1. Fingerprinting of the Higgs boson couplings as a probe of new physics models Academia Sinica, Mar. 7, 2014 Yagyu, Kei (柳生 慶) National Central U. Physics Letters B731, 27-35 (2014), arXiv:1401.0515 [hep-ph] Collaboration with Shinya Kanemura and Mariko Kikuchi (U. of Toyama)

2. 1 Cavity Radiation In the end of 19 th century, people thought that physics has already been completed by Newton’s dynamics and Maxwell’s electromagnetism. However, there were a few phenomena which couldn’t be explained by classical physics such as the spectrum of cavity radiation. Wien’s Low (1896) Rayleigh-Jeans Low (1900) Exp. Wien’s Low Rayleigh-Jeans Low

3. 2 Cavity Radiation In the end of 19 th century, people thought that physics has already been completed by Newton’s dynamics and Maxwell’s electromagnetism. However, there were a few phenomena which couldn’t be explained by classical physics such as the spectrum of cavity radiation. Exp. ~ Planck’s Low Wien’s Low Rayleigh-Jeans Low Planck’s Low (1905)

4. 3 Paradigm Shift Classical Theory -Newton Dynamics -Maxwell Electromagnetism Planck’s Low Einstein’s Light Quantum Hypothesis Early 20 th century Cavity Radiation gave a “Bridge” connecting Classical Theory and Quantum Theory. Quantum Theory - Nuclear Physics - Particle Physics, … Cavity Radiation

5. 4 Gauge Sector G, W, Z, γ Matter Sector Quarks & Leptons Higgs Sector Higgs mechanism Yukawa interaction Today Gauge interaction We have the Standard Model.

6. 5 Gauge Sector G, W, Z, γ Matter Sector Quarks & Leptons Higgs Sector Higgs mechanism Yukawa interaction Today Gauge interaction We have the Standard Model. Well tested before the LHC

7. 6 Gauge Sector G, W, Z, γ Matter Sector Quarks & Leptons Higgs Sector Higgs mechanism Yukawa interaction Today Gauge interaction We have the Standard Model.

8. 7 Gauge Sector G, W, Z, γ Matter Sector Quarks & Leptons Higgs Sector Higgs mechanism Yukawa interaction Today Gauge interaction We have the Standard Model. The LHC has found a Higgs boson with 126 GeV

9. 8 Gauge Sector G, W, Z, γ Matter Sector Quarks & Leptons Higgs Sector Higgs mechanism Yukawa interaction Today Gauge interaction We have the Standard Model. However, still there are unclear things in the Higgs sector.

10. 9 Next Paradigm Shift New Physics Standard Model Higgs Sector EWSB Today Higgs Physics could give a next “Bridge” connecting the Standard Model and New Physics!

11. 10 Three Questions 1. What is the true structure of the Higgs sector? -Minimal or Non-minimal? 2.What is the dynamics behind the Higgs sector? - Weak coupling or Strong coupling 3.How is the Higgs sector related to the phenomena beyond the SM? - Neutrino oscillation, Dark matter, and Baryon asymmetry.

12. 11 Three Questions 1. What is the true structure of the Higgs sector? -Minimal or Non-minimal? 2.What is the dynamics behind the Higgs sector? - Weak coupling or Strong coupling 3.How is the Higgs sector related to the phenomena beyond the SM? - Neutrino oscillation, Dark matter, and Baryon asymmetry.

13. 126 GeV Higgs Explained Minimal (1 doublet) EW data, Flavor, … 12

14. Extra Singlets Doublets Triplets… 126 GeV Higgs Explained Minimal (1 doublet) EW data, Flavor, … 13 Non-Minimal Higgs sectors

15. 126 GeV Higgs Introduce Non-Minimal Higgs sectors Extra Singlets Doublets Triplets… Minimal (1 doublet) New Physics Models Neutrino mass, Dark matter and Baryon asymmetry Explained EW data, Flavor, … 14

16. 126 GeV Higgs Determine Higgs prop. Determine Non-Minimal Higgs sectors Extra Singlets Doublets Triplets… Minimal (1 doublet) Neutrino mass, Dark matter and Baryon asymmetry EW data, Flavor, … 15 New Physics Models

17. 126 GeV Higgs New Physics Models Neutrino mass, Dark matter and Baryon asymmetry Determine Higgs prop. Determine Non-Minimal Higgs sectors Extra Singlets Doublets Triplets… Minimal (1 doublet) Bottom up Approach! EW data, Flavor, … 16

18. 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 17 Measuring effects on the 126 GeV Higgs boson

19. 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 18

20. 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 19 ExperimentsTheory

21. Higgs coupling measurements 20 κVκV κFκF κ V = g hVV (exp)/g hVV (SM), κ F = g hFF (exp)/g hFF (SM) Scaling factors ATLAS-CONF-2013-034CMS-PAS-HIG-13-005

22. Higgs coupling measurements 21 κVκV κFκF κ V = g hVV (exp)/g hVV (SM), κ F = g hFF (exp)/g hFF (SM) Scaling factors ATLAS-CONF-2013-034CMS-PAS-HIG-13-005 1 1.2 1.4 0.8 0.6 The uncertainties for κ F and κ V are about ±40% and ±20%, respectively.

23. The hZZ coupling can be measured by 1 % accuracy at the ILC(250) ! Higgs coupling measurements ILC, TDR ILC, Higgs White Paper, arXiv: 1310.0763 (300/fb) 22

24. 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: 1310.0763 23

25. 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: 1310.0763 24

26. 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 25

27. 1. Electroweak rho parameter Basic Constraints There are two guidelines to restrict Higgs sectors. ρ exp = 1.0004 -0.0004 +0.0003 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 26

28. 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. 27 B0B0 Φ0Φ0 B0B0

29. 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. 28 There are two guidelines to restrict Higgs sectors.

30. 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] 29 Hisano, Tsumura, PRD87 (2013) Kanemura, Kikuchi, KY, PRD88 (2013)

31. Two mixing angles Mixing between CP-even states VEVs where T: isospin, Y:hypercharge 30

32. 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 31

33. Yukawa Gauge Higgs Singlet Model (φ=S) Φ f f S α Y f = m f / Φ V V α ★ The singlet VEV does not contribute to the EWSB. → β=∞ ( =246 GeV) ★ The hff and hVV couplings are universally suppressed. 32 S

34. 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 33

35. 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 34 Ex. GM model: ξ = 2*sqrt(6)/3 Septet model : ξ = 4

36. SM 35

37. SM κ F’ 36

38. SM κ F’ κ F = κ F’ 37

39. SM κ F’ κ F = κ F’ 38

40. Gauge vs Yukawa 39 Singlet Model 2HDM (Type-I) Georgi-Machacek Model [ξ = 2*Sqrt(6)/3]

41. 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] 40

42. 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 41

43. 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:1309.6234 [hep-ph] U(1) symmetry Ko, Omura, Yu, JHEP1201 (2012) … 42

44. 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:1309.6234 [hep-ph] U(1) symmetry Ko, Omura, Yu, JHEP1201 (2012) … There are four independent types of Yukawa interactions. 43

45. 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. 44

46. We define the Higgs basis by introducing β tanβ = / Mass Eigenstates NG bosons Charged Higgs CP-even Higgs CP-odd Higgs SM-like Higgs boson w/126 GeV 45

47. 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)] 46

48. 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 47 Φ = H ±, A, H

49. 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 ] 48

50. 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 49 δ =

51. 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 = 50

52. 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 = 51

53. 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 52

54. 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 53

55. Bottom vs Tau κ V 2 = 0.99, 0.95, (δ ~ 0.005, 0.02) cos(β-α) < 0 54

56. How these predictions can be modified by taking into account radiative corrections? The hff and hVV couplings can be measured with O(1)% accuracy. Radiative Corrections 1-loop level 55 If α is the same order of the EM coupling, the correction is at most O(0.1)%. However, it can be larger than 1% due to nondecoupling effects of extra Higgs boson loops.

57. 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. 56

58. 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., 57

59. The hhh coupling @1-loop in the 2HDM Φ = H, A, H ± Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558 (2003) 58

60. The hhh coupling @1-loop 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 59

61. The hhh coupling @1-loop 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. 60

62. Renormalized hff vertices Renormalized hff vertex Renormalized scale factor at on-shell The counter term contribution 61

63. Parameter Shifts Fermion masses and wave functions CP-even Higgs sector and mixing angle β The VEV Kanemura, Okada, Senaha, Yuan, PRD70 (2004). 62

64. 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). 63 1PI + C.T.

65. 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, PLB731, 2014 64 tanβ = 1 tanβ = 3

66. Nondecoupling [sin(β-α)=1, m H+ =m A =m H (=m Φ ) and M 2 = 0] 65 Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

67. Nondecoupling [sin(β-α)=1, m H+ =m A =m H (=m Φ ) and M 2 = 0] 66 Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

68. Fingerprinting at the tree level cos(β-α) < 0, tanβ = 1, 2, 3 and 4, 67 Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

69. 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. 68 Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

70. 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. 69 Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

71. 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: 1401.0515 70

72. 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 71

73. Higgs Physics = “Bridge” connecting the SM and New Physics. Indirect Search = Comparing fingerprints of the Higgs couplings. Typical patterns of deviations in extended Higgs sectors at tree level 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 1-loop corrections from extra Higgs bosons to the hhh, hff and hVV couplings can be maximally O(100)%, O(5)% and O(1)%, respectively. If 1% deviation in the hZZ couplings is found, we can discriminate four types of 2HDM by precisely measured hff couplings. Summary 72