Particle Physics ≡ EWSB after LHC 8 Abdelhak DJOUADI (LPT CNRS & U. Paris-Sud) I: The SM and EWSB • The Standard Model in brief • The Higgs mechanism • Constraints on M H II: Higgs Physics • Higgs decays • Higgs production a hadron colliders • Implications of the discovery III: Beyond the SM: • Why beyond the SM? • The case of SUSY and the MSSM • What next? Frascati, 12-15/05/14 The SM and the Higgs Physics – A. Djouadi – p.1/51
1. The Standard Model: brief introduction The Standard Model describes electromagnetic, strong and weak interactions: Electromagnetic interaction (QED): Particules de: mati` ere (s=1 / 2) force (s=1) bosons-jauge 3 familles de fermions – subjects: electric charged particles, – mediator: one massless photon, quark up quark charm quark top gluon 8 g 3 u 3 c c → 3 t – conserves P, C, T... et of course Q. Q → +2/3 +2/3 +2/3 0 ∼ 5 MeV 1.6 GeV 172 GeV 0 m → Strong (nuclear) interaction (QCD): quark down quark strange quark bottom photon γ 3 s – quarks appearing in three q,q ,q, 3 d 3 b –1/3 –1/3 –1/3 0 – interacting via exchange of color, ∼ 5 MeV 0.2 GeV 4.9 GeV 0 – mediators: the massless gluons, neutrino µ neutrino e τ neutrino boson Z ν µ ν e ν τ Z 0 – conserves P,C,T and color number; – color=attractive ⇒ confinement! 0 0 0 0 ∼ 0 ∼ 0 ∼ 0 91.2 GeV muon tau electron bosons W Weak (nuclear) interaction: µ e τ W ± – subjects: all fermions; ± 1 –1 –1 –1 – mediators: massive W + , W − , Z! 0.5 MeV 0.1 GeV 1.7 GeV 80.4 GeV (only short range interaction), – does not conserve parity: f L � = f R ; (ex: no ν R ⇒ ν masseless); – does not conserve CP: n P ≫ n ¯ P . Frascati, 12-15/05/14 The SM and the Higgs Physics – A. Djouadi – p.2/51
1. The Standard Model: brief introduction The SM of the electromagnetic, weak and strong interactions is: • relativistic quantum field theory: quantum mechanics+special relativity, • based on gauge symmetry: invariance under internal symmetry group, • a carbon–copy of QED, the quantum field theory of electromagnetism. QED: invariance under local transformations of the abelian group U(1) Q : – transformation of electron field: Ψ ( x ) → Ψ ′ ( x ) = e ie α ( x ) Ψ ( x ) µ ( x )= A µ ( x ) − 1 – transformation of photon field: A µ ( x ) → A ′ e ∂ µ α ( x ) The Lagrangian density is invariant under above field transformations 4 F µν F µν + i ¯ Ψ D µ γ µ Ψ − m e ¯ L QED = − 1 ΨΨ field strength F µν = ∂ µ A ν − ∂ ν A µ and cov. derivative D µ = ∂ µ − ieA µ . Very simple, consistent, aesthetical and extremely successful theory: • minimal coupling: interaction uniquely determined once group fixed, • invariance implies massless photon and allows massive fermions, • mathematically consistent: perturbative, unitary, renormalisable, • very predictive theoretically and very well tested experimentally. Frascati, 12-15/05/14 The SM and the Higgs Physics – A. Djouadi – p.3/51
1. The Standard Model: brief introduction SM is based on the gauge symmetry G SM ≡ SU ( 3 ) C × SU ( 2 ) L × U ( 1 ) Y • The local/gauge symmetry group SU ( 3 ) C describes the strong force: – interaction between quarks which are SU(3) triplets: q, q , q, – mediated by 8 gluons, G a µ corresponding to 8 generators of SU ( 3 ) C Gell-Man 3 × 3 matrices: [ T a , T b ] = if abc T c with Tr [ T a T b ] = 1 2 δ ab – asymptotic freedom: interaction “weak” at high energy, α s = g 2 4 π ≪ 1 s ⇒ the partons are free at high-energy and confined at low-energies... The Lagrangian of the theory is a simple extension of the one of QED: L QCD = − 1 4 G a µν G µν q i D µ γ µ q i ( − � a + i � i ¯ i m i ¯ q i q i ) with G a µν = ∂ µ G a ν − ∂ ν G a µ + g s f abc G b µ G c ν D µ = ∂ µ − ig s T a G a µ . Interactions/couplings are then uniquely determined by SU(3) structure: – fermion gauge boson couplings : − g i ψ V µ γ µ ψ – V self-couplings : ig i Tr( ∂ ν V µ − ∂ µ V ν )[ V µ , V ν ]+ 1 2 g 2 i Tr[ V µ , V ν ] 2 – the gluons are massless while quarks can be massive (like in QED)... Frascati, 12-15/05/14 The SM and the Higgs Physics – A. Djouadi – p.4/51
1. The Standard Model: brief introduction SM is based on the gauge symmetry G SM ≡ SU ( 3 ) C × SU ( 2 ) L × U ( 1 ) Y • SU ( 2 ) L × U ( 1 ) Y describes the electromagnetic+weak=EW interaction: – between the three families of quarks and leptons: f L / R = 1 2 ( 1 ∓ γ 5 ) f I 3L , 3R � ν e L , R = e − = ± 1 � R , Q = ( u 2 , 0 ⇒ L = d ) L , u R , d R e − f f ⇒ Y L = − 1 , Y R = − 2 , Y Q = 1 3 , Y u R = 4 3 , Y d R = − 2 Y f = 2Q f − 2I 3 3 Same holds for the two other generations: ( µ, ν µ , c , s ) and ( τ, ν τ , t , b ) . There is no ν R field (and neutrinos are thus exactly and stay massless). – mediated by the W i µ (isospin) and B µ (hypercharge) gauge bosons corresping to the 3 generators (Pauli matrices) of SU(2) and are massless T a = 1 2 τ a ; [ T a , T b ] = i ǫ abc T c and [ Y , Y ] = 0 . Lagrangian simple: with fields strengths and covariant derivatives as QED W a µν = ∂ µ W a ν − ∂ ν W a µ + g 2 ǫ abc W b µ W c ν , B µν = ∂ µ B ν − ∂ ν B µ ψ , T a = 1 � ∂ µ − igT a W a µ − ig ′ Y � 2 τ a D µ ψ = 2 B µ 4 B µν B µν + ¯ F Li iD µ γ µ F Li + ¯ f Ri iD µ γ µ f R i L SM = − 1 µν W µν a − 1 4 W a Frascati, 12-15/05/14 The SM and the Higgs Physics – A. Djouadi – p.5/51
1. The Standard Model: brief introduction But if gauge boson and fermion masses are put by hand in L SM V V µ V µ and/or m f ¯ 1 2 M 2 ff terms: breaking of gauge symmetry. This statement can be visualized by taking the example of QED where the photon is massless because of the local U(1) Q local symmetry: Ψ ( x ) → Ψ ′ ( x )= e ie α ( x ) Ψ ( x ) , A µ ( x ) → A ′ µ ( x )= A µ ( x ) − 1 e ∂ µ α ( x ) • For the photon (or B field for instance) mass we would have: A A µ A µ → 1 1 A ( A µ − 1 e ∂ µ α )( A µ − 1 e ∂ µ α ) � = 1 A A µ A µ 2 M 2 2 M 2 2 M 2 and thus, gauge invariance is violated with a photon mass. • For the fermion masses, we would have (e.g. for the electron): � � 1 2 ( 1 − γ 5 ) + 1 m e ¯ ee = m e ¯ e 2 ( 1 + γ 5 ) e = m e ( ¯ e R e L + ¯ e L e R ) manifestly non–invariant under SU(2) isospin symmetry transformations. We need a less “brutal” way to generate particle masses in the SM: ⇒ The Brout-Englert-Higgs mechanism ⇒ the Higgs particle H. Frascati, 12-15/05/14 The SM and the Higgs Physics – A. Djouadi – p.6/51
2. The Higgs mechanism in the SM In the SM, if gauge boson and fermion masses are put by hand in L SM breaking of gauge symmetry ⇒ spontaneous EW symmetry breaking: � � φ + introduce a new doublet of complex scalar fields: Φ = , Y Φ =+ 1 φ 0 with a Lagrangian density that is invariant under SU ( 2 ) L × U ( 1 ) Y L S = ( D µ Φ ) † ( D µ Φ ) − µ 2 Φ † Φ − λ ( Φ † Φ ) 2 µ 2 > 0 : 4 scalar particles.. µ 2 < 0 : Φ develops a vev: V( � ) V( � ) � 0 | Φ | 0 � = ( 0 2 ) √ v / 1 with ≡ v = ( − µ 2 /λ ) � � 2 > > 0 0 2 2 + v � > 0 � < 0 = 246 GeV – symmetric minimum: instable – true vaccum: degenerate ⇒ to obtain the physical states, write L S with the true vacuum (diagoalised fields/interactions). Frascati, 12-15/05/14 The SM and the Higgs Physics – A. Djouadi – p.7/51
2. The Higgs mechanism in the SM • Write Φ in terms of four fields θ 1 , 2 , 3 ( x ) and H(x) at 1st order: Φ ( x ) = e i θ a ( x ) τ a ( x ) / v 2 ( θ 2 + i θ 1 1 2 ( 0 1 v + H ( x ) ) ≃ v + H − i θ 3 ) √ √ • Make a gauge transformation on Φ to go to the unitary gauge: Φ ( x ) → e − i θ a ( x ) τ a ( x ) Φ ( x ) = 1 2 ( 0 v + H ( x ) ) √ • Then fully develop the term | D µ Φ ) | 2 of the Lagrangian L S : | D µ Φ ) | 2 = � 2 µ − i g 2 � τ a � �� 2 W a � ∂ µ − ig 1 2 B µ Φ 2 � � � � 0 �� − ig2 ∂ µ − i 2 ( g 2 W 3 2 ( W 1 µ − iW 2 µ + g 1 B µ ) µ ) � � = 1 � � v + H − ig2 ∂ µ + i 2 2 ( g 2 W 3 µ − g 1 B µ ) 2 ( W 1 µ + iW 2 µ ) � � = 1 2 ( ∂ µ H ) 2 + 1 µ | 2 + 1 8 g 2 2 ( v + H ) 2 | W 1 µ + iW 2 8 ( v + H ) 2 | g 2 W 3 µ − g 1 B µ | 2 • Define the new fields W ± µ and Z µ [ A µ is the orthogonal of Z µ ]: g 2 W 3 g 2 W 3 W ± = µ − g 1 B µ µ + g 1 B µ 1 √ √ 2 ( W 1 µ ∓ W 2 µ ) , Z µ = , A µ = √ g 2 2 + g 2 g 2 2 + g 2 1 1 with sin 2 θ W ≡ g 2 / � g 2 2 + g 2 1 = e / g 2 Frascati, 12-15/05/14 The SM and the Higgs Physics – A. Djouadi – p.8/51
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