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 L = ψ(iγ µ µ m)ψ Q ψγ µ ψa µ 1 4 F µνf µν. free fermion propagation (L 0 ) photon kinetic energy fermion photon interaction Theory invariant under local phase transformation (U(1)) ψ ψ = e iqα(x) ψ. (A µ A µ = A µ + µ χ) 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) ψ ψ = e i 2 τ α(x) e i Y 2 β(x) ψ. L = χ L γ (i µ µ g τ W 2 µ g Y ) ( 2 B µ χ L + ψ R i µ g Y ) 2 B µ ψ R + L kin with gauge invariant term describing gauge field kinetics: L kin = 1 4 B µνb µν 1 4 W µν W µν resulting from non-abelian gauge structure B µν.= µ B ν ν B µ Wµν.= µ Wν ν Wµ + g W 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 L kin : [ ( µ ν ν µ L 3 = ie cot θ ) W W W W µ ( Zν µ W ν ν W µ ) W µz ν + W µw ( µ ν ν µ ) ] ν Z Z [ ( µ ν ν µ ie ) W W W ( µ Aν µ W ν ν W µ ) W µa ν + W µw ( µ ν ν µ ) ] ν A A e 2 [ L 4 = 2 sin 2 (W µ θ W µ ) 2 W µ W µ W ν W ν ] e 2 cot 2 [ θ W W µ W µ Z ν Z ν W µ Z µ W ν Z ν ] W [ e cot θ W 2W µ W µ Z ν A ν W µ Z µ W ν A ν W µ Aµ W nuz ν ] e 2[ W µ W µ A ν A ν W µ Aµ W ν A ν ] 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 Λ 2 ) 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 G F, describing two weak interaction vertices at low energies s M W.) p p n ν n W ν e Gernot Knippen TGC and QGC June 17, 2014 6 / 26 e
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 ( L ZZV = e2 MZ 2 [ f γ 4 ( µf µν ) + f4 Z ( µz µν ) ] Z σ ( σ Z ν ) [ f γ 5 ( ρ F ρλ ) + f5 Z ( ρ Z ρλ ) ] ) Z λξ Z ξ 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 NLO and higher order contributions (only CP conserving f V 5 ) Z /γ Z Z MSSM 1-loop (and higher order) contributions from charginos and neutralinos New bosons CP violating coupling f V 4 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 ZZ γ couplings from differential cross section dσ ZZ. dp Z T Analyse ZZ signal channels: ZZ ( ) l + l l + l and ZZ l + l ν ν 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) p T > GeV and c) ET of calorimeter deposites inside R = 0.2 smaller that 15 % of muon p T. 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 p T > 20 GeV and c) fulfill same impact parameter and isolation criteria as standard muons. Gernot Knippen TGC and QGC June 17, 2014 / 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 p T > 20 GeV and b) pass the tight identification requirement. p T 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 / 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(l 1, l 2 ) > 0.2 ambiguity in lepton combinations removed by choosing combination with lowest m l + l M Z at least one lepton pair fulfills 66 < m l + l < 116 GeV (the other m l + 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 ν ν: exactly 2 leptons of same flavour with p T > 20 GeV R(l 1, l 2 ) > 0.3 76 < m l + l < 6 GeV axial-et miss = E T miss pz /p Z T > 75 GeV and E miss T p Z T /p Z T < 0.4 jet veto no additional lepton with < p T 20 GeV 9 8 7 6 5 4 3 2 1 Events / 5 GeV Events / 0.1 4 3 2 1 ATLAS Ldt = 4.6 fb s = 7 TeV Data Z+X W+X Wγ/Wγ* Top WZ WW + - + - ZZ l l l l + - ZZ l l νν Total Uncertainty + - ZZ l l νν -50 0 50 0 150 miss Axial-E T [GeV] ATLAS Ldt = 4.6 fb s = 7 TeV Data Z+X W+X Wγ/Wγ* Top WZ WW + - + - ZZ l l l l + - ZZ l l νν Total Uncertainty + - ZZ l l νν 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 miss Z Z E -p /p 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 where N(BG) = [N(lllj) N(ZZ)] f N(lljj) f 2, 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 approach f V i = 1 (1 + ŝ/λ 2 ) n f V i,0 s 0 with n = 3 and Λ = 3 TeV to ensure unitarity is not violated at LHC energies. To obtain simulated pt Z distributions for different fi V a reweighting method ( M 2 / M SM 2 ) is used. Dependency of couplings on the expected number of events in each pt Z bin is parametrized. Limits on couplings are obtained by using a maximum likelihood fit. Events / GeV Events / GeV ATLAS 1.2 Data + - + - ZZ l l l l L dt = 4.64 fb Background (dd.) 1 Total Uncertainty s= 7 TeV Z Z f 4 =f 5 =0.1 + - + - γ γ 0.8 ZZ l l l l f 4 =f 5 =0.1 γ f 4 =0.1 γ 0.6 f 5 =-0.1 0.4 0.2 2.5 2 1.5 1 0.5 0 50 0 150 200 250 300 350 400 450 pz [GeV] T Data + - ZZ l l νν Background Total Uncertainty Z Z f 4 =f 5 =0.1 γ γ f 4 =f 5 =0.1 γ f 4 =0.1 γ f 5 =-0.1 ATLAS L dt = 4.6 fb 0 0 50 0 150 200 250 300 350 400 450 pz [GeV] T s= 7 TeV + - ZZ l l νν Gernot Knippen TGC and QGC June 17, 2014 13 / 26
Limits on anomalous ntgc Limits from pp ZZ analysis Limits on anomalous ntgc The limit(s) on the coupling(s) is/are obtained assuming all other couplings are zero (as in SM). Z f 4 ATLAS 0.02 0.01 0 L dt = 4.6 fb s=7 TeV Z f 5 γ f 5 Z f 4 γ f 4 ATLAS CMS, s = 7TeV 5.0 fb, Λ = ATLAS, s = 7TeV 4.6 fb, Λ = ATLAS, s = 7TeV 4.6 fb, Λ = 3 TeV LEP, s = 130-209 GeV 0.7 fb, Λ = D0, s = 1.96TeV 1.0 fb, Λ = 1.2 TeV -0.8-0.6-0.4-0.2 0 0.2 0.4 Z f 5-0.01-0.02 0.01 0-0.01-0.02 + - + - ZZ l l (l l /νν) 95% CL -0.02-0.01 0 0.01 0.02 γ f 4 ATLAS 0.02 L dt = 4.6 fb s=7 TeV + - + - ZZ l l (l l /νν) 95% CL -0.02-0.01 0 0.01 0.02 Z f 4 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): L WWV = ig WWV (g V 1 with g γ 1 = 1. ( W + µν W µ W +µ W µν ) V ν + κ V W + µ W ν V µν + λ V MW 2 V µν W ν + ρ W ρµ ) 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 g1 Z = κ Z = κ γ = 1 λ Z = λ γ = 0. Often the differences from the SM g1 Z = g1 Z 1 κ Z = κ Z 1 κ γ = κ γ 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: Select W + W events by ll + E miss T. Measure differential cross section dσ WW dp T region. in selection phase space 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) ( 3 channels: ee, eµ, µµ) cut on invariant lepton mass m ll and ET miss,rel, where E miss T,Rel = { ET miss sin( φ) if φ a < π /2 ET miss if φ π /2 (to remove Drell-Yan background) jet veto p T (ll ) > 30 GeV Events / 5GeV Events 6 ATLAS Data Ldt = 4.6 fb Drell-Yan 5 s = 7 TeV top-quark W+jets 4 non-ww diboson WW µνµν 3 2 700 600 500 400 300 200 0 1 0 20 40 60 80 0 120 140 160 180 200 0 ATLAS miss ET,Rel Data WW µνµν Drell-Yan top-quark W+jets non-ww diboson σ stat+syst Ldt = 4.6 fb [GeV] 0 1 2 3 4 5 6 7 8 9 s = 7 TeV Jet Multiplicity a φ = azimutal angle difference between E miss T 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 κ Z = κ γ, λ Z = λ γ and g Z 1 = 1 LEP scenario HISZ scenario κ γ = cos2 θ ( ) W sin 2 g1 Z κ Z θ W g Z 1 = and λ Z = λ γ 1 cos 2 θ W sin 2 θ W κ Z, cos 2 θ W κ γ = 2 κ Z cos 2 θ W sin 2 θ W and λ Z = λ γ 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 p T (l 1 ) 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 κ Z ATLAS (4.6 fb, Λ=6 TeV) ATLAS (4.6 fb, Λ= ) CMS (36 pb, Λ= ) LEP (2.6 fb ) CDF (3.6 fb, Λ=2 TeV) D0 (1 fb, Λ=2 TeV) λ Z g Z 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 BSM in EFT approach possible. Construct Lagrangian from following constraints: Consider couplings to logitudinal polarization degree of gauge bosons only. Custodial symmetry ( ) M 2 W ρ = = 1 M Z cos θ W should be respected. W W + W W + W + W Z/γ Z/γ 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: L 4 = α 4 16π 2 Tr(V µv ν ) Tr(V µ V ν ) L 5 = α 5 16π 2 Tr(V µv µ ) Tr(V ν V ν ) with V µ = igw ν + ig B µ (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 2 same electric charge leptons 2 jets with p T > 30 GeV & η < 4.5 additional loose lepton veto m ll > 20 GeV m ee M Z > GeV ET miss > 40 GeV b-jet veto m jj > 500 GeV y jj > 2.4 Events/50 GeV Data/Expected Events 2 1 2 0 30 25 20 15 5 ATLAS Preliminary 20.3 fb, s = 8 TeV Data 2012 Syst. Uncertainty ± ± W W jj Electroweak ± ± W W jj Strong Prompt Conversions Other non-prompt Data/Expected Syst. Uncertainty 200 400 600 800 00 1200 1400 1600 1800 2000 m jj [GeV] ATLAS Preliminary 20.3 fb, m jj > 500 GeV s = 8 TeV Data 2012 Syst. Uncertainty ± ± W W jj Electroweak ± ± W W jj Strong Prompt Conversions Other non-prompt 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 α 5 0.6 0.4 0.2 ATLAS Preliminary 20.3 fb, s = 8 TeV ± ± pp W W jj K-matrix unitarization 0-0.2-0.4-0.6 confidence intervals 68% CL 95% CL 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