The low energy theories of the Higgs sector Daniel Egana-Ugrinovic - PowerPoint PPT Presentation

The low energy theories of the Higgs sector Daniel Egana-Ugrinovic Scott Thomas Rutgers University Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 1 / 12

The LHC is turning on: it is time to probe the Higgs sector. Recall that m 2 = 1 . 0008 +0 . 0017 W ρ = (1) Z cos 2 θ W − 0 . 0007 m 2 Delicate relation ρ = 1 only preserved “ easily ” if the BSM Higgs sector contains only singlets or doublets . (or no mixing with the Higgs). Since LHC data is consistent with SM like Higgs couplings (alignment limit), the decoupling limit is a very attractive possibility: → Use EFT’s!! Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 2 / 12

For simplicity we will work at tree level . Example: Higgs mixing with a heavy real singlet. Fermionic and gauge higgs couplings must be diluted accordingly. In EFT this is packaged in WF renormalization through operators η ∂ µ ( H † H ) ∂ µ ( H † H ) (2) m 2 s Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 3 / 12

The 2HDM General 2HDM: 11 parameters only in the potential! . Work in the Higgs basis , < H 2 > = 0 � � 1 H † 2 H † 12 H † m 2 m 2 m 2 V = ˜ 1 H 1 + ˜ 2 H 2 + ˜ 1 H 2 + h.c. + 1 1 H 1 ) 2 + ˜ ˜ λ 1 ( H † λ 6 H † 1 H 1 H † 1 H 2 + . . . (3) 2 From EWSB conditions 12 = − 1 m 2 λ 6 v 2 ˜ ˜ 2 → ED := n D + 2 n ˜ Effective dimension m 2 12 Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 4 / 12

Example 1: Modifications to the Higgs potential Consider the following diagrams at zero momentum H 1 H 1 H 1 λ † ˜ ˜ λ 6 m 2 † H † ˜ 6 ˜ λ 6 H 1 12 1 H † H 1 1 H † H † H † 1 1 1 ˜ 6 ˜ (˜ m 2 λ ∗ λ ∗ λ 6 6 ˜ 12 + h . c . ) ( H † 1 H 1 ) 3 ( H † 1 H 1 ) 2 m 2 m 2 ˜ ˜ 2 2 They are of the same effective dimension (six) Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 5 / 12

Example 2: Modifications to Higgs-fermion interaction Lagrangian and four fermion interactions Q Q H 1 H 1 H 1 ˜ λ u † ˜ ˜ λ † λ u m 2 ˜ 2 ij 6 2 ij 12 H † 1 u ¯ u ¯ � ˜ 2 ij ˜ ˜ 2 ij ˜ � λ u λ ∗ λ u λ ∗ 6 6 H † − Q i H 1 1 H 1 + u j ¯ (4) m 2 m 2 ˜ ˜ 2 2 They are of the same effective dimension (six) Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 6 / 12

Summary of effects We work at ED 6 in the fermionic sector, and 8 in the bosonic sector. After calculating ≈ 20 diagrams we get Is modified at effective dimension: Higgs potential ≥ 6 Higgs-fermion interactions * ≥ 6 Four-fermion interactions * ≥ 6 Higgs kinetic lagrangian ≥ 8 Higgs-gauge boson interactions ≥ 8 ∗ carries CP and/or flavor violation. Compare with the xSM: in that case, Higgs-gauge boson interactions are modified at effective dimension 6. Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 7 / 12

List of results Only one coupling (some sort of “complex” alignment parameter) and the yukawas of the heavy higgs control most of the modifications to the SM Higgs couplings at first order. � v 6 � �� g ϕ VV = 2 m 2 v 4 1 − 1 ˜ 6 ˜ V λ ∗ λ 6 + O m 4 m 6 v 2 ˜ ˜ 2 2 � v 6 � �� g ϕ 2 VV = 2 m 2 v 4 1 − 3˜ λ † 6 ˜ V + O (5) λ 6 m 4 m 6 v 2 ˜ ˜ 2 2 � ˜ � � v 2 � v 4 2 ij ˜ λ f λ ∗ ϕ ij = m f � � 6 λ f i v δ ij − 2 + O √ m 2 m 4 ˜ ˜ 2 2 2 2 No CP violation in the bosonic interactions up to at least effective � ˜ 6 ˜ � ˜ 7 ˜ λ 2 λ 2 λ ∗ � λ ∗ � dimension 10 (or more). Background invariants Arg , Arg are 5 5 irrelevant at ED 6. Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 8 / 12

Further applications: CP violation. In any 2HDM with Glashow-Weinberg conditions, there is only one relevant CP violating phase at ED 6 , carried exclusively in the higgs-fermion interactions. � v 4 θ := v 2 � 6 e − i ξ/ 2 � � � � ˜ λ ∗ sin arg + O m 2 m 2 ˜ ˜ 2 2 Important for EDM’s. We can directly relate an EDM measurement with a higgs-fermion coupling measurement. γ t t t γ ϕ e e e Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 9 / 12

Example: type II 2HDM At large tan β , only significant deviation from SM couplings is in down type yukawas. � v 4 m d ,ℓ 6 e − i ξ/ 2 tan β v 2 � �� λ d ,ℓ 1 + ˜ i λ ∗ ϕ ij = δ ij + O m 2 m 4 v ˜ ˜ 2 2 � v 4 m d ,ℓ 2 tan β v 2 � �� 6 e − i ξ v λ d ,ℓ ϕ 2 ij = v 2 λ d ,ℓ 3˜ λ ∗ i ϕ 3 ij = δ ij + O (6) m 2 m 4 v ˜ ˜ 2 2 Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 10 / 12

Further applications: flavor physics. Flavor physics: flavor violation in four fermion operators from integrating out the heavy doublet and the higgs boson come at the same order . ˜ 2 ij ˜ λ u † λ u λ u ϕ ij λ u 2 mn ϕ mn u † m Q † ( Q i ¯ u j )(¯ n ) ( u i ¯ u j )( u m ¯ u n ) m 2 m 2 ˜ 2 ϕ From heavy higgs From light higgs But they have a different chiral , parametric and flavor violating structure. Important for flavor observables. If we are in the exact alignment limit, only deviation to SM is in four fermion operators induced by integrating out the heavy Higgs. Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 11 / 12

Conclusions The results presented here, unless stated otherise are valid for the most general 2HDM with heavy BSM higgses . Is modified at effective dimension: Higgs potential ≥ 6 Higgs-fermion interactions * ≥ 6 Four-fermion interactions * ≥ 6 Higgs kinetic lagrangian ≥ 8 Higgs-gauge boson interactions ≥ 8 ∗ carries CP and/or flavor violation. Daniel Egana, Scott Thomas. Rutgers University May 4, 2015 12 / 12