Electroweak precision data and Higgs physics A. Freitas University - PowerPoint PPT Presentation

Electroweak precision data and Higgs physics A. Freitas University of Pittsburgh HEFT 2017 1. Overview of electroweak precision tests 2. Effective operator description 3. Connection between EWPO and HEFT

Overview of electroweak precision tests 1/20 W mass µ decay in Fermi Model µ decay in Standard Model ν µ ν µ ν µ µ − µ − ν e G F Z ν e µ − e − W − ν e W − e − ν µ e − µ − ν e QED corr. G 2 e 2 e − γ F (2-loop) √ 2 = (1 + ∆ r ) w M 2 8 s 2 W Γ µ = G 2 F m 5 � m 2 µ e � electroweak corrections 192 π 3 F (1 + ∆ q ) m 2 µ Ritbergen, Stuart ’98 Pak, Czarnecki ’08

Z -pole observables 2/20 Deconvolution of initial-state QED radiation: LEP EWWG ’05 σ had [ nb ] σ 0 σ [ e + e − → f ¯ f ] = R ini ( s, s ′ ) ⊗ σ hard ( s ′ ) 40 ALEPH DELPHI L3 30 OPAL Kureav, Fadin ’85 Berends, Burgers, v. Neerven ’88 Γ Z 20 Kniehl, Krawczyk, K¨ uhn, Stuart ’88 measurements (error bars increased by factor 10) Beenakker, Berends, v. Neerven ’89 10 σ from fit QED corrected Skrzypek ’92 M Z Montagna, Nicrosini, Piccinini ’97 86 88 90 92 94 E cm [ GeV ] e + f e − γ f

Z -pole observables 2/20 Deconvolution of initial-state QED radiation: LEP EWWG ’05 σ had [ nb ] σ 0 σ [ e + e − → f ¯ f ] = R ini ( s, s ′ ) ⊗ σ hard ( s ′ ) 40 ALEPH DELPHI L3 30 OPAL Subtraction of γ -exchange, γ – Z interference, Γ Z 20 box contributions: measurements (error bars increased by factor 10) 10 σ from fit σ hard = σ Z + σ γ + σ γ Z + σ box QED corrected M Z 86 88 90 92 94 E cm [ GeV ] e + f e − γ f e + f γ e − f e + f W W e − f

Z -pole observables 2/20 Deconvolution of initial-state QED radiation: LEP EWWG ’05 σ had [ nb ] σ 0 σ [ e + e − → f ¯ f ] = R ini ( s, s ′ ) ⊗ σ hard ( s ′ ) 40 ALEPH DELPHI L3 30 OPAL Subtraction of γ -exchange, γ – Z interference, Γ Z 20 box contributions: measurements (error bars increased by factor 10) 10 σ from fit σ hard = σ Z + σ γ + σ γ Z + σ box QED corrected M Z 86 88 90 92 94 E cm [ GeV ] Z -pole contribution: R e + f σ Z = + σ non − res ( s − M 2 Z ) 2 + M 2 Z Γ 2 Z e − γ f e + f γ e − f e + f W W e − f

Z -pole observables 2/20 Deconvolution of initial-state QED radiation: LEP EWWG ’05 σ had [ nb ] σ 0 σ [ e + e − → f ¯ f ] = R ini ( s, s ′ ) ⊗ σ hard ( s ′ ) 40 ALEPH DELPHI L3 30 OPAL Subtraction of γ -exchange, γ – Z interference, Γ Z 20 box contributions: measurements (error bars increased by factor 10) 10 σ from fit σ hard = σ Z + σ γ + σ γ Z + σ box QED corrected M Z 86 88 90 92 94 E cm [ GeV ] Z -pole contribution: R e + f σ Z = + σ non − res ( s − M 2 Z ) 2 + M 2 Z Γ 2 Z e − γ f In experimental analyses: e + f 1 σ ∼ Z ) 2 + s 2 Γ 2 γ ( s − M 2 Z /M 2 e − Z f �� e + 1 + Γ 2 Z /M 2 f M Z = M Z Z ≈ M Z − 34 MeV W �� W 1 + Γ 2 Z /M 2 e − Γ Z = Γ Z Z ≈ Γ Z − 0 . 9 MeV f

Z -pole observables 3/20 Total and partial Z widths: Γ f = Γ[ Z → f ¯ � f ] s = M 2 Γ Z = Γ f Z f Γ f ≈ N c M Z 1 �� � V | 2 + R f R f V | g f A | g f A | 2 � 1 + Re Σ ′ s = M 2 12 π Z Z R f V , R f e + A : Final-state QED/QCD radiation; f g f V , g f A , Σ ′ Z : Electroweak corrections e − Z f Branching ratios: R q = Γ q / Γ had ( q = b, c , probes heavy quark generations) R ℓ = Γ had / Γ ℓ ( ℓ = e, µ, τ )

Z -pole observables 4/20 Peak cross section: Z ) = 12 π Γ e Γ q had = σ Z ( s = M 2 σ 0 � (1 + δX ) M 2 Γ 2 q Z Z ⌊ → NNLO correction term Z -pole asymmetries / effective weak mixing angle: FB ≡ σ ( θ < π 2 ) − σ ( θ > π 2 ) 2 ) = 3 A f 4 A e A f σ ( θ < π 2 ) + σ ( θ > π A LR ≡ σ ( P e > 0) − σ ( P e < 0) σ ( P e > 0) + σ ( P e < 0) = A e 1 − 4 | Q f | sin 2 θ f g V f /g Af eff A f = 2 1 + ( g V f /g Af ) 2 = 1 − 4 | Q f | sin 2 θ f eff + 8( | Q f | sin 2 θ f eff ) 2 Most precisely measured for f = ℓ (also f = b, c )

Current uncertainties 5/20 Experiment Theory error Main source α 3 , α 2 α s M W 80385 ± 15 MeV 4 MeV α 2 bos , α 3 , α 2 α s , αα 2 Γ Z 2495 . 2 ± 2 . 3 MeV 0 . 5 MeV s σ 0 α 2 bos , α 3 , α 2 α s 41540 ± 37 pb 6 pb had α 2 bos , α 3 , α 2 α s 0 . 21629 ± 0 . 00066 0 . 00015 R b sin 2 θ ℓ 4 . 5 × 10 − 5 α 3 , α 2 α s 0 . 23153 ± 0 . 00016 eff

Impact on Higgs physics 6/20 Standard Model: Good agreement between measured mass and indirect prediction Very good agreement over large number of observables Erler ’16 1000 Γ Z , σ had , R l , R q (1 σ ) Direct measurements: Z pole asymmetries (1 σ) 500 M W (1 σ) M H = 125 . 09 ± 0 . 24 GeV direct m t (1 σ ) 300 m t = 173 . 34 ± 0 . 81 GeV direct M H 200 precision data (90%) M H [GeV] Indirect prediction: 100 M H = 126 . 1 ± 1 . 9 GeV 50 (with LHC BRs) M H = 96 +22 30 − 19 GeV 20 (w/o LHC data) m t = 176 . 7 ± 2 . 1 GeV 10 150 155 160 165 170 175 180 185 m t [GeV]

Impact on Higgs physics 7/20 Robens, Stefaniak ’13 Higgs singlet extension: Constraints on singlet mass and mixing angle Eberhardt, Nierste, Wiebusch ’13 Two-Higgs-Doublet Model: 0 . 6 π Constraints on couplings of SM-like Higgs 0 . 5 π g THDM � � β − α � � hV V � = sin( β − α ) , 0 . 4 π � � g SM � � � hV V 0 . 3 π g THDM � � � = cos α sin α or sin α hff � � � � g SM 0 . 2 π � � cos α 0.3 1 10 30 � hff tan β

Impact on Higgs physics 8/20 0.3 Oblique parameters: T 68% and 95% CL fit contours for U=0 (SM : H =126 GeV, m =173 GeV) H ref t 0.2 Present fit αT = Σ WW (0) − Σ ZZ (0) Present uncertainties 0.1 M W M Z 0 4 s 2 c 2 S = Σ ZZ ( M 2 Z ) − Σ ZZ (0) α -0.1 SM Prediction M Z M = 125.7 ± 0.4 GeV H m = 173.34 0.76 GeV ± t -0.2 + s 2 − c 2 Σ Z γ ( M 2 − Σ γγ ( M 2 Z ) Z ) Jun '14 G fitter SM -0.3 sc M Z M Z -0.3 -0.2 -0.1 0 0.1 0.2 0.3 S Gfitter coll. ’14

Impact on Higgs physics 8/20 0.3 Oblique parameters: T 68% and 95% CL fit contours for U=0 (SM : H =126 GeV, m =173 GeV) H ref t 0.2 Present fit αT = Σ WW (0) − Σ ZZ (0) Present uncertainties Not adequate for new physics 0.1 M W M Z that affects flavor 0 4 s 2 c 2 S = Σ ZZ ( M 2 Z ) − Σ ZZ (0) α ( Z → ℓℓ , Z → bb , ...) -0.1 SM Prediction M Z M = 125.7 ± 0.4 GeV H m = 173.34 0.76 GeV ± t -0.2 + s 2 − c 2 Σ Z γ ( M 2 − Σ γγ ( M 2 Z ) Z ) Jun '14 G fitter SM -0.3 sc M Z M Z -0.3 -0.2 -0.1 0 0.1 0.2 0.3 S Gfitter coll. ’14

Effective operator description 9/20 c i Λ 2 O i + O (Λ − 3 ) L = � (Λ ≫ M Z ) Effective field theory: i Contributions at tree-level: e + f O φ 1 = ( D µ Φ) † Φ Φ † ( D µ Φ) e − Z f O BW = Φ † B µν W µν Φ O (3) e L e L σ a γ µ L e L e L σ a γ µ L e = (¯ L )(¯ L ) LL R = i (Φ † ↔ O f f R γ µ f R ) D µ Φ)( ¯ f = e, µ τ, b, lq L = i (Φ † ↔ � ν e � ν µ � ν τ � u, c � t � � � � � O F F L γ µ F L ) D µ Φ)( ¯ F = , , , , e µ τ d, s b = i (Φ † ↔ O (3) F D a F L σ a γ µ F L ) µ Φ)( ¯ L

Effective operator description 9/20 c i Λ 2 O i + O (Λ − 3 ) L = � (Λ ≫ M Z ) Effective field theory: i Contributions at tree-level: c φ 1 α ∆ T = − v 2 O φ 1 = ( D µ Φ) † Φ Φ † ( D µ Φ) 2 Λ 2 α ∆ S = − e 2 v 2 c BW O BW = Φ † B µν W µν Φ Λ 2 √ 2 c (3) e O (3) e L e L σ a γ µ L e L e L σ a γ µ L e = (¯ L )(¯ LL L ) ∆ G F = − LL Λ 2 R = i (Φ † ↔ O f f R γ µ f R )  D µ Φ)( ¯     L = i (Φ † ↔   O F F L γ µ F L ) D µ Φ)( ¯  effect on Z → f ¯ f  = i (Φ † ↔  O (3) F  D a F L σ a γ µ F L ) µ Φ)( ¯    L 

Effective operator description 9/20 c i Λ 2 O i + O (Λ − 3 ) L = � (Λ ≫ M Z ) Effective field theory: i Contributions at tree-level:  O φ 1 = ( D µ Φ) † Φ Φ † ( D µ Φ) relevant for Higgs physics,  but strongly bounded from EWPO O BW = Φ † B µν W µν Φ  O (3) e  L e L σ a γ µ L e L e L σ a γ µ L e = (¯ L )(¯ L )  LL      R = i (Φ † ↔   O f f R γ µ f R ) D µ Φ)( ¯     irrelevant for Higgs physics L = i (Φ † ↔ O F F L γ µ F L ) D µ Φ)( ¯        = i (Φ † ↔  O (3) F  D a F L σ a γ µ F L ) µ Φ)( ¯    L

Current constraints on some dim-6 operators 10/20 Assuming flavor universality: Significant correlation/ degeneracy between different operators Pomaral, Riva ’13 Ellis, Sanz, You ’14

Effective operator description 11/20 Contributions at 1-loop-level: O H = 1 2 ∂ µ (Φ † Φ) ∂ µ (Φ † Φ) O B = i ( D µ Φ) † B µν ( D ν Φ) O W = i ( D µ Φ) † W µν ( D ν Φ) O BB = − Φ † B µν B µν Φ O WW = − Φ † W µν W µν Φ + few more → Direct correlation with Higgs production and decay rates Chen, Dawson, Zhang ’13 Hartmann, Shephard, Trott ’16