Results on BSM limits in Electroweak VBS Measurements

Transcription

1 Results on BSM limits in Electroweak VBS Measurements Franziska Iltzsche, Stefanie Todt TU Dresden Universidad Complutense Madrid May 30th, 2017 supported by

2 Vector Boson Scattering in the SM Diagrams α 6 ew q i V V V V q f = q i q f Gauge Boson Self Interaction Predicted by the SM L gauge 1 4 Tr (W µνw µν ) With SU(2) L field strength tensors W a µν = µ W a ν ν W a µ + g W ε abc W b µw c ν Triple and quartic couplings: and Higgs Interaction L φ = D µ φ 2 V(φ) with D µ = µ ig W τ a 2 Wa µ ig Y B µ Introduces and Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 2 / 29

3 Example: W L W L W L W L s invariant mass of WW system [A. Denner, Th. Hahn] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 3 / 29

4 Example: W L W L W L W L E 4 E 4 + E 2 s invariant mass of WW system + + 1/E 2 [A. Denner, Th. Hahn] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 3 / 29

5 Example: W L W L W L W L E 4 E 4 + E 2 Run /E 2 [A. Denner, Th. Hahn] s invariant mass of WW system Coupling to Higgs restores unitarity WW scattering should give insight in electroweak symmetry breaking VBS sensitive to BSM physics Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 3 / 29

6 Overview of VBS Processes O(α 6 ew) : } {{ } Resonant } {{ } Non-resonant O(α 4 ewα 2 s) : Process Final State σ EW [fb] σ EW /σ QCD 8 TeV 13 TeV 8 TeV 13 TeV ZZ lll l jj WZ lll νjj W ± W ± ll νν jj W ± W, ZZ ll νν jj [Based on Table 4.1 CERN-THESIS ] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 4 / 29

7 Overview of VBS the LHC Channel final state Observed (expected) significance comment Experimental Challenges VBS W ± W ± l ± l ± νν jj 5.5 (5.7) σ 13 TeV VBS ZZ llll jj 2.7 (1.6) σ 13 TeV VBS W ± Z lllν jj 1.9 (1.0) σ 8 TeV VBS W ± V l ± νjj jj only BSM interpretation golden channel : very good EW/QCD ratio, mostly experimental backgrounds, good statistics very clean channel, reconstruction of final state, low background but small cross section similar cross section as ssww, but larger QCD backgrounds, reasonable reconstruction of final state large backgrounds, but promising when looking for BSM effects in boosted topology VBS γγ W + W llνν jj 3.4 (2.8) σ VBS Wγ/Zγ lνγ jj / llνγ jj 2.7 (1.5) σ / 3.0 (2.1) σ 8 TeV 8 TeV huge backgrounds (dileptonic ttbar), no sensitivity to BSM EWSB higher statistics due to photon, but no sensitivity to BSM EWSB Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 5 / 29

8 Motivation for VBS LHC, ATLAS and CMS agcs VBS Analyses Resonances in VBS Mass reconstruction LHC and ATLAS Detector 38.5 fb fb fb 1 [arxiv: ] [CMS:Detector] [ATLAS:PublicResults] LHC p+ p+ collider at CERN/Geneva Run 1: s = 8 TeV Run 2: s = 13 TeV Iltzsche,Todt (TU Dresden) ATLAS and CMS Multi-purpose detectors Measure kinematics of decay products Distinguish between leptons, photons, hadrons,... Run 1: 2015/16: End of Run 2: 20.3 fb 1 (ATLAS) 23.3 fb 1 (CMS) 38.8 fb 1 (ATLAS) 45.0 fb 1 (CMS) 100 fb 1 Results on BSM limits in Electroweak VBS Measurements 6 / 29

9 Anomalous Gauge Couplings Used to parameterize strength BSM signal Description based on effective quantum field theory Model independent Standard Model is low-energy limit Anomalous couplings increase of cross section at hight energies Sensitive observables dependent on invariant mass of diboson system and boson p T Can be separated into Anomalous triple gauge couplings (atgcs) Anomalous quartic gauge couplings (aqgcs) Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 7 / 29

10 Anomalous Triple Gauge Couplings [arxiv: ] Parameterization 1: Effective Lagrangian of WWZ Vertex Only terms respecting CP conservation [ ( ) L = ig WWZ g Z 1 W + µν W µ W +µ Wµν Z ν +κ Z W +µ W ν Z µν + λz W M 2 µ +ν Wν ρ Z µ ρ] W g Z 1 = gz 1 1, κ Z = κ Z 1, λ Z are dimensionless parameters Parameterization 2: EFT - Dimension 6 Operators Extend the SM using higher-dimensional operators (dim(o i ) = d i ): L = L SM + i Parameters c WWW, c Λ 2 W, c Λ 2 B Λ 2 Sensitive Analyses: WZ,... c i Λ d i 4 O i O WWW = Tr[W µν W νρ W µ ρ ] O W = (D µ Φ) W µν (D ν Φ) O B = (D µ Φ) B µν (D ν Φ) Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 8 / 29

11 Anomalous Quartic Gauge Couplings [arxiv: ] Parameterization 1: Electroweak Chiral Lagrangian (used by ATLAS Run 1) Symmetric under SU(2) C Terms affecting quartic gauge vertices: α 4 L 4 = α 4 Tr(V µ V ν ) 2 α 5 L 5 = α 5 Tr(V µ V µ ) 2 ( Σ = exp i ) 3 v a=1 wa τ a V µ = Σ (D µ Σ) Parameterization 2: EFT - Dimension 8 Operators (used by CMS) 3 classes of operators: S, M, T S operators, purely affect quartic gauge vertices: ] [ ] f S,0 O S,0 = f S,0 [(D µ Φ) D ν Φ (D µ Φ) D ν Φ ] [ ] f S,1 O S,1 = f S,1 [(D µ Φ) D µ Φ (D ν Φ) D ν Φ Sensitive Analyses: WZ, WV, same sign WW,... Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 9 / 29

12 WZ Analysis: Overview Motivation Well suited for differential cross section measurement over N jets Publications ZZ cross section too low (at least for Run 1) W ± W swamped by t t W ± W ± only for N jets 2 PhysRevD TeV, 20.3 fb 1, incl. xsec, limits on atgcs, aqgcs PhysLetB TeV, 3.2 fb 1, incl. and diff. xsec ATLAS-CONF TeV, 13.3 fb 1, diff. xsec, limits on atgcs Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 10 / 29

13 WZ Analysis: Backgrounds and Cross Section Backgrounds [Numbers from ATLAS-CONF ] Irreducible: Processes with 3 real leptons ZZ, t tv, tz, VVV WZ Reducible: Processes where at least one lepton is mis-identified Zjets, Zγ 83% t t, Wt, WWjets Red Cross section Measurements - σ fid W ± Z /σth W ± Z Irred Measurement vs. theory expectation Run 1 Run 2, 13.3 fb 1 Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 11 / 29

14 WZ Analysis: Backgrounds and Cross Section Backgrounds [Numbers from ATLAS-CONF ] Irreducible: Processes with 3 real leptons ZZ, t tv, tz, VVV WZ Reducible: Processes where at least one lepton is mis-identified Zjets, Zγ 83% t t, Wt, WWjets Red Cross section Measurements - σ fid W + Z /σfid W Z Irred W + vs. W production Run 1 Run 2, 3.2 fb 1 Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 11 / 29

15 WZ Analysis: Limits ( atgcs: Binned profile-likelihood fit of m WZ T = l pl T + Emiss T ) [ 2 ( l pl x + E miss x ) 2 ( + l pl y + E miss y ) 2 ] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 12 / 29

16 WZ Analysis: Limits ( atgcs: Binned profile-likelihood fit of m WZ T = l pl T + Emiss T ) [ 2 ( l pl x + E miss x ) 2 ( + l pl y + E miss y ) 2 ] aqgcs Unbinned profile-likelihood fit after applying cuts on φ(wz) and p l T [CERN-THESIS ] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 12 / 29

17 WV Analysis: Overview [PhysRevD ] Motivation Looking for semi-hadronic WVjj lνqq jj, V = W, Z BR to quarks larger than to leptons BR(V qq ) BR(W ll ), l = e, µ W % % Z % 6.72 % t t+single t Reconstruction of bosons possible Backgrounds High backgrounds from Wjets, t t Suppressed by choice of aqgc phase space 2 signal regions: resolved, merged merged SR using boosted jets and substructure techniques Diboson Multijet WV Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 13 / Wjets

18 WV Analysis: Limits Limits calculated using binned profile-likelihood fit of m T (WV) ( ) [ 2 ( ) 2 ( m T (WV) = i pi x + E miss x + i pi T + Emiss T Less data observed than expected Observed limit harder than expected one i pi y + E miss y ) 2 ] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 14 / 29

19 ssww Analysis: Overview Motivation: Has by far highest σ EW /σ QCD ratio QCD: No gluon-initiated diagrams at LO Publications by ATLAS [CERN-EP ] and CMS [CMS-PAS-SMP ] Backgrounds: Prompt: At least 2 real leptons WZjj, ZZjj, t tv Non-prompt: At least 1 jet mis-reconstructed as lepton Wjets, t t, single t, Multijet Conversion: Lepton with wrong charge or γ reconstructed as lepton Zjets, Wγ, fully lep. t t [ATL-COM-PHYS ] ssww EW 12.4 ssww QCD Non-prompt Prompt Conversion [CERN-EP ] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 15 / 29

20 ssww Analysis: ATLAS Results Cross Section Measurement: Variables sensitive to EW diagrams: m jj, y jj Observed significance 3.6 σ Expected significance 2.3 σ Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 16 / 29

21 ssww Analysis: ATLAS Results Anomalous Quartic Gauge Couplings: Define dedicated aqgc phase space Profile-likelihood fit of event count for m WW,T > 400 GeV Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 17 / 29

22 ssww Analysis: ATLAS Results Anomalous Quartic Gauge Couplings: Define dedicated aqgc phase space Profile-likelihood fit of event count for m WW,T > 400 GeV ssww and WZ analyses complementary to each other WV analysis most sensitive (higher branching fraction to quarks) Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 17 / 29

23 ssww Analysis: CMS - First Observation ssww EW Event selection differs from ATLAS: Include a lepton centrality cut Hadronic τ veto By far smaller prompt background ssww QCD Prompt Charge and flavour separated channels Conversion 13.5 Non-prompt First Observation of ssww EW Interaction 2-dimensional fit in m jj, m ll Obs. significance 5.5 σ Exp. significance 5.7 σ [CMS-PAS-SMP ] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 18 / 29

24 ssww Analysis: CMS - aqgc Limits Limits extracted using a binned fit of m ll in signal region and WZ control region CMS results ununitarized, ATLAS uses K-matrix CMS and ATLAS results not directly comparable For Run 2 analysis, ATLAS also setting limits on f S,0, f S,1 α 4(5) f S,0(1) [arxiv: ] α 4 = f S,0 v 4 Λ 4 8 α 4 + 2α 5 = f S,1 v 4 Λ 4 8 Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 19 / 29

25 Resonance Models in VBS Main motivation: The rise of amplitudes encoded in anomalous couplings may be the low energy tail of a resonance EFT agc approach not valid any more in this regime [M. Sekulla] Georgi-Machacek Higgs Triplet Model as a charged Higgs model [Nucl. Phys. B (1985)] Analyses: ssww,... Resonances in the Simplified Models extension of EWSB [Simplified Models - Snowmass 2013] Analyses: ssww, osww,... Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 20 / 29

26 Georgi-Machacek Model [Nucl. Phys. B (1985)] Theoretical Approach: Extension of the SM Higgs sector Contains a SM-like Higgs doublet + a Higgs bi-triplet (obeys custodial symmetry SU(2) L SU(2) R, in order to re-stablish ρ-parameter EWPT) 10 Higgs bosons: 2 neutral singlets h 0, H 0 ; triplet (H + 3, H0 3, H 3 ); fiveplet (H ++ 5, H + 5, H0 5, H 5, H 5 ) Fiveplet is fermio-phobic production through LHC 3 of the 8 model parameters relevant for VBS: m h, m H5, sin(θ H ) v 5 /v SM (H 5 VV couplings) UV-complete model no unitarisation needed Sensitive Analyses: ssww, WZ,... Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 21 / 29

27 ssww Analysis: CMS - H ±± limits Upper limits on σ VBS (H ±± ) B(H ±± W ± W ± ) and sin(θ H ) s H in the GM H ±± model extracted using a 2-dimensional fit in m jj m ll Additional fit of the W ± Z contribution in a tri-lepton control region [CMS-PAS-SMP ] Observed and expected limits on the parameters as function of m H5 m H ±± Exclusion of sin(θ H ) > 0.18(0.44) and σ BR > 100(30) fb at m H ±± = 200(1000) GeV Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 22 / 29

28 Simplified Model Resonances [Simplified Models - Snowmass 2013] Theoretical Approach: Set of model independent resonances resulting from an Effective Field Theory approach for high-energy VBS (parametrization of EWSB beyond SM Higgs) Decay into longitudinally polarized vector bosons only: Isospin-spin conservation (custodial symmetry) 5 possible resonances Γ = Γ res g2 64π M3 v 2 Type Isospin I Spin J electric charge Q Width Γres σ f ρ 1 1, 0, + 4 v 2 3 M 2 φ 2 0,, 0, +, ++ 1 t 2 2,, 0, +, Simplified Models not-complete model Resonant VBS amplitudes may rise with energy Violation of unitarity at some energy scale Λ Additional unitarization formalism needed: K/T-matrix unitarization Sensitive Analyses: ssww, osww,... Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 23 / 29

29 osww Analysis: Overview Motivation: Study of W + W jj process and limit setting on the production cross section of all five types of neutral simplified model resonances (g = 2.5, m = GeV) Signal generation with the Whizard event generator [arxiv: ] (including K-matrix unitarization) Event selection: Tagging jets with high jet p T to suppress pile-up effect Use jet η-product, lepton centrality and hadronic recoil in addition to usual VBS -selection ζ = min(η jet 1 ηl 1, ηjet 2 ηl 2 ) softjets JVT jp j T f recoil = p ll T Production cross section of neutral resonances in W + W VBS Event yield in signal region: top contributions Zjets Non-prompt Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 24 / Diboson

30 osww Analysis: Resonance Search No excess observed in data Upper limits on σ VBS (qq Rqq) B(R l + νl ν) Calculated using binned profile likelihood fit in three channels (ee, eµ, µµ) in signal region ρ (vector, isovector) and f (tensor, isoscalar) resonance excluded below 230 GeV and 300 GeV Future aim: binned likelihood fit in transverse mass distribution: [ATLAS-CONF ] M 2 T =(P µ l 1 + P µ l 2 + P µ miss )(P µl 1 + P µl2 + P µmiss ) ( ) 2 = M 2 ll + ( p Tl1 + p Tl2 ) 2 + p Tmiss ( p Tl1 + p Tl2 + p Tmiss ) 2 Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 25 / 29

31 Mass reconstruction: X WW lνlν The two neutrino problem in WW leptonic final states: Invariant mass: M 2 X = M 2 WW = P µ WW P µww = E 2 p 2 P µ WW : composite four-momentum of W± W ± system Problem: P µ WW = Pµ l 1 + P µ l 2 + Q µ ν 1 + Q µ ν 2 Separate momenta of neutrinos unknown q ν1, q ν2 6 degrees of freedom p Tmiss Measurement: 2 constraints p Tmiss = q Tνi Solution: Perform minimization over free parameters [arxiv: ] Results in smallest resonance mass consistent with measured p Tmiss Allows for concrete information from every event Lower mass bound on resonance mass: M X M event WW (if true event topology is chosen) Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 26 / 29

32 Mass reconstruction: Transverse projections Projection of transverse masses is ambiguous due to energy component in 4-vectors: Four-momentum: P µ (E, p x, p y, p z ) (2+1)-momentum: p α = (e, p x, p y ) M 0: mass-preserving projection e = Transverse mass: M 2 + p 2T = E 2 p 2 z p α p α = M 2 M = 0: massless projection e o = E sin θ o 2 2 M 2 1 = (p + /p ) α (p + /p ) α M 2 o1 = (p o + /p o ) α (p o + /p o ) α Order of operations (summation of particles, projection) does matter for energy component of P µ : M 2 1 = (p + /p ) α (p + /p ) α M 2 1 = (Pµ + /P µ ) (P µ + /P µ ) Projection discards information early projection weakens bound Additionally discarding mass information (M o1 ) weakens bound even more = M 1 M 1 = M o1 M 1o Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 27 / 29

33 ssww Analysis: Mass Reconstruction Studies Study at s = 8 TeV with spin-0 and spin-2 resonance [CERN-THESIS ] MC Whizard with K-matrix unitarization Use mass reconstruction variables for under-constraint system ( 2 neutrinos vs E miss T measurement problem) m 2 1 (p Tl1, p Tl2, p Tmiss ) = ( M 2 ll + ( p Tl1 + p Tl2 )2 + p Tmiss ) 2 ( p Tl1 + p Tl2 + p Tmiss ) 2 true invariant mass m WW reconstructed mass m 1 narrow spin-2 resonance (after parton shower with E Tmiss smearing) fb 20 GeV dσ true dm WW ± ± W W jj EW = 1 70 GeV dn 1T dm WW t, m=750 GeV, g=2.5 ± ± W W jj EW best significance interval 1 L = 20 fb, s = 8 TeV 4 10 t, m=500 GeV, g=2.5 t, m=600 GeV, g=2.5 t, m=750 GeV, g=2.5 t, m=800 GeV, g= t, m=1000 GeV, g=2.5 t, m=1200 GeV, g= true m WW [GeV] m1t WW [GeV] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak true VBS invariant Measurements mass m WW 28 / 29

34 Summary Several BSM models are being discussed in experimental publications VBS analyses set limits on complete and simplified models, EFT approaches So far no hint for BSM physics found in data VSB signature in experiments challenging Non-trivial to separate QCD background from electroweak signal Pile-up rejection for tagging jets Specific variables sensitive to VBS topology First observation of a process containing VBS in ssww Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 29 / 29

35 Backup Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 1 / 12

36 EW and QCD Diagrams in WW Scattering Up to now only resonant electroweak diagramms: O(α 6 ew) : Not gauge invariantly separable from resonant diagrams: O(α 6 ew) : + + QCD mediated diagrams yielding same final state: O(α 4 ewα 2 s) : W ± W ± has highest EW/QCD ratio [CERN-EP ] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 2 / 12

37 WZ Analysis: Limits 1 atgcs 8TeV aqgcs c i λ Z, g Z 1, κz α 4(5) f S,0(1) α 4(5) = f S,0(1) Λ 4 v 4 16 c WWW Λ 2 = 2 3g 2 M 2 λ Z W c W Λ 2 = 2 M 2 g Z 1 Z c B Λ 2 = 2 M 2 ( κ γ κ Z ) Z Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 3 / 12

38 WZ Analysis: Limits 2 Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 4 / 12

39 ssww Analysis ATLAS: Cutflow Table [CERN-EP ] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 5 / 12

40 ssww Analysis ATLAS: Run 2 Changes Experimental Aspects Lumi: Distance between bunches halved: 50 ns to 25 ns Increased instantaneous lumi s: 8 TeV to 13 TeV σ th,ew : Tripled from 1 to 1 (const. lumi) 12.5 d 4.4 d Theoretical Predictions Run 1: σ th,ew < σ obs,ew Large negative NLO EW corrections Decreases σ th,ew But: σ th,qcd should increase at NNLO gg initiated production possible Decreases σ obs,ew Might cancel, up to now unknown [A. Denner et. al.] Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 6 / 12

41 osww Analysis: Event Selection Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 7 / 12

42 Heavy resonances in VBS new physics in EWSB is introduced via an effective field theory approach effective chiral Lagrangian as perturbative expansion in some new physics energy scale Λ SM evolves as low-energy limit (= leading term) of the new theory model-independent parametrization of high-energy VBS add new degrees of freedom for any possible heavy resonance L = L SM + resonances effective theory new resonant scattering amplitudes rise with energy break unitarity at some energy E > Λ add unitarization formalism manually: K-matrix unitarization = Monte Carlo studies with Whizard event generator (features generic effective theory with resonances and K-matrix unitarization) (arxiv: ) L r Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 8 / 12

43 Minimization Example: M 1T M 2 1 = min { } M 2 p 1 z miss M 2 1 = ( M 2 ll + p2 1T q + 2 1T + q 2 1z + q 2T 2 + q 2z 2 2 ) 2 (q 1z + q 2z) 2 4 Contraints: ( p T + p Tmiss ) 2 p Tmiss = q Ti ( ) m 2 w = 2 p i q 2 it + q 2 iz p it q it p iz q iz Free choices: total z-component of invisible particles p miss z minimization: equal rapidities of visible and invisible system: y = y miss frame-independence of y y = 0 p z = 0 invariant mass of invisible particle collection (ν 1, ν 2 ) /M: ansatz /M = χ otherwise minimization sets it to 0 Problems: W mass constraint leads to quadratic equation in any constraining parameter (same issue as for p z reconstruction in W mass measurement) Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 9 / 12

44 Mass formulas ( ) 2 m 2 1 (p Tl1, p Tl2, p Tmiss ) = M 2 ll + p2 1T + p Tmiss ( p 1T + p Tmiss) 2 m 2 o1(p Tl1, p Tl2, p Tmiss ) = ( p Tl1 + p Tl2 + p Tmiss ) 2 ( p 1T + p Tmiss ) 2 = m 2 eff ( p 1T + p Tmiss ) 2 = m 2 1(massless leptons) m 2 1o(p Tl1, p Tl2, p Tmiss ) = ( p Tl1 + p Tl2 + p Tmiss ) 2 ( p 1T + p Tmiss ) 2 m 2 vec(p l1, p l2, p Tmiss ) = ( p l1 + p l2 + p Tmiss ) 2 ( p Tl1 + p Tl2 + p Tmiss ) 2 ( p zl1 + p zl2 ) 2 m 2 eff (p Tl1, p Tl2, p Tmiss ) = ( p Tl1 + p Tl2 + p Tmiss ) 2 m 2 vis(p l1, p l2 ) = M 2 ll M ll invariant mass of dilepton system p 1 vector sum of lepton momenta p l1, p l2 Iltzsche,Todt (TU Dresden) p 1T vector Results sumonofbsm lepton limitstransverse in Electroweak momenta VBS Measurements p Tl1, p Tl2 10 / 12

45 Collinear mass m col assumption: decay products of W are emitted collinear possibility to reconstruct the momentum of both neutrinos compute fraction x i of W momentum carried away from its visible decay product (lepton) (use momentum conservation in transverse plane) only 0 < x i < 1 are physical m WWcol cannot always be calculated m 2 WWcol =(p W1 + p W1 ) 2 m 2 WWcol =2 (m 2 W + p W1 p W2 ) m 2 WWcol =2 m 2 W + p W T,i = pl T,i x i m 2 W + ( pl1 T x 1 ) 2 m 2 W + ( pl2 T x 2 ) 2 pl1 T p l1 T x 1 x 2 m WWcol fomular holds only for onshell W s which is not true in all the cases Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 11 / 12

46 More mass variables Traditional transverse mass variables: m vis invariant mass of lepton pair (i.e. m ll ) m eff invariant mass of lepton pair + E miss (only transverse plane (hep-ph/ )) m 2 eff (p Tl1, p Tl2, p Tmiss ) = ( p Tl1 + p Tl2 + p Tmiss ) 2 = m 2 o1 + ( p 1T + p Tmiss ) 2 m vec invariant mass of lepton pair + E miss T m 2 vec(p l1, p l2, p Tmiss ) = ( p l1 + p l2 + p Tmiss ) 2 T (with z-component of leptons) ( p Tl1 + p Tl2 + p Tmiss ) 2 ( p zl1 + p zl2 ) 2 m col collinear approach (R.K. Ellis et al., Nucl. Phys. B 297, 221 (1988)) Iltzsche,Todt (TU Dresden) Results on BSM limits in Electroweak VBS Measurements 12 / 12