Fitting Higgs couplings in an EFT approach Oscar boli Universidade - PowerPoint PPT Presentation

Fitting Higgs couplings in an EFT approach Oscar Éboli Universidade de São Paulo in collaboration with Corbett, Gonçalves, Gonzalez-Fraile, Gonzalez-Garcia, Plehn, Rauch HEFT-2015

Goal: comprehensive analysis of couplings of the Higgs • assume a narrow CP-even scalar • use SFitter to fit available LHC data: [SFitter: Gonzalez-Fraile, Klute, Plehn, Rauch, Zerwas] production/decay mode ATLAS CMS X X H → WW X X H → ZZ X X H → γγ H → τ ¯ X X τ H → b ¯ X X b X X H → Z γ H → invisible X X t ¯ tH production X X [159] kinematic distributions X [14] o ff -shell rate X X [37] • frequentist likelihood everywhere • SFitter is flexible to study theoretical uncertainties [flat distribution ; uncorrelated uncertainties for production]

1.How well does the SM describe the Higgs data? [Corbett, OE, Gonçalves, Gonzalez-Fraile, Plehn, Rauch: arXiv:1505.05516] • assume SM operators with free couplings: [nonlinear sigma model: Alonso et al.; Buchalla et al.; Brivio et al,…] � ¯ g m f X L = L SM + ∆ W gm W H W µ W µ + ∆ Z m Z H Z µ Z µ − � ∆ f v H f R f L + h.c. 2 c w τ ,b,t H H v G µ ν G µ ν + ∆ γ F A v A µ ν A µ ν + invisible decays + ∆ g F G corresponding changes in the Higgs couplings: g x = g SM (1 + ∆ x ) x g γ = g SM (1 + ∆ SM + ∆ γ ) ≡ g SM (1 + ∆ SM+NP ) γ γ γ γ g g = g SM (1 + ∆ SM + ∆ g ) ≡ g SM (1 + ∆ SM+NP ) g g g g tree level new physics [keeping values for finite loop masses in calculations] • flips the sign of the SM couplings ∆ x = − 2 • only rate measurements (of course!)

• presenting the SM like solutions with ∆ g = ∆ γ = 0 • slowly increasing the number of free parameters ∆ H • equal tree level deviations L=4.5-5.1(7 TeV)+19.4-20.3(8 TeV) fb -1 , 68% CL: ATLAS + CMS SM (1+ ∆ x ) SM exp. g x = g x 0.4 data 0.2 0 -0.2 injected SM -0.4 Higgs signal -0.6 ∆ H ∆ V ∆ f ∆ W ∆ Z ∆ t ∆ b ∆ τ ∆ Z/W ∆ b/ τ ∆ b/W controls hgg coupling (expected 15% error)

∆ g ∆ γ • adding new loop contributions (7 parameter fit) L=4.5-5.1(7 TeV)+19.4-20.3(8 TeV) fb -1 , 68% CL: ATLAS + CMS 0.8 SM (1+ ∆ x ) SM exp. g x = g x 0.6 data 0.4 0.2 0 slightly -0.2 decrease -0.4 -0.6 -0.8 ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ S S M M W Z t b τ γ g g Z b b γ / / + + / W τ W N N P P effect of ttH (expected 30% error) • analogously < 0.7 (1.8) at 68% (95%) CL ∆ γ Z

• multiple solutions due to degeneracy ∆ x = 0 ⇐ ⇒ ∆ x = − 2 • and contribute to gluon fusion production ∆ t ∆ g 2 2 16 4 4 ∆ t ∆ t ∆ g ∆ g 14 3 3 1 1 12 2 2 0 0 10 1 1 -1 -1 0 0 8 -1 -1 6 -2 -2 -2 -2 4 -3 -3 -3 -3 2 -4 -4 -4 -4 0 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 ∆ (-2 ln L) ∆ g ∆ g ∆ γ ∆ γ plays indirect role ∆ t 7 parameter fit ∆ W > − 1

• further interesting correlations due to σ ( pp → h → γγ ) SM+NP SM+NP 1 1 ∆ g ∆ g 0.6 0.6 SM+NP SM+NP ∆ γ ∆ γ 0.8 0.8 0.4 0.4 0.6 0.6 0.2 0.2 0.4 0.4 0 0 0.2 0.2 -0.2 -0.2 0 0 -0.4 -0.4 -0.2 -0.2 -0.6 -0.6 -0.4 -0.4 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 ∆ b ∆ b ∆ b ∆ b ∆ t and ∆ g ∆ t ∆ W ∆ γ and g 2 i ( m H ) g 2 f ( m H ) σ on-shell i → H → f ∝ Γ H

• adding invisible decays (8 parameter fit) L=4.5-5.1(7 TeV)+19.4-20.3(8 TeV) fb -1 , 68% CL: ATLAS + CMS 0.8 no correlation with ∆ W,Z SM (1+ ∆ x ) SM exp. g x = g x 0.6 data 0.6 0.6 BR inv BR inv 0.4 0.5 0.5 0.2 0.4 0.4 0 0.3 0.3 -0.2 0.2 0.2 -0.4 0.1 0.1 -0.6 0 0 -0.6 -0.4 -0.2 -0.6 -0.4 -0.2 0 0 0.2 0.4 0.6 0.2 0.4 0.6 -0.8 ∆ W ∆ W BR inv ∆ W ∆ Z ∆ t ∆ b ∆ τ ∆ γ ∆ g ∆ γ ∆ g ∆ Z/W ∆ b/ τ ∆ b/W SM+NP SM+NP g 2 i ( m H ) g 2 f ( m H ) σ on-shell BR inv < 0 . 31 at 95% CL i → H → f ∝ Γ H • minor upward shift of all couplings due to correlation with total width • there is no significant deviations from the SM predictions

details of the theoretical uncertainty treatment • flat vs gaussian distributions for the theoretical uncertainties 12 (-2 ln L) ∆ 10 8 data (Gauss) injected SM rates 6 data 4 SM exp. 2 0 -0.5 0 0.5 SM+NP ∆ g • presently statistical errors dominate induced th. uncertainties • gaussian distributions lead to slightly larger 68% CL bands

• correlated vs uncorrelated uncertainties (7 parameter fit): L=4.5-5.1(7 TeV)+19.4-20.3(8 TeV) fb -1 , 68% CL: ATLAS + CMS 0.8 SM (1+ ∆ x ) g x = g x 0.6 0.4 0.2 0 -0.2 -0.4 SM exp. -0.6 SM exp. (corr.) data -0.8 data (corr.) ∆ W ∆ Z ∆ t ∆ b ∆ τ ∆ γ ∆ g ∆ γ ∆ g ∆ Z/W ∆ b/ τ ∆ b/W SM+NP SM+NP • correlated uncertainties lead to slightly smaller errors

2. Linear effective lagrangians to describe the LHC data? • new state belongs to SU(2) doublet • consider SU(2) x U(1) invariant dimension-6 lagrangian f n X L e ff = L SM + Λ 2 O n + · · · n • There are 59 “independent” dimension-six operators [Buchmuller & Wyler; Grzadkowski] • our choice for the boson operators is [Corbett, OE, Gonzalez-Fraile, Gonzalez-Garcia] [Hagiwara, Ishihara, Szalapski, Zeppenfeld] O W W = Φ † ˆ O BB = Φ † ˆ W µ ν ˆ B µ ν ˆ O GG = Φ † Φ G a µ ν G aµ ν W µ ν Φ B µ ν Φ O BW = Φ † ˆ O W = ( D µ Φ ) † ˆ O B = ( D µ Φ ) † ˆ B µ ν ˆ W µ ν Φ W µ ν ( D ν Φ ) B µ ν ( D ν Φ ) O Φ , 2 = 1 O Φ , 4 = ( D µ Φ ) † ( D µ Φ ) O Φ , 1 = ( D µ Φ ) † Φ Φ † ( D µ Φ ) 2 ∂ µ � Φ † Φ Φ † Φ Φ † Φ � � � � � ∂ µ � � ∂ µ + ig 0 B µ / 2 + ig σ a W a ˆ D µ Φ = µ / 2 Φ with W µ ν = ig σ a W a µ ν / 2 ˆ B µ ν = ig 0 B µ ν / 2

2. Linear effective lagrangians to describe the LHC data? • new state belongs to SU(2) doublet • consider SU(2) x U(1) invariant dimension-6 lagrangian f n X L e ff = L SM + Λ 2 O n + · · · n • There are 59 “independent” dimension-six operators [Buchmuller & Wyler; Grzadkowski] • our choice for the boson operators is [Corbett, OE, Gonzalez-Fraile, Gonzalez-Garcia] [Hagiwara, Ishihara, Szalapski, Zeppenfeld] O W W = Φ † ˆ O BB = Φ † ˆ W µ ν ˆ B µ ν ˆ O GG = Φ † Φ G a µ ν G aµ ν W µ ν Φ B µ ν Φ O BW = Φ † ˆ O W = ( D µ Φ ) † ˆ O B = ( D µ Φ ) † ˆ B µ ν ˆ W µ ν Φ W µ ν ( D ν Φ ) B µ ν ( D ν Φ ) O Φ , 2 = 1 O Φ , 4 = ( D µ Φ ) † ( D µ Φ ) O Φ , 1 = ( D µ Φ ) † Φ Φ † ( D µ Φ ) 2 ∂ µ � Φ † Φ Φ † Φ Φ † Φ � � � � � ∂ µ eliminated with EOM � � ∂ µ + ig 0 B µ / 2 + ig σ a W a ˆ D µ Φ = µ / 2 Φ with W µ ν = ig σ a W a µ ν / 2 ˆ B µ ν = ig 0 B µ ν / 2

2. Linear effective lagrangians to describe the LHC data? • new state belongs to SU(2) doublet • consider SU(2) x U(1) invariant dimension-6 lagrangian f n X L e ff = L SM + Λ 2 O n + · · · n • There are 59 “independent” dimension-six operators [Buchmuller & Wyler; Grzadkowski] • our choice for the boson operators is [Corbett, OE, Gonzalez-Fraile, Gonzalez-Garcia] [Hagiwara, Ishihara, Szalapski, Zeppenfeld] O W W = Φ † ˆ O BB = Φ † ˆ W µ ν ˆ B µ ν ˆ O GG = Φ † Φ G a µ ν G aµ ν W µ ν Φ B µ ν Φ O BW = Φ † ˆ O W = ( D µ Φ ) † ˆ O B = ( D µ Φ ) † ˆ B µ ν ˆ W µ ν Φ W µ ν ( D ν Φ ) B µ ν ( D ν Φ ) O Φ , 2 = 1 O Φ , 4 = ( D µ Φ ) † ( D µ Φ ) O Φ , 1 = ( D µ Φ ) † Φ Φ † ( D µ Φ ) 2 ∂ µ � Φ † Φ Φ † Φ Φ † Φ � � � � � ∂ µ constrained by EWPD eliminated with EOM � � ∂ µ + ig 0 B µ / 2 + ig σ a W a ˆ D µ Φ = µ / 2 Φ with W µ ν = ig σ a W a µ ν / 2 ˆ B µ ν = ig 0 B µ ν / 2

2. Linear effective lagrangians to describe the LHC data? • new state belongs to SU(2) doublet • consider SU(2) x U(1) invariant dimension-6 lagrangian f n X L e ff = L SM + Λ 2 O n + · · · n • There are 59 “independent” dimension-six operators [Buchmuller & Wyler; Grzadkowski] • our choice for the boson operators is [Corbett, OE, Gonzalez-Fraile, Gonzalez-Garcia] [Hagiwara, Ishihara, Szalapski, Zeppenfeld] O W W = Φ † ˆ O BB = Φ † ˆ W µ ν ˆ B µ ν ˆ O GG = Φ † Φ G a µ ν G aµ ν W µ ν Φ B µ ν Φ O BW = Φ † ˆ O W = ( D µ Φ ) † ˆ O B = ( D µ Φ ) † ˆ B µ ν ˆ W µ ν Φ W µ ν ( D ν Φ ) B µ ν ( D ν Φ ) O Φ , 2 = 1 O Φ , 4 = ( D µ Φ ) † ( D µ Φ ) O Φ , 1 = ( D µ Φ ) † Φ Φ † ( D µ Φ ) 2 ∂ µ � Φ † Φ Φ † Φ Φ † Φ � � � � � ∂ µ constrained by EWPD eliminated with EOM � � ∂ µ + ig 0 B µ / 2 + ig σ a W a ˆ D µ Φ = µ / 2 Φ with W µ ν = ig σ a W a µ ν / 2 f GG Λ 2 O GG + f BB Λ 2 O BB + f W W Λ 2 O W W + f B Λ 2 O B + f W Λ 2 O W + f Φ , 2 = − α s L HV V Λ 2 O Φ , 2 e ff 8 π ˆ B µ ν = ig 0 B µ ν / 2