th.)

γ ,

W 1.16 ± 0.03 ± 0.13 5.0 fb

(NLO th.)

γ ,

Z 0.98 ± 0.01 ± 0.05 5.0 fb

(NLO th.)

γ ,

Z 0.98 ± 0.01 ± 0.05 19.5 fb

WW+WZ 1.01 ± 0.13 ± 0.14 4.9 fb

WW 1.07 ± 0.04 ± 0.09 4.9 fb

WW 1.00 ± 0.02 ± 0.08 19.4 fb

WW 0.96 ± 0.05 ± 0.08 2.3 fb

WZ 1.05 ± 0.07 ± 0.06 4.9 fb

WZ 1.02 ± 0.04 ± 0.07 19.6 fb

WZ 0.96 ± 0.02 ± 0.05 35.9 fb

ZZ 0.97 ± 0.13 ± 0.07 4.9 fb

ZZ 0.97 ± 0.06 ± 0.08 19.6 fb

ZZ 1.06 ± 0.02 ± 0.04 137 fb

7 TeV CMS measurement (stat,stat+sys) 8 TeV CMS measurement (stat,stat+sys) 13 TeV CMS measurement (stat,stat+sys) CMS measurements

theory

(NLO)

vs. NNLO

CMSTWiki

“Stairway-to-Heaven” Plot

[pb] σ Production Cross Section,

−4

10

−3

10

−2

10

−1

10 1 10 10

10

10

10

CMS Preliminary

March 2019

All results at: http://cern.ch/go/pNj7 W

n jet(s)

≥

Z n jet(s)

≥

γ W ZγWW WZ ZZ

µ ll, l=e,

→ ν, Z

→l : fiducial with W γ γ γ,W γ EW,Z qqW EW qqZ EW WW

→ γ γ

γ qqW EW

ssWW EW

γ qqZ EW

qqWZ EW

qqZZEW WWWWVγZγγWγγtt

=n jet(s)

tt-chtWts-chttγtZq ttZ tγ ttW tttt σ

∆ in exp.

σH

∆ Th.

ggHqqHVBF 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) 137 fb

≤ 13 TeV CMS measurement (L Theory prediction

CMS TWiki

4.2.4. Vector boson scattering

Triple Boson Production

◦ Mediated by 4-point V boson interaction vertex (“quartic vertec”)

◦ In the Standard Model

◦ ^WWWW

◦ ^WWZZ

◦ ^WWZ γ

◦ ^WW γγ

(4 neutral bosons forbidden)

◦ Problem: cross-section extremely small

Vector Boson Scattering

◦ Study quartic vertex in V boson scattering (VBS)

◦ Cross-section for longitudinally polarised states diverges at high energies: in SM cancelled by negative interference with Higgs diagrams

W⁻ W⁺

W⁻ W⁺

H W⁻ W⁺

W⁻ W⁺

H

W⁻ W⁺

W⁻ W⁺

Vector Boson Scattering

◦ 2 W + 2 jets processes common

◦ Jets typically forward

◦ Event selection: 2 jets with

◦ high dijet mass

◦ large rapidity difference

◦ ^{Study W ± W ±}

◦ No gluon-induced initial states

◦ Largely reduced backgrounds

Vector Boson Scattering

◦ ^First observation in 2017

◦ EWK contribution detected at 5 σ significance

σ( pp → ^W

^W

) = 3 . 83 ± ⁰ . 66 ( stat ) ± ⁰ . 35 ( syst ) fb

(SM prediction: 4 . 25 ± 0 . 2 fb)

◦ New evidence also in ZZ channel

[Phys. Lett. B774 (2017) 682]

(GeV) m

500 1000 1500 2000

Events / bin

0 50 100 150

Data EW WW WZ Nonprompt Others Bkg. unc.

(13 TeV) 35.9 fb-1

CMS

Phys.Rev.Lett.120(2018)081801

4.2.5. Anomalous couplings

Anomalous Triple Gauge Couplings (aTGC)

New physics beyond the Standard Model can modify couplings

→ ^expect higher cross sections, especially at high p

(V)

Searching for aTGC

◦ ^Interpret diboson results as limits on aTGCs

◦ Example: CMS WV analysis

◦ Typical assumption: no C or P violation

◦ Expect largest effect at high diboson mass

◦ Observable: invariant WV mass

◦ ^W → ^e

ν _{, W} / _Z → ^qq

◦ Reconstruct p

(ν ) using

W mass constraint

1000 1500 2000 2500 3000 3500

dataσData-Fit -2 0

2 ^{1000 1500 2000 2500 3000 MWV (GeV)3500}

Events / (100 GeV)

10-1

1 10 102

103

,WZ-category ν µ

ν µ

→ Data W

=12 TeV-2 Λ2 WWW/ signal c W+jets t t WW/WZ Single Top Background uncertainty

(13 TeV) 2.3 fb-1

CMS preliminary

CMS-PAS-SMP-16-012

Summary WWZ aTGC

◦ Many different results

◦ Common interpretation e. g. in “LEP parametrisation”

◦ All parameters defined such that they equal 0 in the SM

CMSTWiki

Effective Field Theory

◦ New physics might be out of direct LHC reach

◦ “Integrate out” high-mass particles (like in Fermi theory)

L

= L

+ X

i

C

O

Λ

+ O

₁ Λ

→ parametrise any theory without low-mass particles

◦ Standard Model covers all dimension-4 operators

◦ Dimension 5, 7 violate lepton number

◦ Dimension 6: includes triple gauge couplings

◦ Dimension 8: includes quartic gauge couplings

Summary aTGC in EFT

Summary aQGC in EFT

-4

] aQGC Limits @95% C.L. [TeV

− 200 0 200 400 600 800

May 2019

aC summary plots at: http://cern.ch/go/8ghC Λ4

M,0 /

f ^WVγ [-7.7e+01, 8.1e+01] 19.3 fb^-1 8 TeV

γ

Z [-7.1e+01, 7.5e+01] 19.7 fb^-1 8 TeV

γ

Z [-7.6e+01, 6.9e+01] 20.2 fb^-1 8 TeV

γ

W [-7.7e+01, 7.4e+01] 19.7 fb^-1 8 TeV

ss WW [-6.0e+00, 5.9e+00] 35.9 fb^-1 13 TeV

WZ [-9.1e+00, 9.1e+00] 35.9 fb^-1 13 TeV

→WW γ

γ [-2.8e+01, 2.8e+01] 20.2 fb^-1 8 TeV

→WW γ

γ [-4.2e+00, 4.2e+00] 24.7 fb^-1 7,8 TeV

WV ZV [-6.9e-01, 7.0e-01] 35.9 fb^-1 13 TeV

Λ4 M,1 /

f ^WVγ [-1.3e+02, 1.2e+02] 19.3 fb^-1 8 TeV

γ

Z [-1.9e+02, 1.8e+02] 19.7 fb^-1 8 TeV

γ

Z [-1.5e+02, 1.5e+02] 20.2 fb^-1 8 TeV

γ

W [-1.2e+02, 1.3e+02] 19.7 fb^-1 8 TeV

ss WW [-8.7e+00, 9.1e+00] 35.9 fb^-1 13 TeV

WZ [-9.1e+00, 9.4e+00] 35.9 fb^-1 13 TeV

→WW γ

γ [-1.1e+02, 1.0e+02] 20.2 fb^-1 8 TeV

→WW γ

γ [-1.6e+01, 1.6e+01] 24.7 fb^-1 7,8 TeV

WV ZV [-2.0e+00, 2.1e+00] 35.9 fb^-1 13 TeV

Λ4 M,2 /

f ^WVγ [-5.7e+01, 5.7e+01] 20.2 fb^-1 8 TeV

γ

Z [-3.2e+01, 3.1e+01] 19.7 fb^-1 8 TeV

γ

Z [-2.7e+01, 2.7e+01] 20.2 fb^-1 8 TeV

γ

W [-2.6e+01, 2.6e+01] 19.7 fb^-1 8 TeV

Λ4 M,3 /

f ^WVγ [-9.5e+01, 9.8e+01] 20.2 fb^-1 8 TeV

γ

Z [-5.8e+01, 5.9e+01] 19.7 fb^-1 8 TeV

γ

Z [-5.2e+01, 5.2e+01] 20.2 fb^-1 8 TeV

γ

W [-4.3e+01, 4.4e+01] 19.7 fb^-1 8 TeV

Λ4 M,4 /

f ^WVγ [-1.3e+02, 1.3e+02] 20.2 fb^-1 8 TeV

γ

W [-4.0e+01, 4.0e+01] 19.7 fb^-1 8 TeV

Λ4 M,5 /

f ^WVγ [-2.0e+02, 2.0e+02] 20.2 fb^-1 8 TeV

γ

W [-6.5e+01, 6.5e+01] 19.7 fb^-1 8 TeV

Λ4 M,6 /

f ^Wγ [-1.3e+02, 1.3e+02] 19.7 fb^-1 8 TeV

ss WW [-1.2e+01, 1.2e+01] 35.9 fb^-1 13 TeV

WV ZV [-1.3e+00, 1.3e+00] 35.9 fb^-1 13 TeV

Λ4

/

fM,7 ^Wγ [-1.6e+02, 1.6e+02] 19.7 fb^-1 8 TeV

ss WW [-1.3e+01, 1.3e+01] 35.9 fb^-1 13 TeV

WV ZV [-3.4e+00, 3.4e+00] 35.9 fb^-1 13 TeV

Channel Limits ∫Ldt s

CMS ATLAS