Composite Vectors and Scalars in Theories of Electroweak Symmetry - PowerPoint PPT Presentation

Composite Vectors and Scalars in Theories of Electroweak Symmetry Breaking Antonio Enrique C´ arcamo Hern´ andez. Scuola Normale Superiore di Pisa. LAPTH Seminar, 16th September of 2010. Based on: R. Barbieri, A. E. C´ arcamo Hern´ andez, G. Corcella, R. Torre and E. Trincherini, JHEP 3 (2010)068 A. E. C´ arcamo Hern´ andez and R. Torre, Nuclear Physics B 841 (2010) 188-204. A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 1 / 49

Introduction 1 The Standard Model Role of the Higgs boson in EWPT and WW scattering Quantum Instability of the Higgs boson mass Two paradigms for Electroweak Symmetry Breaking Electroweak Chiral Lagrangian Composite Vectors at the LHC 2 Effective Lagrangian Pair production cross section by Vector Boson Fusion Drell Yan Pair production cross sections Same-sign di-lepton and tri-lepton events at LHC A “composite” scalar-vector system at the LHC 3 The basic Lagrangian Associated production of Vh total cross sections Same-sign di-lepton and tri-lepton events at LHC Conclusions 4 A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 2 / 49

The Standard Model 1 µν F a µν + i ¯ 4 F a L = − ψ D ψ The gauge sector + ψ i λ ij ψ j h + h . c The flavor sector � 2 − V ( h ) � � + � D µ h The EWSB sector + N i M ij N j The ν mass sector (if Majorana) A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 3 / 49

Role of the Higgs boson in EWPT and WW scattering m Limit = 158 GeV July 2010 6 Theory uncertainty 0.5 ∆α (5) ∆α had = 5 0.02758 ± 0.00035 0.4 0.02749 ± 0.00012 incl. low Q 2 data 4 0.3 ∆χ 2 0.2 3 68 % CL 95 % CL ∆Τ 0.1 2 100 0 1 −0.1 m h Excluded Preliminary 0 500 −0.2 30 100 300 m H [ GeV ] −0.3 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 ∆ S q 2 � � T = Π 33 ( 0 ) − Π WW ( 0 ) = Π ZZ ( 0 ) − Π WW ( 0 ) d Π 30 � S = g � , � g ′ M 2 M 2 M 2 dq 2 � q 2 = 0 W Z W A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 4 / 49

� E � 2 A Gauge ≃ g 2 M W � E � 2 A Higgs ≃ − g 2 M W � M H � 2 A = A Gauge + A Higgs ≃ g 2 2 M W The Higgs boson unitarize the WW scattering provided that M H � 700 GeV. A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 5 / 49

Quantum Instability of the Higgs boson mass d 4 k d 4 k k 2 1 � � k 2 − m 2 α Λ 2 ( k 2 − m 2 ) 2 α Λ 2 ( 2 π ) 4 ( 2 π ) 4 � 2 � Λ m 2 H ∼ m 2 0 − ( 115 GeV ) 2 400 GeV To have m H ≈ 100 GeV for Λ ≃ 10 19 GeV an extreme fine tunning of 34 decimals in the bare squared Higgs boson mass has to be performed. This is the hierarchy problem of the Standard Model. A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 6 / 49

Two paradigms for Electroweak Symmetry Breaking There are two pictures of the Electroweak Symmetry Breaking (EWSB): Weakly coupled, as the Standard Model (SM), supersymmetric extensions of the SM, Little Higgs, Gauge Higgs Unification models. Strongly coupled, as Technicolor, Composite Higgs, Strongly Interacting Light Higgs (SILH), Composite Vectors, Randall-Sundrum (RS) models, Higgsless RS bulk models. The lack of direct experimental evidence of the Higgs boson together with the hierarchy problem provides a plausible motivation for considering strongly coupled theories of EWSB. A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 7 / 49

Electroweak Chiral Lagrangian The EWSB without the Higgs boson can be formulated in terms of the Electroweak Chiral Lagrangian (EWCL) [5]:   ij u ( j )  λ u L SB = v 2 − v � D µ U ( D µ U ) † � � � u ( i ) L d ( i ) R  + h . c , 2 ∑ √ ¯ U (1) L ij d ( j ) 4 λ d i , j R where: √ π 0 2 π + � � π ( x ) / v , π ( x ) = τ a π a = U ( x ) = e i ˆ √ ˆ , 2 π − − π 0 B µ = g ′ W µ = g 2 τ a W a 2 τ 3 B 0 D µ U = ∂ µ U − iB µ U + iUW µ , µ , µ , Under SU ( 2 ) L × SU ( 2 ) R , one has: √ U → g R uh † = hug † u ≡ L , U → g L Ug R , (2) where h = h ( u , g L , g R ) is an element of SU ( 2 ) L + R . The local SU ( 2 ) L × U ( 1 ) Y invariance is now manifest in the Lagrangian (1) with: U → g L ( x ) U g † i θ a L ( x ) τ a / 2 � � Y ( x ) , g L ( x ) = exp , i θ Y ( x ) τ 3 / 2 � � g Y ( x ) = exp . (3) A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 8 / 49

In the unitary gauge � U � = 1, it is immediate to see that the chiral Lagrangian (1) gives the mass terms for the W and Z gauge bosons with M 2 W ρ = = 1 . (4) Z cos 2 θ W M 2 A term like � 2 c 3 v 2 � T 3 U † D µ U (5) invariant under the local SU ( 2 ) L × U ( 1 ) Y but not under the global SU ( 2 ) L × SU ( 2 ) R symmetry is therefore forbidden. Its presence would undo the ρ = 1 relation. The effective Lagrangian W µν W µν � − L gauge = − 1 1 B µν B µν � L eff = L gauge + L SB , � � 2 g ′ 2 2 g 2 provides an accurate description of particle physics, beyond the tree level, at energies below the ultraviolet cut-off: Λ = 4 π v ≈ 3 TeV (6) A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 9 / 49

SU ( 2 ) L × U ( 1 ) Y → U ( 1 ) Q SU ( 2 ) L × SU ( 2 ) R × U ( 1 ) B − L → SU ( 2 ) L + R × U ( 1 ) B − L The EWCL suffers, however, of two main problems [5]: The violation of unitarity in WW scattering, evaluated at the tree-level, s below the cutoff Λ . This is due to the fact that A ( W L W L → W L W L ) ≈ v 2 √ s and A ( W L W L → f ¯ f ) ≈ m f v 2 . The inconsistency of the electroweak observables S and T when compared with the experimental data if evaluated at the one-loop level with Λ as ultraviolet cutoff. These problems point toward the existence of new degrees of freedom below the cutoff. This motivates the introduction of new composite particles such as composite scalars and composite vectors in the EWCL. A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 10 / 49

Effective Lagrangian v 2 W µν W µν � − 1 1 � D µ U ( D µ U ) † � B µν B µν � � � L = − 2 g 2 2 g ′ 2 4 + M 2 � − ig V − 1 � � � � V µν ˆ ˆ V V µ V µ V µν [ u µ , u ν ] ˆ � √ V µν 4 2 2 2 − f V + ig K � V µν ( uW µν u † + u † B µν u ) � � V µν V µ V ν � ˆ ˆ √ √ 2 2 2 2 � + g 2 � + g 3 V µ V µ u α u α V µ u α V µ u α V µ V ν [ u µ , u ν ] � � � � + g 1 � + g 5 V µ ( u µ V ν u ν + u ν V ν u µ ) V µ V ν { u µ , u ν } � � � + g 4 + g 2 � V µ V ν ( uW µν u † + u † B µν u ) � V � [ u µ , u ν ] � �� + ig 6 u µ , u ν (7) 8 √ √ π 0 2 π + � � π ( x ) / v , π ( x ) = τ a π a = U ( x ) = e i ˆ √ ˆ , u ≡ U 2 π − − π 0 B µ = g ′ W µ = g 2 τ a W a 2 τ 3 B 0 D µ U = ∂ µ U − iB µ U + iUW µ , µ , µ , 1 ˆ 2 τ a V a u µ = u † µ = iu † D µ Uu † , V µ = µ , V µν = ∇ µ V ν − ∇ ν V µ , √ � u † � Γ µ = 1 u † � � � � ∇ µ V = ∂ µ V + [ Γ µ , V ] , ∂ µ − iB µ u + u ∂ µ − iW µ 2 A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 11 / 49

� � �� v 2 − G 2 A ( s , t , u ) = s s − u s − t V 3 s + M 2 + V v 4 t − M 2 u − M 2 V V where we have set g V M V = G V . A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 12 / 49

0.32 0.3 0.28 0.26 0.24 G V (TeV) 0.22 0.2 0.18 0.16 0.14 0.12 0.5 1 1.5 2 2.5 3 M V (TeV) A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 13 / 49

A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 14 / 49

A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 15 / 49

The various amplitudes have the following asymptotic behaviour: 3 s 2 s 2 A ( W L W L → V L V L ) ∼ , A ( W L W L → V L V T ) ∼ (8) v 2 M 2 v 2 M V V s A ( qq → VV ) ∼ , with a small coefficient (9) M 2 V The scattering amplitudes for the processes W L W L → V L V L and s W L W L → V L V T will grow at most as v 2 and the qq → VV scattering amplitude will go as a constant only when [1]: g K = 1 g 3 = − 1 , f V = 2 g V , (10) g V 4 g 6 = 1 g 1 = g 2 = g 4 = g 5 = 0 , (11) 2 which corresponds to the Gauge Model Scenario ( SU ( 2 ) L × SU ( 2 ) C × SU ( 2 ) R → SU ( 2 ) L + R + C ). A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 16 / 49

Pair production cross section by Vector Boson Fusion A.E. C´ arcamo Hern´ andez (SNS) Composite Vectors and Scalars in EWSB 09/09 17 / 49