Electroweak Symmetry Breaking without Higgs Boson. University College London
Outline The Electroweak Chiral Langrangian (EWChL): Why and How. Application of the EWChL in the V L V L scattering to probe new physics. Few scenarios for the new physics. Performance studies of the ATLAS Detector at the LHC. W L W L with no resonances (Continuum) by J.M. Butterworth, P. Sherwood, S. Stefanidis. W L W L with resonances by S.E. Allwood, J.M. Butterworth, B.E. Cox. W L Z L with resonances by G. Azuelos, P-A. Delsart, J. Idárraga, A. Myagkov. Summary.
Introduction Standard Model: A very good model satisfying theorists and experimentalists. It explains the Electroweak Symmetry Breaking(EWSB) by introducing the Higgs boson. Higgs mass limit (95% CL) GeV 7 6 5 4 3 2 snowmass 21 upper bound: global fit to EW data lower bound: direct searches 1995 1996 1997 1998 1999 2 21 year However, any assumptions and any mass limits are model dependent. Enhanced production of longitudinal vector boson pairs (V L V L ) is one of the most characteristic signals of the new physics.
The Electroweak Chiral Lagrangian(EWChL) (Appelquist et al., Phys.Rev.D22,2(198)) Describes the low energy effects of different strongly interacting models of the EWSB sector. The differences among underlying theories appear through the values of the effective chiral couplings. It includes operators up to order of s 2 ( E 4 ). The analytical complete form can be found in Dobado et al., Phys.Rev.D62,5511, but terms of major importance are: L EWCh = L (2) + L (4) +... = u2 4 Tr{D µud µ U } + α 4 ( Tr{Dµ UD µ U } ) 2 + α5 ( Tr{Dµ UD ν U } ) 2 (1) where the SU(2) L U(1)Y covariant derivative of U is defined as: D µ U µ U + ig τα 2 W α µ U ig U τ3 2 B µ (2) where τ α (α = 1, 2, 3) are the Pauli matrices, ω are the three Goldstone bosons and u = 246 GeV. The α 4, α 5 are expected to be in the range [-.1,.1] (Belyaev et al., Phys.Rev.D59,1522). Different choices for the magnitude and the sign of α 4 and α 5 would correspond to different choices for the underlying (unknown) theory.
Scattering Amplitudes For the V a L V b L V c L V d L in the weak isospin space (V i L = W + L, W L, Zo L ): M(V a LV b L V c LV d L) A(s, t, u)δ ab δ cd + A(t, s, u)δ ac δ bd + A(u, t, s)δ ad δ bc (3) where the key amplitude A(s, t, u) is: A(s, t, u) = s u + 1 ( 2α4 s 2 + α 2 4πu 4 5 (t 2 + u 2 ) ) + + 1 ( t6 ( 16π 2 u (s + 2t) log t ) u6 ( 4 µ (s + 2u) log uµ ) ( s2 2 2 2 log sµ )) 2 Precise measurement of the V L V L V L V L scattering cross-section would allow the extraction of the α 4 and α 5 parameters. (4)
Unitarization The usual EWChL approach doesn t respect unitarity. Unitarity is restored by applying different unitarization protocols, for example: Inverse Amplitude Method (Padé), N/D protocol etc. Unitarization procedure Resonances. The position and the nature of the resonances depend strongly upon the unitarisation procedure. (see Butterworth et al., Phys.Rev.D65,9614 for comparison between the Padé and the N/D protocols.) Using the Padé protocol, we obtain the following mass and width of the resonances: M 2 V = u 2 4(α 4 2α 5 ) + 1 144π 2, Γ V = M3 V 96πu 2 (5) MS 2 = 12u 2 16(11α 5 + 7α 4 ) + 1, 48π 2 Γ S = M3 S 16πu 2 (6) For equal masses, scalar resonances would be 6 times wider than vector resonances.
Few Scenarios α 4.1.5 Vector Resonance Scalar Resonance TC B E D A SM Forbidden Vector & Scalar Resonance C (fb/gev) dσ/dm WW.3.25.2.15 Vector & Scalar Scalar.1 -.5.5 Continuum Vector -.1 -.1 -.5.5.1 2 4 6 8 12 14 16 18 2 α From J.M.Butterworth, B.E.Cox and J.R.Forshaw(Phys.Rev.D65, 9614) 5 M WW (GeV) Scenario α 4 α 5 Resonance Mass (GeV) Scalar(A)..3 989.8 Vector(B).2 -.3 136.3 Scalar + Vector (C).8. 89.6 + 136.3 Continuum (D).. NA PYTHIA has been modified to include the EWChL and to produce the resonances for different parameters.
Signal and Background Processes at LHC - Data Samples For all processes: PYTHIA was used as a generator. Rome Tuning for the Underlying Events. MRST21E (central value) as PDF. Allowed all the decays of the Ws. Q g Q ± W q g g g t t + W Q q Signal: Continuum ; W L ± W L ± W L ± W L ± σ = 44 fb. tt Background: ( lνjj). Q Q W + ± W - W ˆp > 3 GeV σ = 1564 fb. q q + W ± W W+jets Background: ˆp > 25 GeV σ = 626 fb. The generated events were then simulated using the Fast Simulation package for the ATLAS Detector.
Initial Distributions: The Leptonic sector -2 Continuum signal tt background w+jets background.6.5.4.3-3.2-4 3 35 4 45 5 55 6 65 7 Lepton P (GeV) T.1-5 -4-3 -2 1 2 3 4 5 Lepton η -2-2 -3-3 -4 3 35 4 45 5 55 6 65 7 Missing E (GeV) T 3 4 5 6 7 8 9 Leptonic W P (GeV) T Applied Cuts: P W lept T > 32 GeV
-2-3 -2-3 -4 Lept W P T > 32 GeV Continuum signal tt background w+jets background 3 4 5 6 7 8 9 Hadronic W P T (GeV) -5 5 15 2 25 Hadronic W Mass (GeV) Important Keys: Initial Distributions: The Hadronic Sector.8.7.6.5.4.3.2.1.16.14.12.1.8.6.4.2-5 -4-3 -2 1 2 3 4 5 Hadronic W η.2.4.6.8 1 1.2 1.4 1.6 1.8 2 Log(Hadronic W P y ) T Reconstruct the Hadronic W as 1 jet since the Ws are highly boosted. Subjet Analysis with the k (see hep-ph/222) For the leading jet, re-run the k algorithm to find its structure. P T y : scale at which the jet is resolved into 2 subjets O(M W ) Applied Cuts: P W had T η Whad < 2 > 32 GeV 66 GeV < M Whad < 2 GeV 1.55 < log(p T y) < 2
Characteristics of the Hadronic environment After applying the kinematics cuts, we investigate the features of the hadronic environment:.1.8.6.4 Continuum signal tt background w+jets background.14.12.1.8.6.4.2.2 2 3 4 5 6 7 8 9 + jet Invariant Mass (GeV) W lep 2 3 4 5 6 7 8 9 + jet Invariant Mass (GeV) W had.12.1.8.6 1-2.4-3.2-4 -3-2 1 2 3 4 Tag Jets η -4 2 4 6 8 12 14 16 18 2 22 24 WW + tag jets P (GeV) 1-2 -3.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Number of mini-jets Applied Cuts: Top Veto: 13 GeV < M W+jet < 24 GeV Tag Jets: P T > 2 GeV ; E > 3 GeV ; η > 2. Events / GeV for 3 fb 3 2.5 2 1.5 1.5 6 8 12 14 16 18 2 22 24 W lep W had Invariant Mass (GeV) Hard Scatter P T : P WW+tagJets T MiniJets: Number of minijets < 1 < 5 GeV
Results: Continuum Spectrum Cross-section σ (fb) Signal t t W+jets Significance for L = 3 fb 1 Generated 44 1564 626.88 Cuts P T Leptonic W 3.31±.1 422.81±1.46 2889.37±7.58.33 P T Hadronic W 2.59±.1 191.96±.99 1816.92±6.7.33 η Hadronic W 2.59±.1 191.96±.99 1816.92±6.7.33 Mass Hadronic W 2.4±.1 88.8±.68 29.29±2.9.66 Y Scale 1.74±.1 72.29±.61 113.95±1.54.71 Top Veto 1.57±.1 4.±.15 53.13±1.5 1.15 P T, E, η Tag Jets.45±.1.5±.2.38±.9 3.73 P T hard scatter.44±.1.3±.1.21±.7 4.93 Number of Mini-jets.44±.1.3±.1.21±.7 4.93 Only the average value used. Although statistical errors for the background processes must be reduced, other studies give the same order for the average value.
Results: Other Scenarios This report is for W L W L scattering using the EWChL parameters for different scenarios which include Scalar, Vector and Scalar+Vector Resonances (work done by S.E. Allwood). (a) (b) Events per GeV for 3 fb 8 6 4 Scalar (A) Vector (B) W+jets t t Events per GeV for 3 fb 8 6 4 Double Resonance (D) Continuum (E) W+jets t t 2 2 6 8 12 14 16 18 2 22 24 M WW /GeV 6 8 12 14 16 18 2 22 24 M WW /GeV Final cross-section σ (fb) Signal t t W+jets Significance for L = 3 fb 1 Scenario 1 TeV Scalar Resonance 1.5.4.28.17 1.4 TeV Vector Resonance.7.4.28 6.78 Double Resonance 1.33.4.28 12.88 Continuum.44.3.21 4.93
Other work within ATLAS A complete list of notes on the Dynamical EWSB can be found under the Exotics Group at: http://atlas.web.cern.ch/atlas/groups/physics/exotics/ This report is from: G.Azuelos,P-A.Delsart,J.Idárraga (Montreal) and A.Myagkov (Protvino): Study of the EWChL and the higgsless (see Csaki et al., Phys.Rev.Lett.92,182) models. Full simulation/reconstruction under the DC2 production. Signal Processes: qqw Z qqjjll ; qqw Z qqlνll ; qqw Z qqlνjj Background Processes: SM qqwz production ; t t (MC@NLO) ; W+4jets (ALPGEN) 4.5 4 3.5 3 2.5 2 SIGNAL+SMbg TTbg: events in peak region SMbg: 4 events in peak region W4jetsbg: gone after cuts SIGNAL: 14 events in peak region EWChL model Preliminary Gen M Res ~ 115 GeV Resonance peak at resolution S B 7.18 97 GeV 76 GeV For both models, qqwz qqjjll can provide discovery with fb 1. qqwz qqlνll is very clean but with low cross section. Must wait till 3 fb 1. 1.5 1.5 qqwz qqlνjj can also give good sensitivity with fb 1. 2 4 6 8 12 Z(ll)W(jj) Mass [GeV]
Summary The motivation and the functionality of the EWChL have been presented for the V L V L V L V L scattering. Detailed analysis using the Continuum spectrum for the W L W L scattering results in a 5σ significance, for the most pessimistic scenario. Recent analyses are based on both the full and fast simulation of the ATLAS Detector. Though restricted by the statistics, we are confident that ATLAS will be able to see new signatures even with 3 fb 1 of data. ACKNOWLEDGMENT: The current and previous works have been generously supported by: The Department of Physics & Astronomy and the HEP Group at UCL. The Particle Physics and Astronomy Research Council (PPARC). The Alexander S. Onassis Foundation.