Mass Reconstruction Techniques for Resonances in W ± W ± Scattering Stefanie Todt (stefanie.todt@tu-dresden.de) Institut fuer Kern- und Teilchenphysik, TU Dresden DPG Wuppertal March 11, 2015 bluu
Vector boson scattering at the LHC longitudinal scattering of weak bosons directly connected to mechanism of electroweak symmetry breaking (EWSB) sensitive to BSM physics: aqgcs, heavy resonances weak-boson self-couplings Higgs contributions + include non-vbs and non-resonant diagrams SM-EW VVjj process channel of like-charge W ± W ± scattering favourable in the context of the LHC experiments first evidence for Vector Boson Scattering (VBS) in the processes W ± W ± W ± W ± (arxiv:1405.6241) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 1 / 11
Vector boson scattering at the LHC longitudinal scattering of weak bosons directly connected to mechanism of electroweak symmetry breaking (EWSB) sensitive to BSM physics: aqgcs, heavy resonances weak-boson self-couplings Higgs contributions + include non-vbs and non-resonant diagrams SM-EW VVjj process first evidence for Vector Boson Scattering (VBS) in the processes W ± W ± W ± W ± (arxiv:1405.6241) see talk from Ulrike Schnoor T 67.4 Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 1 / 11
mass m and coupling g of resonances free parameters variation of resonance mass m [500 GeV, 1200 GeV] fixed coupling g = 2.5 (g [0, 2.5]) blub blub Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 2 / 11 Heavy resonances in VBS new physics in EWSB is introduced via an effective field theory approach isospin conservation in high energy limit five possible resonances: type weak isospin I spin J electric charge Q width Γ res /Γ 0 σ 0 0 0 6 f 0 2 0 1 5 ρ 1 1, 0, + 4 v 2 3 M 2 φ 2 0,, 0, +, ++ 1 t 2 2,, 0, +, ++ 1 30 partial widths Γ 0 for resonances decaying into longitudinally polarized vector bosons: Γ 0 = g2 64π m3 v 2
Heavy resonances in VBS W ± W ± jj new physics in EWSB is introduced via an effective field theory approach isospin conservation in high energy limit five possible resonances: type weak isospin I spin J electric charge Q width Γ res /Γ 0 σ 0 0 0 6 f 0 2 0 1 5 ρ 1 1, 0, + 4 v 2 3 M 2 φ 2 0,, 0, +, ++ 1 t 2 2,, 0, +, ++ 1 30 resonant scattering of two like-charge W ± bosons resonant scattering in s-channel for doubly charged isotensor resonances: broad scalar φ resonance or narrow tensor t resonance Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 2 / 11
Mass reconstruction: X ±± W ± W ± l ± l ± νν Invariant mass from relativity: mx 2 = mww 2 = P µ WW P µ WW P µ WW : composite four-momentum of W± W ± system Problem: P µ WW = Pµ l 1 + P µ l 2 + P µ ν 1 + P 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:15.2977) find smallest resonance mass consistent with measured p Tmiss allows for concrete information from every event lower mass bound on resonance mass: m X mww event (if true event topology is chosen) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 3 / 11
Mass reconstruction: Transverse projections Calculation of transverse masses define projected (2+1)-momenta analogous to four-momenta: four momentum: P µ = (E, p x, p y, p z ) (2+1)-momentum: p α = (e, p x, p y ) Projection of energy component: mass-preserving projection e = m 2 + p 2 T = E 2 p 2 z p α p α = m 2 massless projection e o = p T p α o p oα = 0wwlwwwwwwwwwww Transverse mass: m 2 1 = (p + q ) α (p + q ) α m 2 o1 = (p o + q o ) α (p o + q o ) α Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 4 / 11
Mass variables Order of operations (summation of particles, projection) does matter for energy component of P µ : m 2 1 = (p + q ) α (p + q ) α m 2 1 = (P µ + Q µ ) (P µ + Q µ ) projection discards information early projection weakens bound additionally discard mass information (m o1 ) weakens bound even more = m 1 m 1 = m o1 m 1o Additional constraint for heavy resonances: one or both W ± bosons are produced on m W mass shell m 1 Star (for WW ) and m 1 bound (for both W on-shell) (arxiv:18.3468, arxiv:11.2452) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 5 / 11
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 T 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 (only transverse plane (hep-ph/96544)) (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)) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 6 / 11
Comparison of resonance types: true m WW MC study with event generator WHIZARD and K-matrix unitarisation at s = 8 TeV (CERN-THESIS-2015-018) cross section / GeV 2 3 W±W±jj EW cross section / GeV 2 3 W±W±jj EW Φ, m=750, g=2.5 t, m=1200, g=2.5 4 Φ, m=500, g=2.5 4 t, m=00, g=2.5 t, m=750, g=2.5 Φ, m=00, g=2.5 t, m=500, g=2.5 5 0 200 400 600 800 00 1200 1400 Φ resonance (broader) m {500, 750, 00} GeV g = 2.5 m WW 5 0 200 400 600 800 00 1200 1400 t resonance (narrow) m {500, 750, 00, 1200} GeV g = 2.5 m WW truth m WW : invariant mass of the W ± W ± system at parton level (w/o parton shower) reconstructed with true (associated) neutrinos (i.e. m l ± ν l l ± ν l ) reference: SM-EW m WW distribution (in red) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 7 / 11
Comparison of mass variables: reconstructed m WW fb 30 GeV signal dσ reco dm WW 60 50 40 30 3 Φ resonance, m = 500 GeV, Γ = 64 GeV, g = 2.5 mass bound variables mass variables without mass bound Φ, m=500 GeV, g=2.5 mass bound variables m o1 m 1o m 1T m 1Tstar m 1Tbound fb 30 GeV signal dσ reco dm WW 50 40 30 3 Φ, m=500 GeV, g=2.5 mass var. w/o bound m vis m eff m vec m col 20 20 0 0 200 300 400 500 600 700 800 reco m WW [GeV] 0 0 200 300 400 500 600 700 800 reco m WW [GeV] m 1, m 1 bound and m o1 drop around resonance mass saturated lower mass bound (respect generic width of resonance) m 1 bound shifted to higher invariant masses with respect to m 1 m eff, m vec, m col fail to give lower mass bound m vis : unsaturated lower mass bound due to minimal information input (no p Tmiss ) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 8 / 11
Discovery potential events at particle level with simulation of detector resolution for E miss T Signal: pp l ± νl ± νjj final state with resonance Background: only SM-EW pp l ± νl ± νjj final state (no contribution from W ± W ± -QCD, WZ) optimize for best statistical significance S B in reconstructed mass window m WW discovery potential 1 60 GeV dn 1T dm WW 1 1 2 t, m=500 GeV, g=2.5 ± W W ± jj EW best significance interval 1 L = 20 fb, s = 8 TeV 3 4 5 0 200 400 600 800 00 1200 1400 m1t WW [GeV] Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 9 / 11
Comparison of Discovery potential: Mass variables Φ resonance, g = 2.5 t resonance, g = 2.5 S discovery potential B 2 Φ resonance, g=2.5 mass bound variables m o1 m 1T m 1Tbound mass var. w/o bound m vec S discovery potential B t resonance, g=2.5 mass bound variables m 1T m 1Tbound mass var. w/o bound m eff m vec 500 600 700 800 900 00 10 1200 resonance mass [GeV] 500 600 700 800 900 00 10 1200 resonance mass [GeV] Best mass variable in terms of discovery potential: for broader resonance (Φ): m o1 (best background rejection) for narrow resonance (t): m 1 bound or m 1 (most kinematic information) only small differences between the different mass variables for different coupling parameters of the resonances Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering / 11
Summary modelling of heavy resonances in W ± W ± scattering with WHIZARD (EFT approach with K-matrix unitarisation) study of different resonances and mass reconstruction variables study discovery potential against SM-EW pp l ± l ± νν background best mass variables: for broader resonance (Φ): m o1 for narrow resonance (t): m 1 bound and m 1 Thanks for your attention! Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 11 / 11
Summary modelling of heavy resonances in W ± W ± scattering with WHIZARD (EFT approach with K-matrix unitarisation) study of different resonances and mass reconstruction variables study discovery potential against SM-EW pp l ± l ± νν background best mass variables: for broader resonance (Φ): m o1 for narrow resonance (t): m 1 bound and m 1 Thanks for your attention! Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 11 / 11
Backup Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
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 unitarisation formalism manually: K-matrix unitarisation = Monte Carlo studies with Whizard event generator (features generic effective theory with resonances and K-matrix unitarisation) (arxiv:0806.4145) L r Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Resonances in W ± W ± W ± W ± need to be of electrical charge ++ or Φ: scalar (Spin 0), isotensor (Isospin 2) t: tensor (Spin 2), isotensor (Isospin 2) arxiv:1307.8170 (Simplified Models - Snowmass 2013) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
W ± W ± jj l ± l ± ννjj final state Signal process: scalar φ resonance tensor t resonance with or same kinematic topology as VBS two energetic forward jets (initial quarks radiating off Ws) both W bosons decay leptonically two same-sign central leptons missing p T from 2 neutrinos in the final state l ± (1) ν tagging jet (4) y tagging jet (3) l ± (2) ν Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Minimization Example: M 1T { } M1 2 = min M 2 1 p z miss ( ( M 2 1 = Mll 2 + p2 1T + q1t2 + q 1z2 + ) ) 2 2 q 2T2 + q 2 2z (q1z + q 2z ) 2 4 Contraints: ( p T + p Tmiss ) 2 p Tmiss = q Ti mw 2 = 2 ( p i q ) it2 + q iz2 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) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Mass formulas ( ) 2 m1 (p 2 Tl1, p Tl2, p Tmiss ) = Mll 2 + 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 p 1T vector sum of lepton transverse momenta p Tl1, p Tl2 Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
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 p W T,i = pl T,i x i m 2 WWcol =(p W1 + p W1 ) 2 mwwcol 2 =2 (mw 2 + p W1 p W2 ) mwwcol 2 =2 m W 2 + 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 Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Comparison of mass variables: reconstructed m WW fb 40 GeV signal dσ reco dm WW 25 20 15 3 5 t resonance, m = 500 GeV, Γ = 2 GeV, g = 2.5 mass bound variables mass variables without mass bound t, m=500 GeV, g=2.5 mass bound variables m o1 m 1o m 1T m 1Tstar m 1Tbound 0 0 0 200 300 400 500 600 700 800 reco m WW [GeV] fb 40 GeV signal dσ reco dm WW 3 20 t, m=500 GeV, g=2.5 18 16 14 12 8 6 4 2 mass var. w/o bound m vis m eff m vec m col 0 0 0 200 300 400 500 600 700 800 reco m WW [GeV] φ and t resonance: maxima shifted to higher m WW for φ, difference in shape (spin dependence of mass variables) same observations for higher resonance masses and lower coupling parameters Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Comparison of mass variables: m WW,reco m WW,true Φ resonance, m = 500 GeV, Γ = 64 GeV, g = 2.5 mass bound variables mass variables without mass bound fb 18 GeV true ) m WW signal dσ reco 2 WW 1 Φ, m=500 GeV, g=2.5 mass bound variables m o1 m 1o m 1T m 1Tstar m 1Tbound fb 18 GeV true ) m WW signal dσ reco WW 1 Φ, m=500 GeV, g=2.5 2 d(m mass var. w/o bound m vis m eff m vec m col d(m 3 3 200 0 0 0 200 reco true m WW m WW [GeV] 200 0 0 0 200 reco true m WW m WW [GeV] difference between reconstructed and true m WW : clear distinction between mass bound variables and other mass variables note: not resonance mass - t resonance mtconstr are all those events in the peak here, were mass was overestimated because there never were two onshell W Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Comparison of mass variables: m WW,reco m WW,true t resonance, m = 500 GeV, Γ = 2 GeV, g = 2.5 mass bound variables mass variables without mass bound fb 30 GeV true ) m WW signal dσ reco 2 WW t, m=500 GeV, g=2.5 mass bound variables m o1 m 1o m 1T m 1Tstar m 1Tbound fb 30 GeV true ) m WW signal dσ reco 2 WW t, m=500 GeV, g=2.5 d(m mass var. w/o bound m vis m eff m vec m col d(m 3 3 200 0 0 0 200 reco true m WW m WW [GeV] 200 0 0 0 200 reco true m WW m WW [GeV] difference between reconstructed and true m WW : clear distinction between mass bound variables and other mass variables note: not resonance mass - t resonance mtconstr are all those events in the peak here, were mass was overestimated because there never were two onshell W Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Comparison of mass variables: relative width σ m reco WW /<mreco WW > Φ resonance, g = 2.5 t resonance, g = 2.5 σ reco reco/<m > mww WW 1.0 0.9 0.8 mass bound variables m o1 m 1o m 1T σ reco reco/<m > mww WW 1.0 0.9 0.8 mass bound variables m o1 m 1o m 1T 0.7 m 1Tbound 0.7 m 1Tbound 0.6 0.6 0.5 0.5 0.4 0.4 0.3 Φ resonance, g=2.5 0.3 t resonance, g=2.5 0.2 500 600 700 800 900 00 10 1200 resonance mass [GeV] 0.2 500 600 700 800 900 00 10 1200 resonance mass [GeV] for both resonance types: m 1 and m 1 bound best resolution especially for high resonance masses statistical errors are too small to be visible mass resolution 25 35% for both resonance types Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Comparison of Discovery potential: Resonances g = 2.5, m o1 discovery potential S B 2 Φ resonance, m=500 GeV t resonance, m=500 GeV m o1 1 0.5 1.0 1.5 2.0 2.5 resonance coupling φ resonance has higher discovery potential than t resonance due to higher total cross section Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11
Object and event selection criteria Leptons p T > 30 GeV η < 2.5 Jets p T > 30 GeV η < 4.5 Event selection criteria exactly two charged dressed leptons, a minimum of two jets, both leptons have the same electric charge, both leptons have to have a minimum distance of R 0.3 to any reconstructed jet in the event and to each other. Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11