Fingerprinting of the Higgs boson couplings as a probe of new physics models The 11 th LHC Physics Monthly Meeting, KIAS, Feb. 18, 2014 Kei Yagyu (National Central U.)

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126 GeV Higgs Explained Minimal (1 doublet) EW data, Flavor, … 4

Extended Higgs sectors Extra Singlets Doublets Triplets… 126 GeV Higgs Explained Minimal (1 doublet) EW data, Flavor, … 5

126 GeV Higgs Introduce Extended Higgs sectors Extra Singlets Doublets Triplets… Minimal (1 doublet) Beyond the SM Neutrino mass, Dark matter and Baryon asymmetry Explained EW data, Flavor, … 6

126 GeV Higgs Determine Higgs prop. Determine Extended Higgs sectors Extra Singlets Doublets Triplets… Minimal (1 doublet) Beyond the SM Neutrino mass, Dark matter and Baryon asymmetry EW data, Flavor, … 7

126 GeV Higgs Beyond the SM Neutrino mass, Dark matter and Baryon asymmetry Determine Higgs prop. Determine Extended Higgs sectors Extra Singlets Doublets Triplets… Minimal (1 doublet) Bottom up Approach! EW data, Flavor, … 8

126 GeV h H ++, H +, H, A,... h 2. Indirect search 1. Direct search H ++, H +, H, A, … Discovery Studying both ways is important to determine the structure of the Higgs sector. Bottom up Approach 126 GeV Energy 9 Measuring effects on the 126 GeV Higgs boson

126 GeV h H ++, H +, H, A,... h 2. Indirect search 1. Direct search H ++, H +, H, A, … Discovery Measuring effects on the 126 GeV Higgs boson Studying both ways is important to determine the structure of the Higgs sector. Bottom up Approach 126 GeV Energy 10

Indirect Search Patterns of deviation in various Higgs couplings strongly depend on the structure of the Higgs sector. Indirect search = Precision test of Higgs couplings hbb hττ hcc hγγ hVV hhh Make a “Fingerprint” from precise measurements. Minimal Singlet Models 2HDMs Triplet Models etc… Compare 11 ExperimentsTheory

The hZZ coupling can be measured by 1 % accuracy at the ILC(250) ! Higgs coupling measurements ILC, TDR ILC, Higgs White Paper, arXiv: (300/fb) 12

The hVV and hff couplings can be measured by 1 % accuracy at the ILC(500) !! Higgs coupling measurements (300/fb) ILC, TDR ILC, Higgs White Paper, arXiv:

The hVV and hff couplings can be measured by 1 % accuracy at the ILC(500) !! Higgs coupling measurements (300/fb) ILC, TDR ILC, Higgs White Paper, arXiv:

Contents Introduction - Bottom up approach (Indirect search) Deviations in the Higgs boson couplings in various Higgs sectors - The hVV and hff couplings at the tree level Higgs boson couplings in the 2HDMs - Tree level - One-loop level Summery 15

1. Electroweak rho parameter Basic Constraints There are two guidelines to restrict Higgs sectors. ρ exp = Models with ρ tree = 1 seems to be a natural choice. TY 10 1/2 32 …… Alignment of (exotic) VEVs Ex. Model with doublet (Y=1/2) + triplet (Y=1) + triplet (Y=0) (Georgi-Machacek model) Satisfy the relation if 16

2. Flavor Changing Neutral Current (FCNC) Tree level FCNC process should be absent. In general, multi-doublet extensions cause FCNC at the tree level Basic Constraints There are two guidelines to restrict Higgs sectors. 17 B0B0 Φ0Φ0 B0B0

B0B0 Φ0Φ0 B0B0 2. Flavor Changing Neutral Current (FCNC) Tree level FCNC process should be absent. In general, multi-doublet extensions cause FCNC at the tree level Basic Constraints Only one Higgs doublet couples to each fermion. 18 There are two guidelines to restrict Higgs sectors.

Simple Extended Higgs Sectors We consider the following simple Higgs sectors; (with ρ tree = 1 and no tree level FCNC) 1. Φ + S (Singlet) 2. Φ + D (Doublet) 3. Φ + Δ (Triplets or larger) [GM model, Septet model] 19 Hisano, Tsumura, PRD87 (2013) Kanemura, Kikuchi, KY, PRD88 (2013)

Two mixing angles Mixing between CP-even states VEVs where T: isospin, Y:hypercharge 20

Yukawa Gauge Deviations in hff and hVV Φ f f φ α Y f = m f / <φ><φ> β Φ V V φ V V <φ><φ> α β 21

Yukawa Gauge Higgs Singlet Model (φ=S) Φ f f S α Y f = m f / Φ V V S V V α ★ The singlet VEV does not contribute to the EWSB. → β=0 ( =246 GeV) ★ The hff and hVV couplings are universally suppressed. 22

Yukawa Gauge Two Higgs Doublet Model (φ=D) Φ (D) f f D (Φ) α Y f = m f / Φ V V D V V α β β ★ There are 2 patterns in κ f for each fermion f. ★ ξ = 1 23

Yukawa Gauge Model with a triplet (or higher) (φ=Δ) Φ f f Δ α Y f = m f / Φ V V Δ V V α β β ★ The hff couplings are universally suppressed. ★ ξ factor can be larger than unity. → κ V > 1 24 Ex. GM model: ξ = 2*sqrt(6)/3 Septet model : ξ = 4

SM 25

SM κ F’ 26

SM κ F’ κ F = κ F’ 27

SM κ F’ κ F = κ F’ 28

Gauge vs Yukawa -π/4 < α < +π/4 0.1 < tanβ < 100 Singlet Model 2HDM (Type-I) Georgi-Machacek Model [ξ = 2*Sqrt(6)/3] 29

30 -π/4 < α < +π/4 0.1 < tanβ < 100 Tau vs Bottom Singlet 2HDM (Type-I) Georgi-Machacek Model 2HDM (Type-II) 2HDM (Type-X) 2HDM (Type-Y)

Contents Introduction - Bottom up approach (Indirect search) Deviations in the Higgs boson couplings in various Higgs sectors - The hVV and hff couplings at the tree level Higgs boson couplings in the 2HDMs - Tree level - One-loop level Summery 31 S. Kanemura, M. Kikuchi, KY, appear in PLB, arXiv: [hep-ph]

2HDMs In general, Yukawa Lagrangian is given by To avoid the tree level FCNC, one of the Yukawa couplings should be forbidden. Z 2 symmetry (softly-broken) Glashow, Weinberg, PRD15 (1977) Z 2 symmetry (unbroken) Barbieri, Hall, Rychkov, PRD74 (2006) S 3 symmetry Kajiyama, Okada, KY, arXiv: [hep-ph] U(1) symmetry Ko, Omura, Yu, JHEP1201 (2012) … 32

2HDMs with the softly-broken Z 2 sym. In general, Yukawa Lagrangian is given by To avoid the tree level FCNC, one of the Yukawa couplings should be forbidden. Z 2 symmetry (softly-broken) Glashow, Weinberg, PRD15 (1977) Z 2 symmetry (unbroken) Barbieri, Hall, Rychkov, PRD74 (2006) S 3 symmetry Kajiyama, Okada, KY, arXiv: [hep-ph] U(1) symmetry Ko, Omura, Yu, JHEP1201 (2012) … There are four independent types of Yukawa interactions. 33

Barger, Hewett, Phillips (1990), Grossman (1994) u d Φ２Φ２ e Φ１Φ１ u d Φ２Φ２ e u d Φ２Φ２ e Φ１Φ１ Type-I Type-II (MSSM) u d Φ２Φ２ e Φ１Φ１ Type-X (Leptophilic) Type-Y (Flipped) Aoki, Kanemura, Tsumura, KY (2008) Four Yukawa Interactions Under the Z 2 symmetry, two doublets are transformed as Φ 1 → +Φ 1 and Φ 2 → -Φ 2. 34

In the Higgs basis, two doublets can be parameterized as: tanβ = / Mass Eigenstates NG bosons Charged Higgs CP-even Higgs CP-odd Higgs SM-like Higgs boson w/126 GeV 35

ξuξu ξdξd ξeξe Type-Icotβ Type-IIcotβ-tanβ Type-Xcotβ -tanβ Type-Ycotβ-tanβcotβ Yukawa/Gauge Interaction h V V = (SM) × sin(β-α) h f f = (SM) × [sin(β-α)+ξ f cos(β-α)] 36

Higgs Potential The Higgs potential under the softly-broken Z 2 sym. and CP-invariance Mass formulae with sin(β-α) ~1 We have 8 parameters in the potential. They can be interpreted by v (=246 GeV), m h (=126 GeV), m H, m A, m H+, sin(β-α), tanβ, and M 2 m h 2 ~ λv 2, m Φ 2 ~ M 2 + λv 2 37

SM-like/Decoupling Limit SM-like limit: taking sin(β-α) → 1 All the Higgs boson couplings become the same value as in the SM Higgs couplings at the tree level. Decoupling limit: taking M 2 (=m Φ 2 ) → ∞ Decoupling limit can be taken only when the SM-like limit is taken. [m Φ 2 ~ M 2 + λv 2 ] 38

Decoupling/SM-like Limit Excluded by unitarity (m H = m A = m H+ = M =) 10% dev. 1% dev. 0.1% dev. cos(β-α) > 0 cos(β-α) < 0 39 δ =

Decoupling/SM-like Limit Excluded by unitarity κ V = sin(β-α) → 1 (m H = m A = m H+ = M =) 10% dev. 1% dev. 0.1% dev. cos(β-α) > 0 cos(β-α) < 0 δ = 40

Decoupling/SM-like Limit Excluded by unitarity (m H = m A = m H+ = M =) 10% dev. 1% dev. 0.1% dev. cos(β-α) > 0 cos(β-α) < 0 δ = 41

Patterns of Deviation in hff Couplings h f f = (SM) × [sin(β-α) + ξ f cos(β-α)] (SM) × [sin(β-α) + cotβ cos(β-α)] (SM) × [sin(β-α) - tanβ cos(β-α)] (SM) × = ~ For cos(β-α) > 0 cos(β-α) < 0 δ ≪ 1 δ = 1 - sin(β-α) If κ V ≠ 1 is found, several patterns of deviation in hff appear. u d cotβ e Type-I u d cotβ e tanβ Type-II u d cotβ e tanβ Type-X u d cotβ e tanβ Type-Y 42

Patterns of Deviation in hff Couplings h f f = (SM) × [sin(β-α) + ξ f cos(β-α)] (SM) × [sin(β-α) + cotβ cos(β-α)] (SM) × [sin(β-α) - tanβ cos(β-α)] (SM) × = ~ For cos(β-α) > 0 cos(β-α) < 0 δ ≪ 1 δ = 1 - sin(β-α) If κ V ≠ 1 is found, several patterns of deviation in hff appear. u d cotβ e Type-I u d cotβ e tanβ Type-II u d cotβ e tanβ Type-X u d cotβ e tanβ Type-Y 43

Bottom vs Tau κ V 2 = 0.99, 0.95, (δ ~ 0.005, 0.02) cos(β-α) < 0 44

How these predictions can be modified by taking into account radiative corrections? The hff and hVV couplings can be measured with O(1)% accuracy. In order to compare precision measurements, to include radiative corrections are essentially important! Radiative Corrections 1-loop level 45

Radiative Corrections in the 2HDMs There are papers for 1-loop corrections to the Higgs boson couplings in 2HDMs. Hollik, Penaranda, Eur. Phys. J. C23 (2002) [in the MSSM Higgs sector] Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558, (2003); Kanemura, Okada, Senaha, Yuan, PRD70 (2004). hhh hVV Kanemura, Okada, Senaha, Yuan, PRD70 (2004). hff Guasch, Hollik, Penaranda, PLB515 (2001) [in the MSSM Higgs sector] We discuss 1-loop corrections to the hff couplings in the four types of the 2HDM. 46

Decoupling/Nondecoupling NP loop effects to the low energy obs. vanish when new particles are heavy. Appelquist, Carazzone (1975) Decoupling theorem 1/M n → 0 (M → ∞) Violation of the decoupling theorem SM NP+SM M → ∞ SM Top mass：m t = y t v Scalar boson mass：m φ 2 = λv 2 + M 2 (with λv 2 > M 2 ) If a particle mass is (mostly) given by the Higgs VEV, the particle loop effect does not vanish even in rather large mass case. E.g., 47

The hhh in the 2HDM Φ = H, A, H ± Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558 (2003) 48

The hhh in the 2HDM Φ = H, A, H ± In the case with M 2 >> λv 2, we can see the decoupling behavior. Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558 (2003) 0 49

The hhh in the 2HDM Φ = H, A, H ± Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558 (2003) ~1 In the case with M 2 < λv 2, nondecoupling effects (quartic power of the masses) appear. 50

Renormalized hff vertices Renormalized hff vertex Renormalized scale factor at on-shell The counter term contribution 51

Parameter Shifts Fermion masses and wave functions CP-even Higgs sector and mixing angle β The VEV Kanemura, Okada, Senaha, Yuan, PRD70 (2004). 52

On-shell Renormalization Conditions = 0 hH p 2 =mh 2 hH p 2 =mH 2 = h h p 2 =mh 2 = 0 f f p 2 =mf 2 = 0 f f p 2 =mf 2 = 0 G0G0 A p 2 =mZ 2 = G0G0 A p 2 =mA 2 = 0 δβ (and δC A ) δZ h, δα and δC h δm f and δZ V f The counter term δv is determined from the EW on-shell RCs. Hollik, Fortsch. Phys. 38, 165 (1990). 53

Decoupling [sin(β-α)=1, m H+ =m A =m H (=m Φ ) and m Φ 2 -M 2 = (300 GeV) 2 ] SM Shinya Kanemura, Mariko Kikuchi and KY, arXiv: tanβ = 1 tanβ = 3

Nondecoupling [sin(β-α)=1, m H+ =m A =m H (=m Φ ) and M 2 = 0] Shinya Kanemura, Mariko Kikuchi and KY, arXiv:

Nondecoupling [sin(β-α)=1, m H+ =m A =m H (=m Φ ) and M 2 = 0] Shinya Kanemura, Mariko Kikuchi and KY, arXiv:

Fingerprinting at the tree level cos(β-α) < 0, tanβ = 1, 2, 3 and 4, Shinya Kanemura, Mariko Kikuchi and KY, arXiv:

Fingerprinting at the 1-loop level cos(β-α) < 0, tanβ = 1, 2, 3 and 4, m H+ = m A = m H (=m Φ ), 100 GeV < m Φ < 1 TeV, 0 < M < m Φ, Unitarity + Vacuum stab. Shinya Kanemura, Mariko Kikuchi and KY, arXiv:

Fingerprinting at the 1-loop level cos(β-α) < 0, tanβ: Scanned m H+ = m A = m H (=m Φ ), 100 GeV < m Φ < 1 TeV, 0 < M < m Φ, Unitarity + Vacuum stab. Shinya Kanemura, Mariko Kikuchi and KY, arXiv:

Fingerprinting at the 1-loop level cos(β-α) < 0, tanβ: Scanned m H+ = m A = m H (=m Φ ), 100 GeV < m Φ < 1 TeV, 0 < M < m Φ, Unitarity + Vacuum stab. Shinya Kanemura, Mariko Kikuchi and KY, arXiv:

One-loop corrected hZZ coupling Even taking the maximal nondecoupling case (M 2 =0), the amount of correction is less than 1%. 1 - sin 2 (β - α) Kanemura, Okada, Senaha, Yuan, PRD70 (2004). Tanβ = 2, m Φ = 300 GeV 61

Indirect Search = Comparing fingerprints of the Higgs couplings. Typical patterns of deviations in extended Higgs sectors at tree level Points: CP-even Higgs mixing and VEV sharing 1. Higgs singlet model → κ f and κ V are universally suppressed. 2. Two Higgs doublet models → 4 patterns in κ f ’s. 3. Triplet models → κ f are universally suppressed and κ V can be larger than 1. Radiative corrections to the Higgs boson couplings Points: (Non)decoupling property of extra Higgs bosons 1-loop corrections from extra Higgs bosons to the hhh, hff and hVV couplings can be maximally O(100)%, O(10)% and O(1)%, respectively. If 1% deviation in the hZZ couplings is found at the ILC(250), we can discriminate the four types of 2HDM by precisely measured hff couplings at ILC(250) or ILC(500). Summary 62

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Vacuum stability + Unitarity 64

Unitarity bound for the Singlet Model Kang, Park, arXiv: [Singlet] 65

Gauge vs Yukawa -π/4 < α < +π/4 0.1 < tanβ < 100 Singlet Model 2HDM (Type-I) Georgi-Machacek Model [ξ = 2*Sqrt(6)/3] Unitarity const. w/ 300 GeV. Kang, Park, arXiv: [Singlet] Kanemura, Okada, Senaha, Yuan, PRD70 (2004) [2HDM] Aoki, Kanemura, PRD77 (2008) [GM] 66

Gauge vs Yukawa -π/4 < α < +π/4 0.1 < tanβ < 100 Singlet Model 2HDM (Type-I) Georgi-Machacek Model [ξ = 2*Sqrt(6)/3] Unitarity const. w/ 500 GeV. Kang, Park, arXiv: [Singlet] Kanemura, Okada, Senaha, Yuan, PRD70 (2004) [2HDM] Aoki, Kanemura, PRD77 (2008) [GM] 67

Top Yukawa 68

Tanβ dependence 69

τ vs b 70

b vs c 71

τ vs c 72

IPI diagram Counter term IPI diagram 2-point function 3-point function = = + + Parameters shift: g → g + δg, g’ → g’ + δg’, v → v + δv, W μ → Z W 1/2 W μ, B μ → Z B 1/2 B μ On-shell Renormalization Scheme 73

LHC:14 TeV, 300 fb -1 ILC1:250 GeV, 250 fb -1 ILC:500 GeV, 500 fb -1 ILCTeV:1 TeV, 1000 fb -1 Higgs coupling measurements Peskin, [hep-ph] 74

Signal GeV ATLAS CMS γγ7.4σ (4.3σ) [ CONF ] 3.2σ (4.2σ) [ PAS-HIG-13-1 ] ZZ* →4l 6.6σ (4.4σ) [ CONF ] 6.7σ (7.1σ) [ PAS-HIG-13-2 ] WW* →lvlv 3.8σ (3.8σ) [ CONF ] 4.0σ (5.1σ) [ PAS-HIG-13-3 ] bbNo excess 1.4 (1.3)×SM exc. [ CONF ] 2.1σ（2.2σ） [ PAS-HIG ] τ ττ τ4.1σ (3.2σ) [ CONF ] 2.9σ (2.6σ) [ PAS-HIG ] Spin 1 is excluded Higgs mechanism Yukawa? Obs. (Exp.) 7+8TeV, ~25/fb There is no room for doubt that it is a Higgs boson. 75

Gauge vs Yukawa Singlet Model 2HDM (Type-I) Georgi-Machacek Model [ξ = 2*Sqrt(6)/3] For details, see Prof. Chiang’s talk 76

Fingerprinting (Gauge vs Fermion) -π/4 < α < +π/4 Singlet Model 2HDM Georgi-Machacek Model [ξ = 2*Sqrt(6)/3] 77

Fingerprinting (Gauge vs Fermion) -π/4 < α < +π/4 0.1 < tanβ < 100 Singlet Model 2HDM Georgi-Machacek Model [ξ = 2*Sqrt(6)/3] 78