Effective field theory for Higgs Physics Margherita Ghezzi Higgs - PowerPoint PPT Presentation

Effective field theory for Higgs Physics Margherita Ghezzi Higgs Hunting 2016 Paris, 1st September 2016 Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 1 / 16

Higgs Effective Lagrangian In searches for new physics we can distinguish among: Direct searches Searches for new resonances. Top-down approach: BSM models (model-dependent) Unknowns: model parameters. Bottom-up approach: EFT (”model-independent”) Unknowns: Wilson coefficients Assumptions: The dynamical degrees of freedom at the EW scale are those of the SM New Physics appears at some high scale Λ >> v (decoupling) Absence of mixing of new heavy scalars with the SM Higgs doublet SU (2) L × U (1) Y is linearly realized at high energies Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 2 / 16

Higgs Effective Lagrangian In searches for new physics we can distinguish among: Direct searches Searches for new resonances. Top-down approach: BSM models (model-dependent) Unknowns: model parameters. Bottom-up approach: EFT (”model-independent”) Unknowns: Wilson coefficients Assumptions: The dynamical degrees of freedom at the EW scale are those of the SM New Physics appears at some high scale Λ >> v (decoupling) Absence of mixing of new heavy scalars with the SM Higgs doublet SU (2) L × U (1) Y is linearly realized at high energies Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 2 / 16

Higgs Effective Lagrangian Compatibility with the SM F f κ ATLAS and CMS 2 LHC Run 1 The Higgs boson looks like a doublet 68% CL Gap between m H and the New 1 95% CL Physics scale Best fit SM expected 0 We look for small deviations from the SM: precision physics era − 1 NLO is the new standard @LHC → γ γ Combined H Many calculations at NNLO QCD − → → 2 H ZZ H WW → τ τ → H H bb Many calculations at NLO EW 0 0.5 1 1.5 2 κ f V Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 3 / 16

Higgs Effective Lagrangian Higgs doublet - EW symmetry is linearly realized c i � � Λ n − 4 O D = n L HEFT = L SM + i n > 4 i L HEFT = L SM + 1 Λ L D =5 + 1 Λ 2 L D =6 + 1 Λ 3 L D =7 + 1 Λ 4 L D =8 + . . . L D =5 and L D =7 : lepton number violating L D =8 and higher: parametrically subleading L D =6 : leading effect ✞ ☎ Λ 2 L D =6 1 L HEFT = L SM + ✝ ✆ C. N. Leung, S. T. Love and S. Rao, Z. Phys. C 31 (1986) 433 Buchm¨ uller and Wyler, NPB 268 (1986) 621 Grzadkowski, Iskrzynski, Misiak and Rosiek, JHEP 1010 (2010) 085 Contino, MG, Grojean, M¨ uhlleitner and Spira, JHEP 1307 (2013) 035 Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 4 / 16

Higgs Effective Lagrangian Higgs doublet - EW symmetry is linearly realized c i � � Λ n − 4 O D = n L HEFT = L SM + i n > 4 i L HEFT = L SM + 1 Λ L D =5 + 1 Λ 2 L D =6 + 1 Λ 3 L D =7 + 1 Λ 4 L D =8 + . . . L D =5 and L D =7 : lepton number violating L D =8 and higher: parametrically subleading L D =6 : leading effect ✞ ☎ Λ 2 L D =6 1 L HEFT = L SM + ✝ ✆ C. N. Leung, S. T. Love and S. Rao, Z. Phys. C 31 (1986) 433 Buchm¨ uller and Wyler, NPB 268 (1986) 621 Grzadkowski, Iskrzynski, Misiak and Rosiek, JHEP 1010 (2010) 085 Contino, MG, Grojean, M¨ uhlleitner and Spira, JHEP 1307 (2013) 035 Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 4 / 16

Higgs Effective Lagrangian Higgs doublet - EW symmetry is linearly realized c i � � Λ n − 4 O D = n L HEFT = L SM + i n > 4 i L HEFT = L SM + 1 Λ L D =5 + 1 Λ 2 L D =6 + 1 Λ 3 L D =7 + 1 Λ 4 L D =8 + . . . L D =5 and L D =7 : lepton number violating L D =8 and higher: parametrically subleading L D =6 : leading effect ✞ ☎ Λ 2 L D =6 1 L HEFT = L SM + ✝ ✆ C. N. Leung, S. T. Love and S. Rao, Z. Phys. C 31 (1986) 433 Buchm¨ uller and Wyler, NPB 268 (1986) 621 Grzadkowski, Iskrzynski, Misiak and Rosiek, JHEP 1010 (2010) 085 Contino, MG, Grojean, M¨ uhlleitner and Spira, JHEP 1307 (2013) 035 Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 4 / 16

Higgs Effective Lagrangian Higgs doublet - EW symmetry is linearly realized c i � � Λ n − 4 O D = n L HEFT = L SM + i n > 4 i L HEFT = L SM + 1 Λ L D =5 + 1 Λ 2 L D =6 + 1 Λ 3 L D =7 + 1 Λ 4 L D =8 + . . . L D =5 and L D =7 : lepton number violating L D =8 and higher: parametrically subleading L D =6 : leading effect ✞ ☎ Λ 2 L D =6 1 L HEFT = L SM + ✝ ✆ C. N. Leung, S. T. Love and S. Rao, Z. Phys. C 31 (1986) 433 Buchm¨ uller and Wyler, NPB 268 (1986) 621 Grzadkowski, Iskrzynski, Misiak and Rosiek, JHEP 1010 (2010) 085 Contino, MG, Grojean, M¨ uhlleitner and Spira, JHEP 1307 (2013) 035 Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 4 / 16

Effective Lagrangian for a Higgs doublet GIMR/Warsaw basis ϕ 6 and ϕ 4 D 2 X 3 ψ 2 ϕ 3 (¯ LL )(¯ ( ¯ RR )( ¯ (¯ LL )( ¯ LL ) RR ) RR ) (¯ l p γ µ l r )(¯ (¯ f ABC G Aν µ G Bρ ν G Cµ ( ϕ † ϕ ) 3 ( ϕ † ϕ )(¯ Q ll l s γ µ l t ) Q ee (¯ e p γ µ e r )(¯ e s γ µ e t ) Q le l p γ µ l r )(¯ e s γ µ e t ) Q G Q ϕ Q eϕ l p e r ϕ ) ρ f ABC � Q (1) q s γ µ q t ) u s γ µ u t ) (¯ u s γ µ u t ) G Aν µ G Bρ ν G Cµ ( ϕ † ϕ ) � ( ϕ † ϕ ) ( ϕ † ϕ )(¯ (¯ q p γ µ q r )(¯ Q uu (¯ u p γ µ u r )(¯ Q lu l p γ µ l r )(¯ Q � Q ϕ � Q uϕ q p u r � ϕ ) qq G ρ � � ⋆ � � Q (3) ( ¯ d p γ µ d r )( ¯ (¯ l p γ µ l r )( ¯ (¯ q p γ µ τ I q r )(¯ q s γ µ τ I q t ) d s γ µ d t ) d s γ µ d t ) ε IJK W Iν µ W Jρ ν W Kµ ϕ † D µ ϕ ϕ † D µ ϕ ( ϕ † ϕ )(¯ Q dd Q ld Q W Q ϕD Q dϕ q p d r ϕ ) qq ρ Q (1) (¯ q s γ µ q t ) u s γ µ u t ) e s γ µ e t ) l p γ µ l r )(¯ Q eu (¯ e p γ µ e r )(¯ Q qe (¯ q p γ µ q r )(¯ ε IJK � W Iν µ W Jρ ν W Kµ Q � lq ρ W Q (3) (¯ e p γ µ e r )( ¯ Q (1) l p γ µ τ I l r )(¯ q s γ µ τ I q t ) (¯ d s γ µ d t ) (¯ q p γ µ q r )(¯ u s γ µ u t ) Q ed qu X 2 ϕ 2 ψ 2 Xϕ ψ 2 ϕ 2 D lq Q (1) u p γ µ u r )( ¯ d s γ µ d t ) Q (8) q p γ µ T A q r )(¯ u s γ µ T A u t ) (¯ (¯ qu ↔ ud (¯ Q (1) D µ ϕ )(¯ Q ϕG ϕ † ϕ G A µν G Aµν Q eW l p σ µν e r ) τ I ϕW I ( ϕ † i l p γ µ l r ) µν ϕl Q (8) u p γ µ T A u r )( ¯ Q (1) q p γ µ q r )( ¯ (¯ d s γ µ T A d t ) (¯ d s γ µ d t ) ↔ ud qd ϕ † ϕ � (¯ Q (3) µ ϕ )(¯ Q ϕ � G A µν G Aµν Q eB l p σ µν e r ) ϕB µν ( ϕ † i D I l p τ I γ µ l r ) ϕl Q (8) q p γ µ T A q r )( ¯ G (¯ d s γ µ T A d t ) qd ↔ Q ϕW ϕ † ϕ W I µν W Iµν Q uG (¯ q p σ µν T A u r ) � ϕ G A Q ϕe ( ϕ † i D µ ϕ )(¯ e p γ µ e r ) µν (¯ LR )( ¯ RL ) and (¯ LR )(¯ LR ) B -violating ↔ ϕ † ϕ � q p σ µν u r ) τ I � Q (1) Q ϕ � W I µν W Iµν Q uW (¯ ϕ W I ( ϕ † i D µ ϕ )(¯ q p γ µ q r ) � � � � µν ϕq (¯ p e r )( ¯ d s q j W Q ledq l j t ) Q duq ε αβγ ε jk ( d α p ) T Cu β ( q γ j s ) T Cl k r t ↔ Q (3) � � � � Q ϕB ϕ † ϕ B µν B µν Q uB (¯ q p σ µν u r ) � ϕ B µν ( ϕ † i D I µ ϕ )(¯ q p τ I γ µ q r ) Q (1) ϕq (¯ q j p u r ) ε jk (¯ q k s d t ) ε αβγ ε jk ( q α j p ) T Cq β k ( u γ s ) T Ce t Q qqu quqd r ↔ ϕ † ϕ � � � � � Q ϕ � B µν B µν Q dG (¯ q p σ µν T A d r ) ϕ G A Q ϕu ( ϕ † i D µ ϕ )(¯ u p γ µ u r ) Q (8) Q (1) (¯ q j p T A u r ) ε jk (¯ q k s T A d t ) ε αβγ ε jk ε mn ( q α j p ) T Cq β k ( q γ m s ) T Cl n B µν qqq quqd r t ↔ � � � � D µ ϕ )( ¯ Q ϕW B ϕ † τ I ϕ W I µν B µν Q dW (¯ q p σ µν d r ) τ I ϕ W I Q ϕd ( ϕ † i d p γ µ d r ) Q (1) (¯ Q (3) l j p e r ) ε jk (¯ q k s u t ) ε αβγ ( τ I ε ) jk ( τ I ε ) mn ( q α j p ) T Cq β k ( q γ m s ) T Cl n µν qqq lequ r t ε αβγ � � � � ϕ † τ I ϕ � W I µν B µν (¯ q p σ µν d r ) ϕ B µν i ( � ϕ † D µ ϕ )(¯ u p γ µ d r ) Q (3) (¯ Q ϕ � Q dB Q ϕud l j p σ µ ν e r ) ε jk (¯ q k s σ µ ν u t ) Q duu ( d α p ) T Cu β ( u γ s ) T Ce t W B lequ r 15 bosonic operators 25 four-fermion operators (assuming barionic number 19 single-fermionic-current conservation) operators 15+19+25=59 independent operators (for 1 fermion generation) Grzadkowski, Iskrzynski, Misiak, Rosiek, JHEP 1010 (2010) 085 Margherita Ghezzi EFT for Higgs Physics Higgs Hunting 2016 5 / 16