Mass Reconstruction Techniques for Resonances in W ± W ± Scattering

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1 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

2 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: ) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 1 / 11

3 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: ) 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

4 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 f ρ 1 1, 0, + 4 v 2 3 M 2 φ 2 0,, 0, +, ++ 1 t 2 2,, 0, +, 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

5 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 f ρ 1 1, 0, + 4 v 2 3 M 2 φ 2 0,, 0, +, ++ 1 t 2 2,, 0, +, 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

6 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: ) 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

7 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

8 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: , arxiv: ) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 5 / 11

9 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

10 Comparison of resonance types: true m WW MC study with event generator WHIZARD and K-matrix unitarisation at s = 8 TeV (CERN-THESIS ) 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= Φ resonance (broader) m {500, 750, 00} GeV g = 2.5 m WW 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

11 Comparison of mass variables: reconstructed m WW fb 30 GeV signal dσ reco dm WW 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 Φ, m=500 GeV, g=2.5 mass var. w/o bound m vis m eff m vec m col reco m WW [GeV] 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

12 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 t, m=500 GeV, g=2.5 ± W W ± jj EW best significance interval 1 L = 20 fb, s = 8 TeV m1t WW [GeV] Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 9 / 11

13 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 resonance mass [GeV] 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

14 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

15 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

16 Backup Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11

17 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: ) L r Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11

18 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: (Simplified Models - Snowmass 2013) Stefanie Todt Institut fuer Kern- und Teilchenphysik, TU Dresden Mass Reconstruction Techniques for Resonances in W ± W ± Scattering 12 / 11

19 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

20 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

21 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

22 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

23 Comparison of mass variables: reconstructed m WW fb 40 GeV signal dσ reco dm WW 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 reco m WW [GeV] fb 40 GeV signal dσ reco dm WW 3 20 t, m=500 GeV, g= mass var. w/o bound m vis m eff m vec m col 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

24 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 reco true m WW m WW [GeV] 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

25 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 reco true m WW m WW [GeV] 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

26 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 mass bound variables m o1 m 1o m 1T σ reco reco/<m > mww WW mass bound variables m o1 m 1o m 1T 0.7 m 1Tbound 0.7 m 1Tbound Φ resonance, g= t resonance, g= resonance mass [GeV] 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

27 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 o 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

28 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

Results on BSM limits in Electroweak VBS Measurements

Results on BSM limits in Electroweak VBS Measurements Franziska Iltzsche, Stefanie Todt TU Dresden Seminar @ Universidad Complutense Madrid May 30th, 2017 supported by Vector Boson Scattering in the SM