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 fb•1 •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 j ⊲ To any continuous symmetry of the Lagrangian we can associate a conserved current