Higgs boson couplings in the nonminimal Higgs sectors

Higgs boson couplings in the non-minimal Higgs sectors Kei Yagyu University of Florence HPNP 2017 1 st March, University of Toyama

　Contents p Introduction 　　- Bottom-Up approach - Implications to the study of h couplings p 2 important examples 　　- 2 HDMs and Higgs singlet Model - Pattern of deviations in h couplings at the tree level p Deviations in Higgs boson couplings at one-loop level p Summary

Minimal or Non-Minimal? p LHC Run-I: Existence of one SU(2)L doublet scalar field. p Question: minimal or non-minimal? If non-minimal, then what is the number of multiplets? what are their representations? what kinds of symmetries behind? what is the scale of the 2 nd Higgs boson? … Minimal Higgs: There is no strong motivation/reason. Non-Minimal Higgs: There are motivations. Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 1/22

　Motivations of non-minimal Higgs BSM Higgs Sector p Supersymmetry At least 2 -doublets p p. NGB Higgs Depends on the global sym. breaking Talk by Stefania Ex：SO(6)/SO(4)×SO(2) → 2 HDM p Extended Gauge Models Non-minimal Higgs sectors can 　 e. g. , 331, 3221 etc appear as low energy eff. theory p BSM Phenomena　 Extra scalar multiplets play a role (ν-mass, DM, BAU, Muon g-2） to explain them. Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 2/22

　Motivations of non-minimal Higgs BSM Higgs Sector p Supersymmetry At least 2 -doublets p p. NGB Higgs Depends on the global sym. breaking Talk by Stefania Ex：SO(6)/SO(4)×SO(2) → 2 HDM p Extended Gauge Models Non-minimal Higgs sectors can 　 e. g. , 331, 3221 etc appear as low energy eff. theory p BSM Phenomena　 (ν-mass, DM, BAU, Muon g-2） Probe Extra scalar multiplets play a role to explain them. Higgs is a Probe of New Physics!! Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 2/22

　Bottom-Up Approach p How can we narrow down the various possibilities of the Higgs sector? 1. Effective field theory or Generic, but less prediction power Renormallizable models Specific, but high precision calculations possible 2. Electroweak rho parameter: ρexp = 1. 0004 + 0. 0003 - 0. 0004 T: isospin, Y: hypercharge, v: VEV Φ + singlets + doublets (+ inert scalars) + higher reps. /w small VEV or VEV alignments Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 3/22

　Bottom-Up Approach p How can we narrow down the various possibilities of the Higgs sector? 1. Effective field theory or Generic, but less prediction power Renormallizable models Specific, but high precision calculations possible 2. Electroweak rho parameter: ρexp = 1. 0004 + 0. 0003 - 0. 0004 Φ + singlets + doublets + “higher reps. ” + inert scalars 3. FCNCs: These must be tiny from exp. (e. g. , B 0 -B 0 mixing) It constrains the structure of multi-doublet models Natural way to avoid tree FCNCs: Natural Flavor Conservation (NFC) 4. What else? Higgs Couplings!! Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 4/22

　In this talk p We consider simple non-minimal Higgs sectors, i. e. , Φ + X, and discuss the deviation in the h couplings from the SM value. Possible situations after Run-II Discovery of new Higgs Yes B: Fingerprint identification A C No A: Fingerprint identification (with fixed parameters) Extraction of the 2 nd Higgs mass Yes C: Constraint on model parameters Coup. deviation 　　Consistency check B D No D: Constraint on model parameters Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 5/22

Current and Future Measurements κX = gh. XX(Exp)/gh. XX(SM) Present (LHC Run-I: ATLAS + CMS) ar. Xiv: 1606. 02266 [hep-ex] Future ar. Xiv: 1310. 8361 [hep-ex] ~10% ~20% ~15% ~20% ~10% To compare future precise measurements, precise calculations are necessary! Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 6/22

　Contents p Introduction 　　- Bottom-Up approach - Implications to the study of h couplings p 2 important examples 　　- 2 HDMs and Higgs singlet Model - Pattern of deviations in h couplings at the tree level p Deviations in Higgs boson couplings at one-loop level p Summary

Ex. 1 2 HDM p The Higgs basis Davidson, Haber PRD 71 (2005) V Ge 6 24 v~ tanβ = v 2/v 1 NG boson CP-even Higgs Charged Higgs CP-odd Higgs SM-like Higgs with 125 Ge. V Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 7/22

Ex. 1 2 HDM with NFC Glashow, Weinberg (1977) p Natural Flavor Conservation (NFC) Scenario p This can be realized by imposing a (softly-broken) Z 2 symmetry. Φu, d, e : Either Φ 1 or Φ 2 Barger, Hewett, Phillips, PRD 41 (1990); Grossman, NPB 426 (1994) Type-I u d Φ２ e Type-II Φ２ Φ１ u d e Type-X (Leptophilic) Φ２ Φ１ Φ２ u d Type-Y (Flipped) e Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors Φ１ u d e 8/22

Ex. 1 2 HDM with NFC p Kinetic term p Yukawa couplings V V ξd ξe Type I cotβ Type II cotβ -tanβ Type X cotβ -tanβ Type Y cotβ -tanβ cotβ f = (SM) × sin(β-α) h ξu h f = (SM) × 　[sin(β-α) +ξf cos(β-α)] Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 9/22

Ex. 2 Higgs Singlet Model (HSM) p We consider a model with an SU(2) singlet real scalar field S. p Singlet VEV (v. S) does not contribute to EWSB and fermion mass gen. → We can simply take v. S = 0 without loss of generality. p The double-singlet mixing is induced from the Φ†Φ S term. The h couplings deviate only by the mixing α at the tree level. p V f = (SM) × cos α h V = (SM) × cos α h f Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 10/22

Alignment/Decoupling limit p Alignment limit: κV → 1 p Decoupling limit: M 2 nd → ∞ HSM Blasi, De Curtis , KY M 2 nd → ∞ : κV → 1 2 HDM ・Perturbative uni. ・Vacuum stab. ・S and T Allowed Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 11/22

Alignment/Decoupling limit p p Alignment limit: κV → 1 Decoupling limit: M 2 nd → ∞ HSM Blasi, De Curtis , KY Speed of the decoupling is quite different. 2 HDM ・Perturbative uni. ・Vacuum stab. ・S and T Allowed Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 11/22

Alignment/Decoupling limit p p Alignment limit: κV → 1 Decoupling limit: M 2 nd → ∞ HSM Blasi, De Curtis , KY Speed of the decoupling is quite different. 2 HDM ・Perturbative uni. ・Vacuum stab. ・S and T Allowed Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 11/22

Coupling deviations at the tree level ΔκX = κX - 1 Tanβ = 1. 5 Tanβ = 3 Type-I, Y : tanβ > 1 → smaller Δκτ Type-II, X: tanβ > 1 → larger Δκτ HSM : ΔκV = Δκτ 1σ Depending on |Δκτ|, we can classify HSM/Type-I, Y/Type-II, X Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 12/22

Coupling deviations at the tree level ΔκV = (-1 ± 0. 4)%, tanβ ≥ 1 Type-I and Y (Type-II and X) can be distinguished by the sign of Δκb!! Type-II seems to be favored. 1σ But, we need more data to really say excluded or determined. Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 14/22

　Contents p Introduction 　　- Bottom-Up approach - Implications to the study of h couplings p 2 important examples 　　- 2 HDMs and Higgs singlet Model - Pattern of deviations in h couplings at the tree level p Deviations in Higgs boson couplings at one-loop level p Summary

　Higgs couplings at 1 -loop level p From the tree level calculation of κV, κτ and κb, we can extract the structure (representations and types of Yuk. ) of the Higgs sector. p At future e+e- colliders, h couplings can be measured 　　with O(1)% or better accuracy. 1 -loop corrections to the Higgs boson couplings can be O(1)%. p 1 -to-1 correspondence between κV and mixing parameters is broken. Pattern of deviations can be changed. Inner parameters can be extracted. Systematic 1 -loop calculations in various Higgs sectors are inevitable! Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 15/22

H-COUP Kanemura, Kikuchi, Sakurai, KY Fortran code to calculate the h couplings at 1 -loop level in non-minimal Higgs sectors based on the (modified) on-shell renormalization scheme. h. VV htt hbb hττ hhh 2 HDMs (Type-I, ✔ ✔ ✔ II, X✔and Y) ✔ p HSM Type-I ✔ ✔ Model ✔ p Inert Doublet hγγ h. Zγ hgg ✔ ✔ ✔ ✔ Kanemura, Kikuchi, KY, NPB 907 (2016) Kanemura, Kikuchi, KY, NPB 917 (2017) Kanemura, Okada, Senaha, Yuan, Type-II ✔ ✔ ✔ ✔ Type-X ✔ ✔ ✔ ✔ Type-Y ✔ ✔ ✔ ✔ Kanemura, Kikuchi, Sakurai, PRD 94 (2016) ✔ ✔ Aoki, Kanemura, Kikuchi, KY, PLB 714 (2012) HSM p p IDM HTM Higgs Triplet Model ✔ ✔ H-COUP Ver. 1. 0 (will be public soon) PRD 70 (2004) Kanemura, Kikuchi, KY, PLB 731 (2014) Kanemura, Kikuchi, KY, NPB 896 (2015) Aoki, Kanemura, Kikuchi, KY, PRD 87 (2022) Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 16/22

Important diagram mΦ 2 = M 2 + λhΦΦ v 2 λhΦΦ/v = 0. 6, 1. 2, 1. 6 Wave func. ren. = - 2 HDM tanβ = 1, M 2 > 0 sin(β－α) = 1 1 -loop corrections to the h. VV (hff) couplings can be -O(1)% level. Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 17/22

Issue of Gauge Dependence N. K. Nielsen, Nucl. Phys. B 101, 173 (1975) Nielsen Identity: = On-shell condition: Gauge dependence reminds in renormalized mixing angles, e. g. , α, β. Pinch tech. Vertex corrs. pinching We can extract Self-energy like “pinch terms”. These cancel the δξ part in 2 p functions! Box graphs pinching Self-energy like Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 18/22

Issue of Gauge Dependence Expression of ΠAG^PT: Krause, Muhlleitner, Santos, Ziesche, JHEP 1609 (2016) Typically, the difference is O(0. 1)% level. Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 19/22

ΔκV-Δκτ at 1 -loop level Tree Level Type-II, X Type-I, Y 1 -loop Level (mΦ >300 Ge. V) Type-II, X HSM Type-I, Y tanβ ≥ 1, Λcutoff ≥ 3 Te. V Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 20/22

ΔκV-Δκτ at 1 -loop level Tree Level Type-II, X 1 -loop Level (fixed mΦ) 300 500 600 Type-I, Y HSM 500 300 1000 500 1500 600 tanβ ≥ 1, Λcutoff ≥ 3 Te. V Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 20/22

Δκb-Δκτ at 1 -loop level ΔκV = (-0. 5 ± 0. 4)% Type-II, X Type-I, Y HSM Type-I Type-Y Type-II Type-X HSM tanβ ≥ 1, Λcutoff ≥ 3 Te. V Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 21/22

Δκb-Δκτ at 1 -loop level ΔκV = (-1. 0 ± 0. 4)% Type-II, X Type-I, Y HSM Type-I Type-Y Type-II Type-X HSM tanβ ≥ 1, Λcutoff ≥ 3 Te. V Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 21/22

Δκb-Δκτ at 1 -loop level ΔκV = (-2. 0 ± 0. 4)% Type-II, X Type-I, Y HSM Type-I Type-Y Type-II Type-X HSM tanβ ≥ 1, Λcutoff ≥ 3 Te. V Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 21/22

Summary 　　　HSM |Δκτ| ≃|ΔκV| (Type-I, Y w/tanβ≫ 1) Δκτ < 0 ΔκV ≠ ０ |Δκτ|≳|ΔκV| Δκτ < 0 Δκb > 0 Type-Y 2 HDM Δκb < 0 Type-I 2 HDM Δκb > 0 Type-X 2 HDM Δκb < 0 Type-II 2 HDM |Δκτ|>|ΔκV| Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 22/22

Summary 　　　HSM/ |Δκτ| ≃|ΔκV| All 2 HDMs Δκτ < 0 ΔκV ≠ ０ |Δκτ|≳|ΔκV| Δκτ < 0 Δκb > 0 Type-Y 2 HDM Δκb < 0 Type-I/II 2 HDM Δκb > 0 Type-X 2 HDM Δκb < 0 Type-II 2 HDM |Δκτ|>|ΔκV| If |ΔκV|≾ 1%, then loop effects →important！ Kei Yagyu (U. of Florence) Higgs boson couplings in the non-minimal Higgs sectors 22/22

Buck up Enomoto and Watanabe, JHEP 1605, 002 (2016)

hhh coupling Tree Level, 1 -loop Level Kanemura, Kikuchi, KY, NPB 917 (2017)

Important diagrams = - κX = gh. XX(MHM)/gh. XX(SM), ΔκX = κX - 1 = ΔκV (ΔκF) ~ - 0. 6% for mΦ = 300 Ge. V, Δκh ~ +30% for mΦ = 300 Ge. V, λhΦΦ = 1. 5 v (Φ=H, A, H±)

Upper limit on λhΦΦ from triviality 2 HDMs HSM V = λΦS|Φ|2 S 2 + λS S 4 +…

κV VS κF Kanemura, Tsumura, KY, Yokoya, PRD 90 (2014) p Singlet Model κV = κF = cos α p 2 HDM-I κV ~ [tanβ-1α]cosβ 　 κF = cos α/sin β p Triplet Model κV ~ [tanβ-sqrt(8/3)α]cosβ κF = cos α/sin β p Seplet Model κV ~ [tanβ-4 α]cosβ κF = cos α/sin β

Higgs potential of 2 HDM (CPC + Z 2) p Higgs potential with softly-broken Z 2 symmetry and CP-conservation p 8 parameters v (=246 Ge. V), mh (=125 Ge. V), m. H, m. A, m. H+, sin(β-α), tanβ, and M 2 p Mass parameters [sin(β-α) ~1] mh 2 ~ λv 2, mΦ 2 ~ M 2 + λ’v 2 Φ = H±, A, H

Higgs potential of HSM p The most general potential p 7 parameters v (=246 Ge. V), mh (=125 Ge. V), m. H, sin(α), λS, λΦS, and μS p Scalar Masses

Renormalization 1. Count the # of parameters in the Lagrangian. 2. Prepare the same # of counter terms by shifting the parameters. 3. Set the same # of ren. conditions to determine the CT’s. 4. Calculate the renormalized quantities.

Renormalized Higgs Couplings 4. Calculate the renormalized quantities. Tree h. WW h. ZZ hff hhh １ PI Counter term

Renormalization in the Higgs sector 1. Count the # of parameters in the Lagrangian. ・Parameters in the potential (8) : mh, m. H, m. A, m. H+, α, β, v, M 2 ・Tadpoles (2) : T h, TH ・Wave functions (12) : Zeven(2×２), Zodd(2×２), Z±(2×２) ・Total (22) 2. Prepare the same # of counter terms by shifting the parameters. ・Parameter shift : mφ → mφ + δmφ, α → α+δα, … ・Tadpole shift : ・Field shift : Th → 0 + δTh, TH → 0 + δTh

Renormalization in the Higgs sector δv 3. Set the same # of ren. conditions. : Ren. in EW sector Hollik δM 2 : Minimal subtraction Kanemura, Okada, Senaha, Yuan Tadpole condition On-shell condition I =0 H, h Φ Φ δTh, δTH (2) =0 δmφ (4) @ p 2 = m Φ 2 On-shell condition II Φ =0 Φ @ p 2 = m Φ 2 On-shell condition III Φ Φ’ =0 @ p 2 = mΦ’ 2 δZφ (6) δα, δCHh, δCh. H δβ, δCAG, δCGA δCG+H-, δCH+G- (8)

Uncertainty for QCD corrections Lepage, Mackenzie and Peskin, 1404. 0319 [hep-ph]

湯川カップリング（3 HDM, Type-Z） Δκf = ΔκV + ξ f 1(RH)21 + ξ f 2(RH)31 ΔκV =-1%, ΔκU < 0, (RH) 21 and (RH) 31 scanned ξd 1 = -tanβ ξd 2 = -tanγ/cosβ ξe 1 = -tanβ ξe 2 = cotγ/cosβ tanγ = 1 tanγ = 2 tanγ = 1/2 Kei Yagyu (U. of Southampton) 12/25

S波振幅行列の固有値 Kanemura, Kubota, Takasugi (1993) [Diagonalized all the neutral channels] Akeroyd, Arhrib, Naimi (2000) Ginzburg, Ivanov (2003) [Diagonalized all the singly-charged channels] [Extended to the CPV 2 HDM]