Electroweak Theory and Higgs Mechanism Stefano Pozzorini 2016 CTEQ & MCnet School, DESY Hamburg 7 July 2016 Standard Model of Particle Physics Gauge interactions (3 parameters) SU(3) SU(2) U(1) symmetry, universality × × Symmetry breaking sector (2 parameters) W; Z masses via gauge interactions minimal and weakly coupled but many alternatives (2HDM, little Higgs, extra dim) Yukawa sector (20 parameters) fermion masses via Yukawa interactions rich flavour structure, mixing and CP violation Simple and highly predictive 9 almost all natural phenomena down to 10− times the atomic scale renormalizable very accurate predictions and tests ) 1 / 12 Huge progress in perturbative calculations EW 2 3 dσ = dσLO + αS dσNLO + αEW dσNLO + αS dσNNLO + αS dσN3LO Perturbative calculations for hard scattering processes more general, automated and widely applicable methods drastic improvements for vast range of LHC processes ) when order automation availability precision 2009{now NLO QCD+EW full 2 2; 3; 4(5) processes (10%) ! O 2011{now NNLO QCD partial 15 2 2 processes few % ! 2015{now N3LO QCD { gg H 1% ! ∼ crucial ingredient of any SM precision test and many new-physics searches ) 2 / 12 Success of LHC and Standard Model at Run 1 (+2) Standard Model Production Cross Section Measurements Status: Nov 2015 80 µb 1 − total (x2) 11 ATLAS Preliminary 10 inelastic Theory [pb] 1 20 µb− 63 µb 1 − Run 1,2 √s = 7, 8, 13 TeV LHC pp √s = 7 TeV σ 6 0.1 < pT < 2 TeV 10 1 Data 4.5 4.9 fb− − 0.3 < mjj < 5 TeV 105 LHC pp √s = 8 TeV 1 Data 20.3 fb− 4 10 nj 0 ≥ 1 LHC pp = 13 TeV 35 pb− √s 1 3 nj 0 Data 85 pb− 10 nj 1 n 0 ≥ ≥ j ≥ 1 e, µ+X 35 pb− n 2 nj 1 j ≥ ≥ t-chan 2 nj 1 WW 10 ≥ n 2 nj 3 j Wt 1 total ≥ n 2 ≥ 13.0 fb− j ≥ 1 WZ ggF n 4 nj 3 2.0 fb 1 10 j ≥ n 4 − H WW ≥ nj 3 j → W γ ≥ ≥ ZZ n 5 nj 4 j ≥ ≥ s-chan nj 5 n 4 ≥ j nj 6 H ττ 1 ≥ ≥ → Zγ nj 6 ≥ nj 7 n 5 ≥ VBF j ≥ H WW 1 → n 8 10− j ≥ n 6 j ≥ H γγ → 2 nj 7 10− n 7 ≥ j ≥ H ZZ 4ℓ → → 3 10− pp Jets Dijets W Z t¯t t VV γγ H Vγ t¯tW t¯tZ t¯tγ Zjj Wγγ W±W±jj R=0.4 R=0.4 EWK EWK y <3.0 y <3.0 fiducial fiducial total total total fiducial fiducial fiducial total total fiducial fiducial fiducial fiducial | | |y ∗|<3.0 njet=0 (N)NLO calculations already crucial to explain several measurements 3 / 12 2012 Higgs Boson Discovery (48 years after hypothesis) 100 ATLAS Data (*) (*) ZZ H→ZZ →4l Z+jets,tt 80 s = 7 TeV: ∫Ldt = 4.8 fb­1 ­1 H(125 GeV) Events/5 GeV s = 8 TeV: ∫Ldt = 5.8 fb Syst.Unc. 60 40 20 0 20 40 60 80 100 m34 [GeV] at +0:5 125:5 0:2 (stat) 0:6 (syst) ATLAS mH = ± 125:7 0:3 (stat)− 0:3 (syst) CMS ± ± Higgs mass measurement has turned the SM into a fully predictive theory at the quantum level! 4 / 12 Theory Inputs III: Production Modes First Higgs measurements [Run1 combination ATLAS-CONF-2015-044] ggH VBF VH H ATLAS and CMS Preliminary ATLAS LHC Run 1 CMS ATLAS+CMS Theory predictions mostly NNLO QCD+NLO EW ± 1σ µ ± 2σ few to 10% uncertainty (already outdated) ggF µ backgrounds typically less precise VBF µ WH 102 s= 8 TeV pp µ H (NNLO+NNLL QCD + NLO EW) ZH 10 LHC HIGGS XS WG 2012 H+X) [pb] µ ttH pp qqH (NNLO QCD + NLO EW) (pp pp 1 WH (NNLO QCD + NLO EW) µ pp ZH (NNLO QCD +NLO EW) pp ttH (NLO QCD) 0 0.5 1 1.5 2 2.5 3 3.5 4 Parameter value 10-1 Pp collisions ATLAS and CMS Preliminary ATLAS LHC Run 1 CMS 10-2 80 100 120 140 160 180 200 ATLAS+CMS M [GeV] ± σ ChannelsH establishedSM ggF, H, bbH over theory uncertainty: ~10% 5σ (15%{25% unc.) µγγ 1 VBF, VH, ZH: 2-3% ggH+VBF production and H γγ;ZZ;WW;ττ µZZ April 2016 Eilam Gross, KITP, 2016 ! 5 µWW ¯ Some tensions driven by ttH(WW ) and ZH(WW ) µττ +0:7 bb +0:29 µttH = 2:3 0:6 and µ = 0:69 0:27 µbb − − 0 0.5 1 1.5 2 2.5 3 3.5 4 still limited precision and room for surprises Parameter value ) 5 / 12 Searches for Physics Beyond the Standard Model (BSM) Motivations dark matter in the universe quantum instability of Higgs mass ... High discovery potential at LHC vast campaign of SM tests and BSM searches at higher energies precise SM predictions crucial for direct/indirect BSM sensitivity and interpretation of possible discoveries Millennium XXL simulation of cosmic web: Cluster formation at the intersection of filaments 6 / 12 This talk 1 Gauge symmetry and symmetry breaking 2 Electroweak Standard Model 3 Theoretical implications of a light Higgs Boson 4 Higgs production and decays at the LHC Reference and Acknowledgement This lecture is largely based on slides kindly made available by Laura Reina see lectures by L. Reina at 2011 Maria Laach & 2013 CTEQ schools And additional material taken from lectures by Sally Dawson at 2012 CERN{FERMILAB & 2015 CTEQ schools 7 / 12 Particles and forces are a realization of fundamental symmetries of nature Very old story: Noether’s theorem in classical mechanics ∂L ∂L L(qi, q˙i) such that = 0 pi = conserved ∂qi −→ ∂q˙i to any symmetry of the Lagrangian is associated a conserved physical quantity: ⊲ q = x p linear momentum; i i −→ i ⊲ q = θ p angular momentum. i i −→ i Generalized to the case of a relativistic quantum theory at multiple levels: ⊲ q φ (x) coordinates become “fields” “particles” i → j ↔ ⊲ (φ (x), ∂ φ (x)) can be symmetric under many transformations. L j µ j ⊲ To any continuous symmetry of the Lagrangian we can associate a conserved current µ ∂ µ J = L δφj such that ∂µJ = 0 ∂(∂µφj) The symmetries that make the world as we know it . ⊲ translations: conservation of energy and momentum; ⊲ Lorentz transformations (rotations and boosts): conservation of angular momentum (orbital and spin); ⊲ discrete transformations (P,T,C,CP,...): conservation of corresponding quantum numbers; ⊲ global transformations of internal degrees of freedom (φj “rotations”) conservation of “isospin”-like quantum numbers; ⊲ local transformations of internal degrees of freedom (φj(x) “rotations”): define the interaction of fermion (s=1/2) and scalar (s=0) particles in terms of exchanged vector (s=1) massless particles “forces” −→ Requiring different global and local symmetries defines a theory AND Keep in mind that they can be broken From Global to Local: gauging a symmetry Abelian case A theory of free Fermi fields described by the Lagrangian density = ψ¯(x)(i∂/ m)ψ(x) L − is invariant under a global U(1) transformation (α=constant phase) ψ(x) eiαψ(x) such that ∂ ψ(x) eiα∂ ψ(x) → µ → µ and the corresponding Noether’s current is conserved, J µ = ψ¯(x)γµψ(x) ∂ J µ = 0 → µ The same is not true for a local U(1) transformation (α = α(x)) since ψ(x) eiα(x)ψ(x) but ∂ ψ(x) eiα(x)∂ ψ(x)+ igeiα(x)∂ α(x)ψ(x) → µ → µ µ Need to introduce a covariant derivative Dµ such that D ψ(x) eiα(x)D ψ(x) µ → µ Only possibility: introduce a vector field Aµ(x) trasforming as 1 A (x) A (x) ∂ α(x) µ → µ − g µ and define a covariant derivative Dµ according to Dµ = ∂µ + igAµ(x) modifying to accomodate D and the gauge field A (x) as L µ µ 1 = ψ¯(x)(iD/ m)ψ(x) F µν (x)F (x) L − − 4 µν where the last term is the Maxwell Lagrangian for a vector field Aµ, i.e. F (x)= ∂ A (x) ∂ A (x) . µν µ ν − ν µ Requiring invariance under a local U(1) symmetry has: promoted a free theory of fermions to an interacting one; −→ defined univoquely the form of the interaction in terms of a new vector −→ field Aµ(x): = gψ¯(x)γ ψ(x)Aµ(x) Lint − µ no mass term AµA allowed by the symmetry this is QED. −→ µ → Non-abelian case: Yang-Mills theories Consider the same Lagrangian density = ψ¯(x)(i∂/ m)ψ(x) L − where ψ(x) ψ (x) (i = 1,...,n) is a n-dimensional representation of a → i non-abelian compact Lie group (e.g. SU(N)). is invariant under the global transformation U(α) L iαaT a a a 2 ψ(x) ψ′(x)= U(α)ψ(x) , U(α)= e =1+ iα T + O(α ) → a where T ((a = 1,...,dadj)) are the generators of the group infinitesimal transformations with algebra, [T a,T b]= if abcT c and the corresponding Noether’s current are conserved. However, requiring to be invariant under the corresponding local transformation U(x) L U(x)=1+ iαa(x)T a + O(α2) brings us to replace ∂µ by a covariant derivative D = ∂ igAa (x)T a µ µ − µ a in terms of vector fields Aµ(x) that transform as 1 Aa (x) Aa (x)+ ∂ αa(x)+ f abcAb (x)αc(x) µ → µ g µ µ such that 1 D U(x)D U − (x) µ → µ 1 D ψ(x) U(x)D U − (x)U(x)ψ = U(x)D ψ(x) µ → µ µ i 1 F [D ,D ] U(x)F U − (x) µν ≡ g µ ν → µν The invariant form of or Yang Mills Lagrangian will then be L 1 1 = (ψ,D ψ) TrF F µν = ψ¯(iD/ m)ψ F a F µν LY M L µ − 4 µν − − 4 µν a a a where Fµν = Fµν T and F a = ∂ Aa ∂ Aa + gf abcAb Ac µν µ ν − ν µ µ ν We notice that: as in the abelian case: • mass terms of the form Aa,µAa are forbidden by symmetry: gauge −→ µ bosons are massless the form of the interaction between fermions and gauge bosons is −→ fixed by symmetry to be = gψ¯(x)γ T aψ(x)Aa,µ(x) Lint − µ at difference from the abelian case: • gauge bosons carry a group charge and therefore ..