Particle Physics at the LHC

Triple Gauge Couplings and Quartic Gauge Couplings Particle Physics at the LHC

Gernot Knippen

Faculty of Mathematics and Physics University of Freiburg

June 17, 2014

Gernot Knippen TGC and QGC June 17, 2014 1 / 26 Table of content

1 Theoretical fundamentals Theory of electroweak interactions Eﬀective ﬁeld theory 2 Limits on anomalous nTGC Lagrangian and possible contributions pp → ZZ analysis Limits from pp → ZZ analysis 3 Limits on cTGC Lagrangian pp → WW analysis Limits from pp → WW analysis 4 Limits on aQGC Lagrangian pp → W ±W ±jj analysis Limits from pp → W ±W ±jj analysis 5 Summary & Outlook

Gernot Knippen TGC and QGC June 17, 2014 2 / 26 Theoretical fundamentals Theory of electroweak interactions QED Lagrangian

Quantum electrodynamics described by

1 L = ψ¯(iγµ∂ − m)ψ − Qψγ¯ µψA − F F µν . µ µ 4 µν

free fermion propagation (L0) photon kinetic energy fermion photon interaction

Theory invariant under local phase transformation (U(1))

ψ → ψ0 = eiQα(x)ψ.

0 (Aµ → Aµ = Aµ + ∂µχ)

Gernot Knippen TGC and QGC June 17, 2014 3 / 26 Theoretical fundamentals Theory of electroweak interactions Electroweak Lagrangian

Theory invariant under SU(2)L ⊗ U(1)

0 i ~τ~α(x) i Y β(x) ψ → ψ = e 2 e 2 ψ.

~τ Y Y L =χ ¯ γµ i∂ − g W~ − g 0 B χ + ψ¯ i∂ − g 0 B ψ + L L µ 2 µ 2 µ L R µ 2 µ R kin

with gauge invariant term describing gauge ﬁeld kinetics: 1 1 L = − B Bµν − W~ W~ µν kin 4 µν 4 µν resulting from non-abelian gauge structure

. . Bµν .= ∂µBν − ∂νBµ W~ µν .= ∂µW~ ν − ∂νW~ µ + gW~ µ × W~ ν

Gernot Knippen TGC and QGC June 17, 2014 4 / 26 Theoretical fundamentals Theory of electroweak interactions Gauge boson self-coupling in the electroweak theory

Cubic and quartic interaction terms resulting from Lkin:

h µ ν ν µ † µ ν † ν µ† † µ ν ν µ i L3 = − ie cot θW ∂ W − ∂ W WµZν − ∂ W − ∂ W WµZν + WµWν ∂ Z − ∂ Z h µ ν ν µ † µ ν † ν µ† † µ ν ν µ i − ie ∂ W − ∂ W WµAν − ∂ W − ∂ W WµAν + WµWν ∂ A − ∂ A

e2 h i h i L = − (W †W µ)2 − W µ†W µ†W W ν − e2 cot2 θ W †W µZ Z ν − W †Z µW Z ν 4 2 µ ν W µ ν µ ν 2 sin θW h † µ ν † µ ν † µ ν i − e cot θW 2WµW Zν A − WµZ Wν A − WµA WnuZ 2h † µ ν † µ ν i − e WµW Aν A − WµA Wν A

W + W − W + W − Z/γ

Z/γ

W − W + W − W + Z/γ

Gernot Knippen TGC and QGC June 17, 2014 5 / 26 Theoretical fundamentals Effective field theory Effective field theory (EFT) Assumption: New physics separated by different (energy) scale Λ from accessible region. (s Λ2) → Describe observations by parametrized, most general Lagrangian which recovers the Standard Model in the limit Λ → ∞. (Unitary should be preserved.) → Model independent approach for physics BSM.

Example: Fermi theory of β decay (quartic coupling with coupling strength GF , describing two weak interaction vertices at low energies s MW .) p p

n ν¯ ←→ n ν¯ W −

e− e− Gernot Knippen TGC and QGC June 17, 2014 6 / 26 Limits on anomalous nTGC

Limits on anomalous neutral triple gauge couplings

Gernot Knippen TGC and QGC June 17, 2014 6 / 26 Limits on anomalous nTGC Lagrangian and possible contributions Neutral triple gauge couplings (nTGC) Forbidden in Standard Model but possibly realized as “anomalous” coupling (in EFT approach).

Construct Lagrangian from general process properties: • 9 total helicity states but only 7 valid (angular momentum conservation) • bose statistics have to be respected

→ Eﬀective ZZV Lagrangian: violating CP invariance

2 e γ µν Z µν σ LZZV = 2 − f4 (∂µF ) + f4 (∂µZ ) Zσ (∂ Zν) MZ ! γ ρ Z ρ ˜λξ − f5 (∂ Fρλ) + f5 (∂ Zρλ) Z Zξ conserving CP invariance

Gernot Knippen TGC and QGC June 17, 2014 7 / 26 Limits on anomalous nTGC Lagrangian and possible contributions SM and some new physics contributions to nTGC

SM Z

NLO and higher order contributions Z ∗/γ∗ V (only CP conserving f5 ) Z

MSSM 1-loop (and higher order) contributions from charginos and neutralinos

New bosons V CP violating coupling f4 sensitive to two-Higgs-doublet model in 1-loop corrections.

Gernot Knippen TGC and QGC June 17, 2014 8 / 26 Limits on anomalous nTGC pp → ZZ analysis Limits on anomalous nTGC from ZZ production in pp collisions

CERN-PH-EP-2012-318

Strategy: Obtain limits on anomalous ZZZ and ZZγ couplings from diﬀerential dσZZ cross section Z . dpT Analyse ZZ signal channels: ZZ (∗) → l+l−l+l− and ZZ → l+l−νν¯

Gernot Knippen TGC and QGC June 17, 2014 9 / 26 Limits on anomalous nTGC pp → ZZ analysis Extended-lepton selection

Aim: Increase selection acceptance in the ZZ (∗) → l+l−l+l− channel by using leptons which are normally not used due to detector geometry.

Forward spectrometer muons Muons outside the nominal ID range with 2.5 < |η| < 2.7. Are required to have a) full track in muon spectrometer, b) pT > 10 GeV and c) X ET of calorimeter deposites inside ∆R = 0.2 smaller that 15 % of muon pT .

Calorimeter-tagged muons Muons in the muon spectrometer limited coverage range |η| < 0.1. Are required to a) have calorimeter deposit consistent with muon which is matched to ID track b) have pT > 20 GeV and c) fulﬁll same impact parameter and isolation criteria as “standard muons”.

Gernot Knippen TGC and QGC June 17, 2014 10 / 26 Limits on anomalous nTGC pp → ZZ analysis Extended-lepton selection

Aim: Increase selection acceptance in the ZZ (∗) → l+l−l+l− channel by using leptons which are normally not used due to detector geometry.

Calorimeter-only electrons Electrons outside the ID range with 2.5 < |η| < 3.16. Are required to a) have pT > 20 GeV and b) pass the tight identiﬁcation requirement. pT is calculated from calorimeter energy and electron direction. Charge is assigned depending on the charge of the other electron(s).

At most one lepton from each extended category!

Gernot Knippen TGC and QGC June 17, 2014 10 / 26 Limits on anomalous nTGC pp → ZZ analysis Signal region deﬁnitions

ZZ(∗) → l+l−l+l−: • exactly 4 isolated leptons, two same-ﬂavour opposite charge pairs (e+e−e+e−, e+e−µ+µ− or µ+µ−µ+µ−)

• ∆R(l1, l2) > 0.2 • ambiguity in lepton combinations removed by choosing combination with lowest |ml +l − − MZ |

• at least one lepton pair fulﬁlls 66 < ml +l − < 116 GeV (the other ml +l − > 20 GeV)

Gernot Knippen TGC and QGC June 17, 2014 11 / 26 Limits on anomalous nTGC pp → ZZ analysis Signal region deﬁnitions

ZZ → l+l−νν¯: 1010 9 ATLAS Data WW 10 + - + - 8 -1 Z+X ZZ→l l l l ∫ Ldt = 4.6 fb - 10 W+X ZZ→l+l νν 107 s = 7 TeV Wγ/Wγ* Total Uncertainty 6 Top → + -νν 10 WZ ZZ l l 5

Events / 5 GeV 10 • exactly 2 leptons of same ﬂavour with 104 103 pT > 20 GeV 102 10 1 • ∆R(l1, l2) > 0.3 10-1 -50 0 50 100 150 Axial-Emiss [GeV] • 76 < ml +l − < 106 GeV T miss ~miss p~Z Z • axial-ET = −ET · /pT > 75 GeV and miss Z Z ATLAS Data WW |E −p | 4 + - + - T T /p < 0.4 -1 Z+X ZZ→l l l l T 10 ∫ Ldt = 4.6 fb - W+X ZZ→l+l νν γ γ 3 s = 7 TeV W /W * Total Uncertainty 10 Top + - Events / 0.1 → νν • jet veto WZ ZZ l l 102

• no additional lepton with 10 10 < pT ≤ 20 GeV 1 10-1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 |Emiss-pZ|/pZ T T T

Gernot Knippen TGC and QGC June 17, 2014 11 / 26 Limits on anomalous nTGC pp → ZZ analysis Background estimation for the ZZ (∗) → l +l −l +l − channel

Background estimated via data-driven (dd.) method

N(BG) = [N(lllj) − N(ZZ)] × f − N(lljj) × f 2,

where • N(lllj) = number of events with 3 leptons and 1 lepton-like jet satisfying all selection criteria • N(lljj) = number of events with 2 leptons and 2 lepton-like jet satisfying all selection criteria • N(ZZ) = MC estimate for real leptons classiﬁed as lepton-like jet • f = ratio of the probability for a non-lepton to satisfy the full lepton selection criteria to the probability for a non-lepton to satisfy the lepton-like jet criteria.

Gernot Knippen TGC and QGC June 17, 2014 12 / 26 Limits on anomalous nTGC Limits from pp → ZZ analysis Determining limits on anomalous nTGC

• Couplings are parametrized in form-factor

1.2 ATLAS Data approach + - + - -1 ZZ → l l l l ∫ L dt = 4.64 fb Background (dd.) 1 Total Uncertainty Events / GeV s= 7 TeV fZ=fZ=0.1 + - + - γ4 γ5 0.8 ZZ → l l l l 1 f4=f5=0.1 γ V V f =0.1 f = f −→ 0 γ4 i n i,0 0.6 f5=-0.1 (1 + sˆ/Λ2) s→∞ 0.4 with n = 3 and Λ = 3 TeV to ensure 0.2

0 50 100 150 200 250 300 350 400 450 unitarity is not violated at LHC energies. pZ [GeV] T • To obtain simulated pZ distributions for T Data ATLAS + - V 2.5 ZZ→l l νν Background -1 diﬀerent f a reweighting method L dt = 4.6 fb i Total Uncertainty ∫ 2 fZ=fZ=0.1 2 2 4γ γ5 s= 7 TeV |M| |M | f =f =0.1 ( / ) is used. Events / GeV SM 4γ 5 f =0.1 → + -νν γ4 ZZ l l 1.5 f =-0.1 • Dependency of couplings on the expected 5 1 number of events in each pZ bin is T 0.5

parametrized. 0 0 50 100 150 200 250 300 350 400 450 pZ [GeV] • Limits on couplings are obtained by using a T maximum likelihood ﬁt. Gernot Knippen TGC and QGC June 17, 2014 13 / 26 Limits on anomalous nTGC Limits from pp → ZZ analysis Limits on anomalous nTGC Z 4 f ATLAS 0.02 The limit(s) on the coupling(s) is/are obtained ∫ L dt = 4.6 fb-1 s=7 TeV assuming all other couplings are zero (as in SM). 0.01

-0.01 Z f5 + - + - ATLAS -0.02 ZZ → l l (l l /νν) 95% CL -0.02 -0.01 0 0.01 0.02 γ γ f4 f5 CMS, s = 7TeV 5.0 fb-1, Λ = ∞ Z 5

ATLAS, s = 7TeV f -1 ATLAS 4.6 fb , Λ = ∞ 0.02 -1 ATLAS, s = 7TeV ∫ L dt = 4.6 fb s=7 TeV Z -1 f 4.6 fb , Λ = 3 TeV 4 LEP, s = 130-209 GeV 0.01 0.7 fb-1, Λ = ∞ D0, s = 1.96TeV 1.0 fb-1, Λ = 1.2 TeV 0 γ f 4 -0.01

+ - + - -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 -0.02 ZZ → l l (l l /νν) 95% CL -0.02 -0.01 0 0.01 0.02 Z f4

Gernot Knippen TGC and QGC June 17, 2014 14 / 26 Limits on cTGC

Limits on charged triple gauge couplings

Gernot Knippen TGC and QGC June 17, 2014 14 / 26 Limits on cTGC Lagrangian Charged triple gauge couplings (cTGC) Already realized as ZWW and γWW in Standard Model but further coupling contributions from new physics possible in EFT approach.

Construct Lagrangian from general process properties: • 9 total helicity states but only 7 valid (angular momentum conservation) • demand C and P conservation

→ Eﬀective WWV Lagrangian (V = Z and γ):

V + −µ +µ − ν + − µν LWWV = igWWV g1 WµνW − W Wµν V + κV Wµ Wν V

λV µν +ρ − + 2 V Wν Wρµ MW γ with g1 = 1.

Gernot Knippen TGC and QGC June 17, 2014 15 / 26 Limits on cTGC Lagrangian The values of cTGC

In the SM the general cTGC couplings are given by

Z g1 = κZ = κγ = 1 λZ = λγ = 0.

Often the diﬀerences from the SM

Z Z ∆g1 = g1 − 1 ∆κZ = κZ − 1

∆κγ = κγ − 1

and not the absolute values are denoted.

Gernot Knippen TGC and QGC June 17, 2014 16 / 26 Limits on cTGC pp → WW analysis Limits on anomalous charged TGC from W +W − production in pp collisions

CERN-PH-EP-2012-242

Analysis strategy: + − 0 miss • Select W W events by “ll + ET ”. dσ • Measure diﬀerential cross section WW in selection phase space dpT region. • Extract limits on couplings from diﬀerential cross section.

Gernot Knippen TGC and QGC June 17, 2014 17 / 26 Limits on cTGC pp → WW analysis Selection criteria

• two opposite charged leptons (at least one matched to trigger reconstructed lepton) 106 ATLAS Data ∫ Ldt = 4.6 fb-1 Drell-Yan 105 s = 7 TeV top-quark W+jets (→ 3 channels: ee, eµ, µµ) 4 Events / 5GeV 10 non-WW diboson WW→µνµν miss 103 • cut on invariant lepton mass m 0 and E , ll T ,Rel 102

where 10 1 0 20 40 60 80 100 120 140 160 180 200 ( miss Emiss [GeV] a π T,Rel miss ET × sin(∆φ) if ∆φ < /2 ET ,Rel = miss π ATLAS Data E if ∆φ ≥ /2 700 WW→µνµν Events T Drell-Yan 600 top-quark 500 W+jets non-WW diboson σ (to remove Drell-Yan background) 400 stat+syst

300 -1 ∫ Ldt = 4.6 fb • jet veto 200 s = 7 TeV 100

0 0 • p (ll ) > 30 GeV 0 1 2 3 4 5 6 7 8 9 T Jet Multiplicity

a miss ∆φ = azimutal angle diﬀerence between ET and nearest lepton or jet

Gernot Knippen TGC and QGC June 17, 2014 18 / 26 Limits on cTGC Limits from pp → WW analysis “Coupling-scenarios” investigated

equal coupling scenario

Z ∆κZ = ∆κγ, λZ = λγ and g1 = 1

LEP scenario 2 cos θW Z ∆κγ = 2 ∆g1 − ∆κZ and λZ = λγ sin θW

HISZ scenario 1 ∆g Z = ∆κ , 1 2 2 Z cos θW − sin θW cos2 θ ∆κ = 2∆κ W and λ = λ γ Z 2 2 Z γ cos θW − sin θW

Gernot Knippen TGC and QGC June 17, 2014 19 / 26 Limits on cTGC Limits from pp → WW analysis Obtaining limits on cTGC

Similar to the pp → ZZ analysis (form factor approach, reweighting method, dependency of pT (l1) on couplings).

Limits are obtained by the maximum likelihood principle. (Point in parameter space is discarded if the negative log-likelihood function increases by more that 1.92 units above the minimum.)

Gernot Knippen TGC and QGC June 17, 2014 20 / 26 Limits on cTGC Limits from pp → WW analysis Limits on cTGC

95% C.L. limits from WW production

ATLAS (4.6 fb-1, Λ=6 TeV) ATLAS (4.6 fb-1, Λ=∞) ∆κ CMS (36 pb-1, Λ=∞) Z LEP (2.6 fb-1) CDF (3.6 fb-1, Λ=2 TeV) D0 (1 fb-1, Λ=2 TeV)

λ Z

∆gZ 1

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Gernot Knippen TGC and QGC June 17, 2014 21 / 26 Limits on aQGC

Limits on anomalous quartic gauge couplings

Gernot Knippen TGC and QGC June 17, 2014 21 / 26 Limits on aQGC Lagrangian Quartic gauge couplings (QGC)

In SM realized as WWWW , WWZZ, WW γZ and WW γγ. Further contributions from physics W − W + BSM in EFT approach possible.

Construct Lagrangian from following constraints: W + W − • Consider couplings to logitudinal polarization degree of gauge bosons only. − Z/γ • Custodial symmetry W

M 2 ρ = W = 1 MZ cos θW W + Z/γ should be respected.

Gernot Knippen TGC and QGC June 17, 2014 22 / 26 Limits on aQGC Lagrangian Quartic gauge couplings (QGC)

→ Two eﬀective anomalous vector boson scattering (VBS) Lagrangian terms: α L = 4 Tr(V V ) Tr(V µV ν) 4 16π2 µ ν α L = 5 Tr(V V µ) Tr(V V ν) 5 16π2 µ ν 0 with Vµ = −igWν + ig Bµ (in unitary gauge)

Gernot Knippen TGC and QGC June 17, 2014 22 / 26 Limits on aQGC pp → W ±W ±jj analysis Limits on aQGC from W ±W ±jj production in pp collisions

± ± “Evidence√ of the electroweak production of W W jj in pp collisions at s = 8 TeV with the ATLAS detector” (ATLAS-CONF-2014-013)

• Published in March 2014. • First analysis being able to give direct constraints on QGC from VBS. • Limits on aQGC determined from measured cross section in signal region phase space.

W ±W ±jj electroweak W ±W ±jj strong

Gernot Knippen TGC and QGC June 17, 2014 23 / 26 Limits on aQGC pp → W ±W ±jj analysis Signal region deﬁnition

ATLAS Preliminary Data 2012 -1 102 20.3 fb , s = 8 TeV Syst. Uncertainty W±W±jj Electroweak W±W±jj Strong 10 Prompt Events/50 GeV Conversions Other non-prompt

• 2 same electric charge leptons 1

• -1 2 jets with pT > 30 GeV & |η| < 4.5 10 • additional loose lepton veto Data/Expected m [GeV] Syst. Uncertaintyjj 2 • mll > 20 GeV Data/Expected • |m − M | > 10 GeV 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ee Z mjj [GeV] miss • E > 40 GeV 30 T ATLAS Preliminary Data 2012 -1

Events 20.3 fb , s = 8 TeV Syst. Uncertainty 25 ± ± m > 500 GeV W W jj Electroweak • b-jet veto jj W±W±jj Strong 20 Prompt Conversions Other non-prompt • mjj > 500 GeV 15

• |∆yjj | > 2.4 10 5

0 1 2 3 4 5 6 7 8 9 |∆y | jj

Gernot Knippen TGC and QGC June 17, 2014 24 / 26 Limits on aQGC Limits from pp → W ±W ±jj analysis Limits on aQGC 5 α ATLAS Preliminary 0.6 20.3 fb-1, s = 8 TeV ± ± pp → W W jj 0.4 K-matrix unitarization 0.2

-0.2 confidence intervals 68% CL -0.4 95% CL -0.6 expected 95% CL Standard Model -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 α 4

Gernot Knippen TGC and QGC June 17, 2014 25 / 26 Summary & Outlook Summary & Outlook

Summary • Effective field theory approach yields possibility to probe physics BSM in model independent way. • LHC experiments could improve the limits on anomalous nTGC from LEP and reach a similar precision on limits on cTGC. • New analysis (03/2014) gives first direct constraints on aQGC from pp → W ±W ±jj. • No physics BSM observed! (But higher precision may show contributions!)

Outlook • Run 2 of LHC will probably increase sensitivity. • Triboson production analysis (yielding limits on aQGC) may be realizable for new phase.

Gernot Knippen TGC and QGC June 17, 2014 26 / 26 The END

The END

Gernot Knippen TGC and QGC June 17, 2014 26 / 26