Polarized Weak Bosons at the LHC Giovanni Pelliccioli Universit at - PowerPoint PPT Presentation

Polarized Weak Bosons at the LHC Giovanni Pelliccioli Universit¨ at W¨ urzburg, Institut f¨ ur Theoretische Physik und Astrophysik Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 1/16

Outline 1.................. Motivations 2.................. Theory & Monte Carlo 3.................. Phenomenology 4.................. Conclusions Based on works performed in collaboration with A. Ballestrero, E. Maina (INFN, Uni. Torino) and A. Denner (Uni. W¨ urzburg). Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 2/16

1. Motivations Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 3/16

LHC physics and polarizations • LHC luminosities accumulated in Run 2 ( ≈ 150 fb − 1 ) at 13 TeV CoM energy and foreseen in next runs (300 fb − 1 in Run 3, and 3000 fb − 1 in High-Lumi) − → precise measurements of electroweak bosons production processes. • Polarization observables for W / Z non trivial to disentangle (unstable bosons!), but: 1. are important probes of Standard Model (SM) gauge and Higgs sectors 2. and may provide discrimination power between SM and beyond-SM physics. • ATLAS measured polarizations in W ± Z production [ATLAS 1902.05759]. More measurements expected in diboson and vector boson scattering (VBS). • VBS plays a crucial role: unitarity cancellations in on-shell longitudinal scattering W + W + W + W + W + W + W + W + h W W Z Z Z Z Z Z Z Z − s + s v 2 (1 − cos θ ) v 2 (1 − cos θ ) Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 4/16

Longitudinal vector boson scattering • Longitudinal cross section depends on the specific realization of ElectroWeak Symmetry Breaking mechanism (EWSB). • New physics could interfere with the SM: search for beyond-SM effects. Accurate theory predictions for polarized VBS needed, to be used in LHC experimental analyses. p j At the LHC: two weak bosons radiated from quark-lines scatter, then decay into V V stable particles. Quarks b ecome two V tagging jets with large invariant mass and V large rapidity separation. j p Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 5/16

2. Theory & Monte Carlo Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 6/16

Separating polarizations A natural definition for resonant diagrams, in the unitary gauge: − g µν + k µ k ν / M 2 A unpol V = P µ D ν k 2 − M 2 V + iM V Γ V � λ ′ ε µ λ ′ ε ∗ ν λ ′ = P µ D ν k 2 − M 2 V + iM V Γ V ε µ λ ε ∗ ν V λ − → P µ D ν = A λ k 2 − M 2 V + iM V Γ V At the cross section level, � � |A unpol | 2 = → |A λ | 2 ∝ polarized cross section |A λ | 2 A ∗ + λ A λ ′ − λ λ � = λ ′ � �� � � �� � incoherent sum interference terms Note that pol. vectors are not Lorentz invariant ( ε µ λ (Λ · p ) � = Λ µν ε ν λ ( p )). Decay leptons angular distributions reflect polarization state of the decayed V boson. d cos θ ∗ If no lepton cuts, interferences vanish: analytic expression for the decay rate d σ/ ℓ . If lepton cuts, analytic expression doesn’t hold anymore: interferences don’t vanish. • Bottleneck: not all diagrams that contribute to multiboson processes are resonant! Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 7/16

Selecting resonant diagrams To define polarizations in multiboson, we need a factorized amplitude (production ⊗ propagator ⊗ decay): not possible for all contributions. E.g. diboson (fully leptonic): ℓ + Double-resonant and non-double-resonant W + ℓ + q diagrams at LO. For the latter polarizations q ℓ − ν W − Z/γ cannot be defined: drop them, providing a ℓ − W − q ¯ recipe to recover gauge invariance. q ¯ ν ν ν For VBS, many more diagrams (double-res., single-res. and non-res.): W W W W W + . . . Separating resonant contributions is delicate: the only “truth” is the full computation. • Our strategy: Double Pole Approximation (DPA) [Denner et al. 0006307]: project weak bosons on-shell, mantaining off-shell kinematics in Breit-Wigner modulation. • Then separating polarizations is straightforward. Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 8/16

Going beyond leading-order • The LO implementation available in PHANTOM (2 → 6 proc.) and MOCANLO (general). • NLO QCD is in principle easy (no coupling to EW boson leptonic decays), but ◮ on top of Born (B), virtuals (V) and reals (R) contribute: no IR singularities; q ¯ ℓ + ℓ + W + W + g q ν ν g ℓ ′− ℓ ′− W − W − q q ¯ ¯ ν ′ ν ′ ◮ subtraction counterterms needed, e.g. dipoles D in Catani-Seymour formalism � � � d φ rad D ) d =4 δ ( n ) d φ n +1 ( R δ ( n +1) − D δ ( n ) d σ nlo / d ξ = d φ n ( B + V + + ξ ) d =4 (1) ξ ξ ◮ DPA only used for LO kinematics (B,V), need for analogous prescription for R and subtraction counterterms (most involved part of the computation); ◮ separation of polarizations required for all contributions in Eq. 1. Implemented in MOCANLO+RECOLA completely for processes without final state jets, e.g. diboson, close to completion for processes with final state jets, e.g. VBS. • NLO EW much more involved: V and R mix production and decay sub-amplitudes. Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 9/16

3. Phenomenology Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 10/16

Vector boson scattering at the LHC@13TeV (1) ew ) with PHANTOM : W + W − [1710.09339], Extensive study of VBS signal at LO EW ( α 6 W + W + [in preparation], ZZ and W + Z [1907.04722] (fully leptonic, opposite flavors). VBS signal: two jets with M jj > 500 − 600 GeV , | ∆ η jj | > 2 . 5 − 3 . 6. W + Z (pp → jj µ + ν µ e + e − ): final state known, up to single- ν reco., resonable rate. • Singly-polarized (no lepton cuts): � 1% agreement with analytic results (cos θ ∗ ℓ ). • Effect of lepton cuts and ν -reco. on cos θ ∗ ℓ : non vanishing interferences, but still discriminating power among polarization modes. σ θ σ θ d / dcos (pb), M > 200 GeV d / dcos (pb), M > 200 GeV µ µ + + − zw − zw × 3 × 3 10 10 0.14 Full unpolarized SM: Full unpolarized 0.35 + + W longit SM: W longit (MC) + + 0.12 W left SM: W left (MC) 0.3 + W right + SM: W right (MC) Sum of polarized (pb) Sum of polarized (pb) 0.1 0.25 − → + + µ µ 0.08 θ θ 0.2 / dcos / dcos 0.15 0.06 σ σ d d 0.1 0.04 0.05 0.02 0 1.1 − 1 − 0.8 − 0.6 − 0.4 − 0.2 0 0.2 0.4 0.6 0.8 1 1.1 − 1 − 0.8 − 0.6 − 0.4 − 0.2 0 0.2 0.4 0.6 0.8 1 RATIO/FULL RATIO/FULL 1.05 1.05 1 1 0.95 0.95 0.9 0.9 − − − − − − 1 − 0.8 − 0.6 − 0.4 − 0.2 0 0.2 0.4 0.6 0.8 1 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 θ θ cos cos µ µ + + Without lepton cuts and ν reco With lepton cuts and ν reco Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 11/16

Vector boson scattering at the LHC@13TeV (2) • Singly-transverse distributions (both for W + and for Z ) show (almost) model independence in shape and cross-section (SM, Singlet Ext., Higgsless SM). • Two different fit techniques using SM distribution templates: few % accurate results. → promising results for model indepent extraction of pol. fractions from LHC data. • Investigated the reweighting method, often used by experimentalists to generate polarized signals, reweighting unpolarized events: proved to be very inaccurate. Longitudinal cross-section (most interesting!) overestimated by 50% at large M WZ . Very good description of polarized signals in VBS, with DPA techniques, in all VBS channels, with fully-leptonic (opposite-flavor) decays. Giovanni Pelliccioli (Uni. W¨ urzburg, TP2) - Polarized Weak Bosons at the LHC - CortonaYoung, 27-29.5.2020 12/16