Particle Physics: Introduction to the Standard Model Electroweak measurements and the Higgs boson Frédéric Machefert frederic@cern.ch Laboratoire de l accélérateur linéaire (CNRS) Cours de l École Normale Supérieure 24, rue Lhomond, Paris March 23th, 217 1 / 33
Part X Electroweak measurements and the Higgs boson 2 / 33
1 2 3 3 / 33
Study properties of the W ± boson Study properties of the Z boson Study properties of the t quark Theory+Experiment to discover the Higgs boson 4 / 33
W e ν el W polarization vector electron final state anti-neutrino final state EW vertex γ = γ and γ ν = γ γ νγ T fi M 2 M 2 = ǫ µ ū(k)( i = ǫ µ ū(k)( i e 1 γ 2 sinθw γ 5 µ 2 )v(k ) e 1 γ 2 sinθw γ 5 µ 2 )v(k ) ǫ ν v (k )( 1 γ 5)γ 2 ν i 2 sinθw γ u(k) = ǫ µ e 1 γ ū(k)( i 2 sinθw γ 5 µ )v(k ) 2 ǫ ν v (k )( 1 γ 5)γ γ 2 νγ i 2 sinθw γ u(k) e e 5 / 33
common factors and v initial state Spin average and polarisation vector relationship Spinor relationship (γ µ kγ µ ) = 2 k and Tr(, 1, 2, 3γγ 5) = M 2 = = = = = = e 2 2 sin 2 θ W ǫ µ ǫ ν ū(k)γ µ 1 γ 5 2 v(k )v (k ) 1 γ 5 2 γ γ νu(k) e 2 8 sin 2 θ W ǫ µ ǫ ν ū(k)γ µ(1 γ 5)v(k ) v(k )(1+γ 5)γ νu(k) e 2 3 8 sin 2 θ W ( g µν )ū(k)γ µ(1 γ 5)v(k ) v(k )(1+γ 5)γ νu(k) e 2 24 sin 2 θ W Tr( kγ µ(1 γ 5) k (1+γ 5)γ µ ) e 2 24 sin 2 θ W [Tr( kγ µ k γ µ ) Tr( kγ µγ 5 k γ 5γ µ )] e 2 24 sin 2 θ W [Tr( kγ µ k γ µ )+Tr( kγ µ k γ µ )] 6 / 33
Tr(γ µγ νγ ργ σ) = 4(g µνg ρσ + g µσg νρ g µρg νσ) m 2 W ± = s = (k+k ) 2 = k 2 + k 2 + 2kk 2kk ME isotropical (as should be for unpolarized decay! M 2 = = = = = e 2 12 sin 2 θ W [Tr( kγ µ k γ µ )] e 2 3 sin 2 θ W k µ k ρ g νσ (g µνg ρσ + g µσg νρ g µρg νσ) e 2 3 sin 2 θ W (k k + k k k k 4) 2e 2 3 sin 2 θ W k k e 2 3 sin 2 θ W m 2 W ± dγ eνel = Γ eνel = 1 M 2 64π 2 s dω 1 1 64π 2 m W ± e 2 3 sin 2 θ W m 2 W ±4π 7 / 33
W ± partial widths Γ eνel = 1 e 2 m 16π 3 sin 2 θ W ± W e 2 sin 2 θ W = 8 G 2 m 2 W ± Γ eνel = G 1 6π 2 m3 W ± Γ ud = G 1 6π 2 m3 W ± 3 V ud 2 (1+ α S (m2 W ±) π ) To include the radiative corrections means inclusive: Γ ud = Γ ud(g) Branching ratios Γ = Γ eνel +Γ µνµl +Γ τντl Γ ud +Γ cs (3+2 3)Γ eν B(lν) 3% tb final state excluded by mass 18GeV 8GeV V ij for i j excluded V ij 1 8 / 33
Hadron colliders q W + ν, q q q l +, q q leptons or jets each vertex G F LHC: sea q LHC NLO: gluon (splitting) ŝ = m ± W x1 x 2 s = m ± W no leptons :) each vertex g S jet-jet mass only difference to signal LHC: 1 4 lepton-jet rejection s 3 2m ± W (gluon 5%) 9 / 33
The discovery machine SPPS transformed to SP PS s 6 GeV TeVatron stochastic cooling p p s 1.96TeV 1fb 1 fb cross sections measureable LHC pp s 14TeV luminosity of anti-protons gluon PDFs dominate QCD cross sections increase more rapidly than the signal 211: 7TeV 5fb 1 212: 8TeV 25fb 1 215: 14TeV-X 1 / 33
Transverse Energy 2-body decay E T m± W 2 particles massless maximal energy half of the mother mass Events /.25 GeV 1 W eν χ 2 /dof = 6 / 62 5 3 4 5 E T (e) (GeV) Experimental issues finite width final state radiation detector effects ISR 11 / 33
Transverse Mass m T = m( E T, p l ) E T negative sum of activity ignore longitudinal component Events /.5 GeV 15 1 5 W µν χ 2 /dof = 58 / 48 maximal mass is m ± W less sensitive to NLO 6 7 8 9 1 m T (µν) (GeV) Experimental Results CDF 8.413 ±.48 GeV D 8.41 ±.43 GeV 12 / 33
Lepton Colliders CM system is lab system ŝ = s (modulo ISR) initial state charge zero pair production e e + γ W + W e W + e Z W + e + W e + W 13 / 33
Signatures W + W qqqq 5% W + W lνqq 4% W + W lνlν 1% 9% useful with ν = E Number of events per GeV/c 2 225 2 175 15 125 1 WW qq ZZ ALEPH eνqq channel 75 5 25 3 4 5 6 7 8 9 1 11 12 2C Mass (GeV/c 2 ) Semi-leptonic low background use separately leptonic decay and hadronic decay 14 / 33
Number of events per GeV/c 2 7 6 5 4 3 WW qq ZZ ALEPH 4q channel Fully hadronic QCD background jet reconstruction and calibration Color reconnection (jet algo) 2 1 3 4 5 6 7 8 9 1 11 12 5C Mass (GeV/c 2 ) Experimental Results ALEPH 8.44 ±.51 GeV DELPHI 8.336 ±.67 GeV L3 8.27 ±.55 GeV OPAL 8.415 ±.52 GeV PDG 8.399 ±.23 GeV 15 / 33
WW Cross section threshold scan sensitive to W mass width washes out threshold WW Interpretation 1 t channel alone: insufficient 2 addingγw + W still insufficient 3 unitarity not proven σ WW (pb) 2 LEP PRELIMINARY YFSWW and RacoonWW 17/2/25 σ WW (pb) 3 LEP PRELIMINARY 17/2/25 2 1 18 17 1 16 YFSWW/RacoonWW no ZWW vertex (Gentle) 19 195 2 25 16 18 2 s (GeV) only ν e exchange (Gentle) 16 18 2 s (GeV) 16 / 33
σ had [nb] 4 3 2 ALEPH DELPHI L3 OPAL Γ Z σ A FB (µ).4.2 A FB from fit QED corrected average measurements A FB ALEPH DELPHI L3 OPAL 1 measurements (error bars increased by factor 1) σ from fit QED corrected -.2 86 88 9 92 94 E cm [GeV] Experimental Issues measure beam energy precisely measure efficiency precisely M Z -.4 88 9 92 94 E cm [GeV] Predictions/Measurements Radiative corrections important Interference zero on peak M Z 17 / 33
σ had [nb] 3 2 1 Results ALEPH DELPHI L3 OPAL average measurements, error bars increased by factor 1 2ν 3ν 4ν 86 88 9 92 94 E cm [GeV] 3 generations 91.1875 ±.21GeV 2.4952 ±.23 GeV Cross-section (pb) 1 5 1 4 1 3 1 2 1 CESR DORIS PEP KEKB PEP-II Results PETRA TRISTAN Z SLC LEP I e + e hadrons W + W - LEP II 2 4 6 8 1 12 14 16 18 2 22 Centre-of-mass energy (GeV) Impressive agreement over decades in time different machines different energies 18 / 33
Forward/backward asymmetry A FB (f) = 1 dσ d cosθ d cosθ dσ 1 d cosθ d cosθ 1 dσ d cosθ d cosθ+ dσ 1 d cosθ d cosθ Measurements A FB is a measurement of sin 2 θ W leptons easy hadrons hard leptons with polarization Open question Do leptons behave differently than hadrons? A,l fb.2399 ±.53 A l (P τ ).23159 ±.41 A l (SLD).2398 ±.26 A,b fb.23221 ±.29 A,c fb.2322 ±.81 Q had fb.2324 ±.12 Average.23153 ±.16 m H [GeV] 1 3 1 2 χ 2 /d.o.f.: 11.8 / 5 α (5) had =.2758 ±.35 m t = 178. ± 4.3 GeV.23.232.234 sin 2 θ lept eff 19 / 33
Experimental issues jet reconstruction jet calibration b tagging W mass constraint all final states used Experimental result PDG 172.9±.6±.9 GeV ) 2 Events/(5 GeV/c ) 2 Events/(1 GeV/c 18 16 14 12 1 8 6 4 2 1-tag m jj 5 6 7 8 9 21 11 12 m jj (GeV/c ) 16 14 12 1 8 6 4 2-1 Data (5.6 fb ) Signal+Bkgd Bkgd only mreco t 1-tag 1 15 2 25 3 35 reco 2 m t (GeV/c ) 2 / 33
Perturbativity and Unitarity unitarity of WW scattering (see WW) width smaller than mass upper limit on Higgs boson mass Triviality RGE solution Quartic coupling (only Higgs sector for large λ): λ(q 2 ) = λ(v 2 )[1 3 4π 2 λ(v 2 ) log Q2 v 2 ] 1 Q v λ = Landau pole Q = λ = (trivial) φ 4 must be trivial if valid at all scales navigate between the poles 21 / 33
Stability RGE solution including fermions (small λ): λ(q 2 ) = λ(v 2 ) 1 16π 2 [+ 3 16 ( 12 m4 t v 4 + 2g 4 2 +(g 2 2 + g 2 1) 2 )] log Q2 v 2 λ small top yukawa can turn λ < Higgs potential unbounded Consequences Λ: cut-off scale for new physics m H 7 GeV window for SM valid up to GUT scale at 125GeV 22 / 33
Measurement Fit O meas O fit /σ meas 1 2 3 α (5) had (m Z ).275 ±.33.2759 m Z [GeV] 91.1875 ±.21 91.1874 Γ Z [GeV] 2.4952 ±.23 2.4959 σ had [nb] 41.54 ±.37 41.478 R l 2.767 ±.25 2.742 A,l fb.1714 ±.95.1646 A l (P τ ).1465 ±.32.1482 R b.21629 ±.66.21579 R c.1721 ±.3.1722 A,b fb.992 ±.16.139 A,c fb.77 ±.35.743 A b.923 ±.2.935 A c.67 ±.27.668 A l (SLD).1513 ±.21.1482 sin 2 θ lept eff (Q fb ).2324 ±.12.2314 m W [GeV] 8.399 ±.23 8.378 Γ W [GeV] 2.85 ±.42 2.92 m t [GeV] 173.2 ±.9 173.27 July 211 EW measurements internally compatible 1 2 3 largest deviation: asymmetry χ 2 6 5 4 3 2 March 212 Theory uncertainty α (5) had =.275±.33.2749±.1 incl. low Q 2 data 1 LEP LHC excluded excluded 4 1 2 m H [GeV] Indirect Higgs Search m Limit = 152 GeV logarithmic dependence on Higgs boson mass: m H = 94 +29 24GeV 23 / 33
σ(pp H+X) [pb] 1 1 1 2 1 pp H (NNLO+NNLL QCD + NLO EW) pp qqh (NNLO QCD + NLO EW) pp WH (NNLO QCD + NLO EW) pp ZH (NNLO QCD +NLO EW) pp tth (NLO QCD) s= 7 TeV 1 2 3 4 5 1 M H [GeV] Higgs boson production gluon fusion (NLO> 2) VBF (O(2%)) associated production radiation off heavy quark LHC HIGGS XS WG 21 Experimental issues huge QCD background for jets mass information? mass resolution? total cross section mb = 1 3 b signal pb = 1 12 b pile-up 24 / 33
Higgs BR + Total Uncert 1 1 ττ cc bb gg WW ZZ LHC HIGGS XS WG 211 Higgs BR + Total Uncert 1 1 ττ cc bb gg WW ZZ tt LHC HIGGS XS WG 211 2 1 2 1 γγ Zγ γγ Zγ 3 1 1 12 14 16 18 2 M H [GeV] 3 1 1 2 3 4 5 1 M H [GeV] Low mass Higgs boson heaviest fermion dominates: b gauge boson pairs (one off-shell) kick in thresholds visible High mass Higgs boson gauge bosons dominate top threshold 35 GeV s dependence in gauge bosons 25 / 33
Higgs to WW WW EW production no mass peak Events / 1 GeV 14 Data SM (sys stat) 12 1 8 ATLAS s = 8 TeV, Ldt = 5.8 fb (*) H WW eνµν/µνeν + /1 jets WW WZ/ZZ/Wγ t t Single Top Z+jets W+jets H [125 GeV] 6 4 2 5 1 15 2 25 3 [GeV] m T Using the spin correlation Higgs Spin- W opposite charged leptons emitted in the same direction 26 / 33
1 11 12 13 14 15 16 Higgs to γγ Rare decay (via triangle) as γ is massless 1 3 SM background from continuum di-photon production (EM couplings) excellent mass resolution necessary Σ weights / 2 GeV Events Bkg Events / 2 GeV 35 ATLAS 3 25 2 15 1 5 2 1 2 1 8 6 s=7 TeV, Ldt=4.8fb s=8 TeV, Ldt=5.9fb (a) (b) Data Sig+Bkg Fit Bkg (4th order polynomial) H γγ Data S/B Weighted Sig+Bkg Fit (m =126.5 GeV) H (m =126.5 GeV) H Bkg (4th order polynomial) 4 Σ weights Bkg 2 (c) 81 11 12 13 14 15 16 4 4 (d) 8 1 11 12 13 14 15 16 m γ γ [GeV] 27 / 33
Higgs to ZZ ZZ EW production good mass resolution required e, µ: low B Events/5 GeV 25 2 Data (*) Background ZZ Background Z+jets, tt Signal (m =125 GeV) H Syst.Unc. ATLAS (*) H ZZ 4l 15 1 s = 7 TeV: Ldt = 4.8 fb s = 8 TeV: Ldt = 5.8 fb 5 1 15 2 25 m 4l [GeV] 28 / 33
Local p 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 1 1 1 ATLAS 211 212 s = 7 TeV: Ldt = 4.6 4.8 fb s = 8 TeV: Ldt = 5.8 5.9 fb Obs. Exp. ±1 σ 11 115 12 125 13 135 14 145 15 m H [GeV] σ 1σ 2σ 3σ 4σ 5σ 6σ Local p value 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 1 1 1 2 1 Combined obs. Exp. for SM H H γγ H ZZ H WW CMS Preliminary H ZZ + WW + γγ s = 7 TeV, L = 5.1 fb s = 8 TeV, L = 5.3 fb 1σ 2σ 3σ 4σ 5σ 6σ 7σ 116 118 12 122 124 126 128 13 Higgs boson mass (GeV) A new resonance discovery convention: 5σ independent discovery in two experiments A success of particle physics discovery 5 years after the prediction 29 / 33
Signal Strengths ATLAS (Moriond 213) ATLAS Preliminary W,Z H bb s = 7 TeV: Ldt = 4.7 fb s = 8 TeV: Ldt = 13 fb H ττ s = 7 TeV: Ldt = 4.6 fb s = 8 TeV: Ldt = 13 fb (*) H WW lνlν s = 7 TeV: Ldt = 4.6 fb s = 8 TeV: Ldt = 2.7 fb H γγ s = 7 TeV: Ldt = 4.8 fb s = 8 TeV: Ldt = 2.7 fb (*) H ZZ 4l s = 7 TeV: Ldt = 4.6 fb s = 8 TeV: Ldt = 2.7 fb Combined µ = 1.3 ±.2 s = 7 TeV: Ldt = 4.6 4.8 fb s = 8 TeV: Ldt = 13 2.7 fb m H = 125.5 GeV +1 Signal strength (µ) Signal Strengths CMS (Moriond 213) Combined µ =.8 ± H bb µ = 1.15 ± H ττ µ = 1.1 ± H γγ µ =.77 ± H WW µ =.68 ± H ZZ µ =.92 ±.14.62.41.27.2.28 s = 7 TeV, L 5.1 fb CMS Preliminary p =.65 SM s = 8 TeV, L 19.6 fb = 125.7 GeV m H.5 1 1.5 2 2.5 Best fit σ/σ SM 3 / 33
Higgs couplings global sensitivity 15% smallest errors for gauge boson couplings Higgs couplings future luminosity 3fb 1 global sensitivity 5% precision of the order 1-2% ILC % precision 31 / 33
Gauge couplings Planck scale (gravity) 1 18 GeV unification of g 1, g 2, g 3 at 1 16 GeV? Standard Model: close miss Supersymmetry fermionic degree of freedom has a bosonic counter part unification g 1, g 2, g 3 at 1 16 GeV light < 14GeV Higgs boson stabilizes the Higgs boson mass dark matter candidate 6 5 4 3 2 1 1-1 2-1 3-1 1 2 1 6 1 1 1 14 Q [GeV] Experimental evidence half discovered? or nada? 32 / 33
Future The Standard Model is alive and kicking The Higgs boson has been discovered: What are the couplings of the Higgs boson? What is the self-coupling of the Higgs boson? Is it a Spin- particle? Neutrinos Mixing in the leptonic sector Is the Neutrino Majorana or DIRAC? Are there new physics beyond the Standard Model? Supersymmetry Extra Dimensions... What happens up to the Planck scale at 1 18 GeV? Desert from EW to GUT scale? Unification of the 3 forces at the GUT scale? 33 / 33