Resonances and Unitarity in Weak Boson Scattering at the LHC Jrgen - PowerPoint PPT Presentation

0/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Resonances and Unitarity in Weak Boson Scattering at the LHC Jürgen Reuter Albert-Ludwigs-Universität Freiburg Alboteanu/Kilian/JR, arXiv:0806.4145 ( JHEP ); M. Mertens, 2005; Kilian/Kobel/Mader/JR/Schumacher, work in progress; Beyer/Kilian/Krstonoši´ c/Mönig/JR/Schmitt/Schröder, EPJC 48 (2006), 353 [ILC version] Seminar, PSI, January 22, 2009

1/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Doubts on the Standardmodel – describes microcosm (too good?) |O meas − O fit |/ σ meas Measurement Fit 0 1 2 3 ∆α (5) ∆α had (m Z ) 0.02758 ± 0.00035 0.02768 m Z [ GeV ] m Z [ GeV ] 91.1875 ± 0.0021 91.1875 Γ Z [ GeV ] Γ Z [ GeV ] 2.4952 ± 0.0023 2.4957 – 28 free parameters σ 0 σ had [ nb ] 41.540 ± 0.037 41.477 R l R l 20.767 ± 0.025 20.744 A 0,l A fb 0.01714 ± 0.00095 0.01645 A l (P τ ) A l (P τ ) 0.1465 ± 0.0032 0.1481 R b R b 0.21629 ± 0.00066 0.21586 R c R c 0.1721 ± 0.0030 0.1722 A 0,b A fb 0.0992 ± 0.0016 0.1038 A 0,c A fb 0.0707 ± 0.0035 0.0742 A b A b 0.923 ± 0.020 0.935 A c A c 0.670 ± 0.027 0.668 A l (SLD) A l (SLD) 0.1513 ± 0.0021 0.1481 sin 2 θ lept (Q fb ) sin 2 θ eff 0.2324 ± 0.0012 0.2314 m W [ GeV ] m W [ GeV ] 80.398 ± 0.025 80.374 Γ W [ GeV ] Γ W [ GeV ] 2.140 ± 0.060 2.091 m t [ GeV ] m t [ GeV ] 170.9 ± 1.8 171.3 0 1 2 3 – Higgs ?, form of Higgs potential ? Hierarchy Problem M H [GeV] δm f ∝ v ln(Λ 2 /v 2 ) chiral symmetry: 750 no symmetry for quantum corrections to 500 Higgs mass 250 H ∝ Λ 2 ∼ M 2 Planck = (10 19 ) 2 GeV 2 δM 2 Λ[GeV] 20000 GeV 2 = ( 1000000000000000000000000000000020000 – 10 12 10 15 10 18 10 3 10 6 10 9 1000000000000000000000000000000000000 ) GeV 2

2/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Open Questions 60 – Unification of all interactions (?) 50 U(1) B ∼ 10 − 9 40 – Baryon asymmetrie ∆ N B − ∆ N ¯ -1 missing CP violation 30 SU(2) α i 20 Standard Model – Flavour: three generations 10 SU(3) 0 – Tiny neutrino masses: m ν ∼ v 2 10 10 12 10 14 10 16 10 10 2 10 4 10 6 10 8 10 18 µ (GeV) M – Dark Matter: ◮ stable ◮ only weakly interacting ◮ m DM ∼ 100 GeV – Quantum theory of gravity – Cosmic inflation – Cosmological constant

3/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Ideas for New Physics since 1970

4/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Model-Independent Description of the EW sector ◮ Higgs boson still not observed ◮ Aim: describe any physics beyond the SM as generically as possible ◮ Implement what we know about the SM ◮ Implements SU (2) L × U (1) Y gauge invariance ◮ Building blocks (including longitudinal modes): � − i � W a v w a τ a ψ ( SM fermions ) , µ ( a = 1 , 2 , 3) , B µ , Σ = exp ◮ Minimal Lagrangian including gauge interactions 2 g ′ 2 tr [ B µν B µν ] + v 2 1 1 X 2 g 2 tr [ W µν W µν ] − 4 tr [( D µ Σ)( D µ Σ)] L min = ψ ( i / D ) ψ − ψ

5/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 The Fundamental Building Blocks ◮ V = Σ( D Σ) † (longitudinal vectors), T = Σ τ 3 Σ † (neutral component) ◮ Unitary gauge (no Goldstones): w ≡ 0 , i.e., Σ ≡ 1 . � √ → − i g 2( W + τ + + W − τ − ) + 1 � Zτ 3 V − 2 c w → τ 3 T − ◮ Gaugeless limit (only Goldstones) ( g, g ′ → 0 ): � √ √ � → i 2 ∂w + τ + + 2 ∂w − τ − + ∂zτ 3 + O ( v − 2 ) V − v √ 2 i → τ 3 + 2 w + τ + − w − τ − � + O ( v − 2 ) � T − v So T projects out the neutral part: � w + ∂w − − w − ∂w + �� tr [ TV ] = 2i ∂z + i � + O ( v − 3 ) v v

6/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Electroweak Chiral Lagrangian Complete Lagrangian contains infinitely many parameters α i L i + 1 L (5) + 1 α (5) α (6) X ψ L Σ Mψ R + β 1 L ′ X X X L (6) + . . . L eff = L min − 0 + i i v 2 v ψ i i i 0 = v 2 L ′ 4 tr [ TV µ ] tr [ TV µ ] L 1 = tr [ B µν W µν ] L 6 = tr [ V µ V ν ] tr [ TV µ ] tr [ TV ν ] L 2 = itr [ B µν [ V µ , V ν ]] L 7 = tr [ V µ V µ ] tr [ TV ν ] tr [ TV ν ] L 3 = itr [ W µν [ V µ , V ν ]] 1 4 tr [ TW µν ] tr [ TW µν ] L 8 = L 4 = tr [ V µ V ν ] tr [ V µ V ν ] 2 tr [ TW µν ] tr [ T [ V µ , V ν ]] i L 9 = 2 (tr [ TV µ ] tr [ TV µ ]) 2 L 5 = tr [ V µ V µ ] tr [ V ν V ν ] 1 L 10 = Indirect info on new physics in β 1 , α i , . . . (Flavor physics only in M ) Electroweak precision observables (LEP I/II, SLC): ∆ S = − 16 πα 1 α 1 = 0 . 0026 ± 0 . 0020 ∆ T = 2 β 1 /α QED β 1 = − 0 . 00062 ± 0 . 00043 ∆ U = − 16 πα 8 α 8 = − 0 . 0044 ± 0 . 0026

7/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Anomalous triple and quartic gauge couplings " # λ γ “ ν W + µν − W + ν W − µν ” ν A µν + g γ W − + κ γ W − µ W + W − ν W + νρ A ρµ L T GC = i e 1 A µ µ M 2 W " # ν Z µν + λ Z + i e c w “ ν W + µν − W + ν W − µν ” g Z W − + κ Z W − µ W + W − ν W + νρ Z ρµ 1 Z µ M 2 µ s w W = κ γ,Z = 1 , λ γ,Z = 0 and δ Z = β 1+ g ′ 2 α 1 g V V ′ = 1 , h ZZ = 0 SM values: g γ,Z 1 c 2 w − s 2 1 / 2 w ∆ κ γ = g 2 ( α 2 − α 1 ) + g 2 α 3 + g 2 ( α 9 − α 8 ) ∆ g γ 1 = 0 1 = δ Z + g 2 ∆ κ Z = δ Z − g ′ 2 ( α 2 − α 1 ) + g 2 α 3 + g 2 ( α 9 − α 8 ) ∆ g Z w α 3 c 2 − g 2 ∆ g γγ = ∆ g γγ ∆ g ZZ = 2∆ g γZ = 0 w ( α 5 + α 7 ) 1 2 2 1 c 4 = δ Z + g 2 ∆ g γZ = ∆ g γZ ∆ g W W = 2 c 2 w ∆ g γZ + 2 g 2 ( α 9 − α 8 ) + g 2 α 4 w α 3 1 2 c 2 1 1 + g 2 + 2 g 2 ( α 9 − α 8 ) − g 2 ( α 4 + 2 α 5 ) ∆ g ZZ = 2∆ g γZ ∆ g W W = 2 c 2 w ∆ g γZ w ( α 4 + α 6 ) 1 1 c 4 2 1 h ZZ = g 2 [ α 4 + α 5 + 2 ( α 6 + α 7 + α 10 )]

7/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Anomalous triple and quartic gauge couplings L QGC = e 2 h i g γγ 1 A µ A ν W − µ W + ν − g γγ 2 A µ A µ W − ν W + ν + e 2 c w h A µ Z ν “ ” i g γZ W − µ W + ν + W + µ W − − 2 g γZ A µ Z µ W − ν W + 1 ν 2 ν s w + e 2 c 2 h i w g ZZ Z µ Z ν W − µ W + ν − g ZZ Z µ Z µ W − ν W + 1 2 ν s 2 w e 2 e 2 » ” 2 – “ g W W W − µ W + ν W − µ W + ν − g W W W − µ W + h ZZ ( Z µ Z µ ) 2 + + 1 2 µ 2 s 2 4 s 2 w c 4 w w = κ γ,Z = 1 , λ γ,Z = 0 and δ Z = β 1+ g ′ 2 α 1 g V V ′ = 1 , h ZZ = 0 SM values: g γ,Z 1 c 2 w − s 2 1 / 2 w ∆ κ γ = g 2 ( α 2 − α 1 ) + g 2 α 3 + g 2 ( α 9 − α 8 ) ∆ g γ 1 = 0 1 = δ Z + g 2 ∆ κ Z = δ Z − g ′ 2 ( α 2 − α 1 ) + g 2 α 3 + g 2 ( α 9 − α 8 ) ∆ g Z w α 3 c 2 − g 2 ∆ g γγ = ∆ g γγ ∆ g ZZ = 2∆ g γZ = 0 w ( α 5 + α 7 ) 1 2 2 1 c 4 = δ Z + g 2 ∆ g γZ = ∆ g γZ ∆ g W W = 2 c 2 w ∆ g γZ + 2 g 2 ( α 9 − α 8 ) + g 2 α 4 w α 3 1 2 c 2 1 1 + g 2 + 2 g 2 ( α 9 − α 8 ) − g 2 ( α 4 + 2 α 5 ) ∆ g ZZ = 2∆ g γZ ∆ g W W = 2 c 2 w ∆ g γZ w ( α 4 + α 6 ) 1 1 c 4 2 1 h ZZ = g 2 [ α 4 + α 5 + 2 ( α 6 + α 7 + α 10 )]

8/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Parameters and Scales, Resonances α i measurable at ILC ◮ α i ≪ 1 (LEP) ◮ α i � 1 / 16 π 2 ≈ 0 . 006 (renormalize divergencies, 16 π 2 α i � 1 ) Translation of parameters into new physics scale Λ : α i = v 2 / Λ 2 ◮ Operator normalization is arbitrary ◮ Power counting can be intricate To be specific: consider resonances that couple to EWSB sector Resonance mass gives detectable shift in the α i ◮ Narrow resonances ⇒ particles ◮ Wide resonances ⇒ continuum β 1 ≪ 1 ⇒ SU (2) c custodial symmetry (weak isospin, broken by hypercharge g ′ � = 0 and fermion masses) J = 0 J = 1 J = 2 ω 0 ( γ ′ /Z ′ ?) σ 0 (Higgs ?) f 0 (Graviton ?) I = 0 ρ ± , ρ 0 ( W ′ /Z ′ ?) π ± , π 0 (2HDM ?) a ± , a 0 I = 1 φ ±± , φ ± , φ 0 (Higgs triplet ?) t ±± , t ± , t 0 I = 2 — accounts for weakly and strongly interacting models

9/39 J. Reuter Resonances and Unitarity in Weak Boson Scattering at the LHC PSI, 22.1.2009 Model-Independent Way – Effective Field Theories � How to clearly separate effects of heavy degrees of freedom? Toy model: Two interacting scalar fields ϕ, Φ � �� � � � 2 ( ∂ϕ ) 2 − 1 2 Φ( � + M 2 )Φ − λϕ 2 Φ − . . . + J Φ+ jϕ 1 Z [ j, J ] = D [Φ] D [ ϕ ] exp i dx Low-energy effective theory ⇒ integrating out heavy degrees of freedom (DOF) in path integrals, set up Power Counting Completing the square: � − 1 1 + ∂ 2 λ � Φ ′ = Φ + ϕ 2 ⇒ − → M 2 M 2 � − 1 2Φ ′ ( M 2 + ∂ 2 )Φ ′ + λ 2 1 + ∂ 2 1 2( ∂ Φ) 2 − 1 2 M 2 Φ 2 − λϕ 2 Φ = − 1 � 2 M 2 ϕ 2 ϕ 2 . M 2