1. Higgs decays to γγ and Zγ in models with Higgs extensions
Kei Yagyu (National Central U.)
Collaboration with
Cheng-Wei Chiang (National Central U.)
arXiv: [hep-ph]
Academia Sinica, September 14th

2. Plan of Talk Introduction Extended Higgs sectors
- SM Higgs sector
- Current states of the Higgs search at LHC
Extended Higgs sectors
Higgs decays into γγ and Zγ
Summary

3. Higgs, 希格斯, ヒッグス God particle? - Trigger the electroweak
symmetry breaking
- The Higgs VEV: Unique mass scale
(Excepted for ΛQCD)
- Origin of Mass: Gauge bosons → Higgs mechanism
Quarks & Leptons → Yukawa interaction
The “God” really has been discovered at the LHC ??

4. Higgs sector in the SM
V (φ)
Higgs potential
Φ: isospin SU(2) scalar doublet
f +
f 0
F =
Higgs VEV φ0 φ+
SU(2)L×U(1)Y → U(1)EM
Physical state: Only one neutral component h
Origin of Mass
Gauge boson mass
Fermion mass
Higgs mass
<F> F f V g2 y λ
mV2 = g2v2
mf = y v
mh2 = λv2
All the masses of particles are given by the Higgs VEV.

5. Higgs sector in the SM
V (φ)
Higgs potential
Φ: isospin SU(2) scalar doublet
f +
f 0
F =
Higgs VEV φ0 φ+
SU(2)L×U(1)Y → U(1)EM
Physical state: Only one neutral component h
Higgs Interaction
Gauge interaction
Yukawa interaction
Self interaction F f V g2 y λ
∝ mV2 / v2
∝ mf / v
∝ mh2/v2
All the Higgs interactions are proportional to the mass

6. Higgs search at collider experiments
e+e- (LEP, ILC),
pp (Tevatron),
pp (LHC),… ・
Higgs boson
Production
Decay
Beam
Detector
Depends on
Detector
performance, …
Collision particle,
Center of mass energy, …
Theory
(Model)
Theory
(Model)
We should know the production and decay property of the Higgs boson.

7. Branching fraction f h h h W+, Z W-, Z γ, g γ, g
‣ bb mode: Large branching ratio, but huge background
‣ γγ, ZZ(*) → 4 lepton mode: Tiny branching ratio, but small background

8. Higgs boson production at the LHC
Gluon Fusion ~ 10 pb
W/Z association
V. Sharma, talk at Moriond (2011)
Vector Boson Fusion ~ 1 pb
Top quark association

9. Current states of the Higgs search at the LHC
‣ The Higgs-like particle has been found at around 126 GeV
at the LHC with 5σ.
h → γγ
h → ZZ* → 4 lepton
Historic Milestone but only the Beginning. 　
R. Heuer, July 4th, CERN

10. Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
[hep-ex], CMS
[hep-ex], ATLAS

11. Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
[hep-ex], CMS
[hep-ex], ATLAS
H → ZZ and H→ WW modes are good agreement to the SM prediction.

12. Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
[hep-ex], CMS
[hep-ex], ATLAS
Obs. H → γγ signal seems to be large compared to the SM prediction.

13. Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
[hep-ex], CMS
[hep-ex], ATLAS
H → ττ and H → bb modes have large uncertainty.
At CMS, H → ττ mode did not seem to be discovered yet.

14. SM-like Higgs boson?
At present, observed new resonance at 126 GeV looks like the SM-like Higgs boson.
(-Consistent with the precision measurements at LEP,
- Observed from expected events γγ and ZZ → H is spin 0 or 2)
Large deviation from the SM in H→γγ mode
No observation from H→ττ mode
We need to collect more data in order to clarify the property
of the new particle w/126 GeV.
Still there are possibilities to consider non-minimal Higgs sectors!

15. Extended Higgs sector

16. Explanation by extended Higgs sectors
Tiny neutrino masses
- The type II seesaw model
- Radiative seesaw models
(e.g. Zee model)
Dark matter
- Higgs sector with an unbroken discrete symmetry
Baryon asymmetry of the Universe
- Electroweak baryogenesis
BAU can be explained in the scenario based on the EWBG
Introduced extended Higgs sectors
SU(2) doublet Higgs + Singlets, Doublets and Triplets, …
Beyond the SM
Extended Higgs sectors
Determine

17. What is the true Higgs sector?
There are hints to determine the structure of the Higgs sector.
1. Electroweak rho parameter
ρexp =
Additional Doublets or Singlets
Additional Triplets or Higher isospin reps.
→ ρtree = 1
→ In general, ρtree ≠ 1
Small triplet VEV or Custodial sym.
(Georgi-Machacek model)
2. Flavor Changing Neutral Current (FCNC)
Tree level FCNC process should be suppressed.
Extension of Multi-doublets → In general, there appears the FCNC at the tree level.
A discrete Z2 symmetry is often imposed to avoid the tree level FCNC.
Glashow, Weinberg

18. Testing an extended Higgs sector at colliders
Direct way：Discovery of extra Higgs bosons
Ex. Charged Higgs boson, CP-odd Higgs boson, …
Indirect way:
Precise measurement for the Higgs couplings
Ex. hhh, hff, hVV

19. Testing an extended Higgs sector at colliders
Direct way：Discovery of extra Higgs bosons
Ex. Charged Higgs boson, CP-odd Higgs boson, …
Indirect way:
Precise measurement for the Higgs couplings
Ex. hhh, hff, hVV
We discuss the 2 Higgs doublet model and
the Higgs triplet model as important examples.

20. Two Important examples
2 Higgs Doublet Model (2HDM)
- Many new physics models deduce the 2HDM.
ex. MSSM, Dynamical Sym. breaking models,
Radiative seesaw models, and so on.
　- Source of the CP-violation
Higgs Triplet Model (HTM)
- Tiny neutrino masses can be generated via
the type-II seesaw mechanism.
Cheng, Li (1980);
Schechter, Valle, (1980);
Magg, Wetterich, (1980);
Mohapatra, Senjanovic, (1981).

21. Higgs potential in the 2HDM
The Higgs potential under the softly broken Z2 sym. (Φ1 → + Φ1, Φ2 → -Φ2)
Physical scalar states: 8-3 = 5
Goldstone bosons
Tanβ = v2/v1
This is the Higgs potential under the discrete symmetry to avoid FCNC.
If model is invariant under that phi1 translate to phi1 and phi2 translate to –phi2, then Higgs potential is restricted as following formula.
Physical degrees of freedom are 5.Because of 3 degrees of freedom out of 8 translate to longitudinal component of the the gauge bosons due to the Higgs mechanism.
The five physical states are them as I said.
The ratio of vevs is defined by tanb
And the soft breaking mass parameter is defined as M.
CP-even Higgs
Charged Higgs
CP-odd Higgs
Mass formulae (sin(β-α) ~1 )
SM-like Higgs boson
Extra Higgs bosons

22. Four types of the Yukawa interaction
Imposing Z2 symmetry →　Only one of the two doublet couples to each fermion.
Bs → sγ
Barger, Hewett, Phillips PRD 41 (1990) t s b γ W－ H－
Grossman NPB 426 (1994)
Type-I
Type-II (MSSM) u d Φ２ e u d Φ２ e Φ１
Aoki, Kanemura, Tsumura, Yagyu, PRD 80, 2009 u d Φ２ e Φ１
Type-X
Type-Y
Next we discuss the type of Yukawa interaction in the THDM.
There are four types of the Yuakwa interactions under the discrete symmetry to avoid FCNC.
This table express the charge assignments of the discrete symmetry.
Phi1 is first Higgs doublet, Phi2 is second Higgs doublet, Q is left handed quark doublets, L is left handed lepton doublets, u is right handed up-type quarks, d is right handed down-type quarks, and e is right handed charged leptons.
Under these assignments we call the Yukawa interaction to Type-I, Type-II, and X,Y.
Especially the Type-II THDM corresponds to the MSSM Yukawa interaction.
In this type, phi1 couples to …
On the other hand, the Type-X THDM is adopted to AKS model. In the Type-X THDM, phi1 couples to …
The point of phenomenological difference between Type-II and Type-X can see the b to s gamma constraint.
That is to say the Type-II THDM receive strongly constraint of the mass of the charged Higgs boson from bsr, while the Type-X doesn’t receive.
In this talk, we mainly discuss the Type-X THDM and the MSSM Higgs sector. u d Φ２ e Φ１
In the Type-I and Type-X 2HDM, a light charged Higgs boson can be allowed.

23. CP-odd Higgs (A) decay in the case with sin(β-α) = 1, mA = mH =150 GeV
Type II (MSSM-like)
Type X
They are decay branching ratio of charged Higgs boson for the same parameter sets.
Tau nu decay mode dominate in the Type-I, II, and X, while cbbar decay mode dominate in only the Type-Y.
(μ+)
(μ-)
Kanemura, Tsumura, Yokoya, PRD 85 (2012)

24. Higgs potential in the HTM
The Higgs potential
Physical scalar states: = 7
NG bosons
Doubly-charged Higgs
CP-even Higgs
Singly-charged Higgs
CP-odd Higgs
Mass formulae (vΔ/vφ << 1 )
Triplet-like
SM-like
A, H H+
H++
Case I (λ5 >0)
Case II (λ5<0)
Mass2

25. Branching ratio of H++
With mass splitting
(mH++ - mH+ = 10 GeV)
Without mass splitting
Here, I show the decay branching ratios of H++.
These upper two figures show the decay branching ratio of H++ as a function of the v delta.
The left figures shows the case of delta m = 0.
As you can see, H++ decays into the diboson when v delta is lager than 10-4 to 10-3.
The location of the cross points, where main decay mode is changing from l+l+ to W+W+
depends on the mass of the H++. Heavier H++ tends to decay into W+W+ in smaller values of v delta.
The right figure shows the case of delta m = 10 GeV.
In this case, in the wide regions of the vdelta, H++ decays into H+W+.
The bottom figure shows the decay branching ratio of H++ as a function of the delta m.
Even when delta m is greater than one GeV, main decay mode of H++ becomes H+W+.
So, as mentioned by several authors,
phenomenology of delta m not = 0 is drastically different from that of delta m =0.
Phenomenology with the mass splitting is drastically different from that without the mass splitting

26. Mass reconstruction h
H, A H+
H++
114 GeV
119 GeV
130 GeV
140 GeV
vΔ = GeV
Aoki, Kanemura, KY, PRD85(2012)
qq’ → H++H- → (l+l+ννbb)(jjbb)
qq’ → H+H → (l+νbb)(bb)
qq → HA → (bb)(bb)
MT, Minv MT MT
33 fb
12 fb
130 fb
42 fb
8.0 fb (14 TeV)
2.8 fb (7 TeV)
Signal only
mH++
mH+
mH, mA
All the masses of the Δ-like scalar bosons may be reconstructed.

27. Higgs decays into the γγ and Zγ

28. Testing an extended Higgs sector at colliders
Direct way：Discovery of extra Higgs bosons
Ex. Charged Higgs boson, CP-odd Higgs boson, …
Indirect way:
Precise measurement for the Higgs couplings
Ex. hhh, hff, hVV
We discuss Higgs decays into the diphoton (hγγ) and
the Z + photon (hZγ).

29. Higgs to the diphoton channel
CMS, ICHEP
ATLAS, ICHEP
The signal strength σOBS/σSM exceeds 1 at the both experiments:
1.56± 0.43 (CMS), 1.9±0.5 (ATLAS).
‣ If this excess is really established,
it must be explained by effects of new physics beyond the SM!
We focus on new physics effects to the H → γγ and H → Zγ modes.

30. h → γγ and h → Zγ decays in the SM
‣The hγγ and hγZ verteces are induced at the 1-loop level.
Top quark loop contribution
W boson loop contribution
(Z)
(Z)
‣Decay rate
Ellis, Gaillard, Nanopoulos, (1976) ;
Ioffe, Khoze, (1978);
Shifman, Vainshtein, Voloshin, Zakharov, (1979)
Cahn, Chanowitz, Fleishon, (1979);
Bergstrom, Hulth, (1985)

31. h → γγ and h → Zγ decays in the SM
‣The hγγ and hγZ verteces are induced at the 1-loop level.
Top quark loop contribution
W boson loop contribution
(Z)
(Z)
‣Decay rate
Ellis, Gaillard, Nanopoulos, (1976) ;
Ioffe, Khoze, (1978);
Shifman, Vainshtein, Voloshin, Zakharov, (1979)
Cahn, Chanowitz, Fleishon, (1979);
Bergstrom, Hulth, (1985)
‣Input parameters: mh = 126 GeV, mt = 173 GeV
Mode
Top-loop
W-loop
Decay rate
Branching
h → γγ
-1.84
8.38
10.7 keV
0.28 %
h → Zγ
-0.643
12.1
7.12 keV
0.18 %
W and top loop effects
are destructive
with each other.

32. h → γγ and h → Zγ decays in the SM
‣The hγγ and hγZ verteces are induced at the 1-loop level.
Top quark loop contribution
W boson loop contribution
(Z)
(Z)
‣Decay rate
Ellis, Gaillard, Nanopoulos, (1976) ;
Ioffe, Khoze, (1978);
Shifman, Vainshtein, Voloshin, Zakharov, (1979)
Cahn, Chanowitz, Fleishon, (1979);
Bergstrom, Hulth, (1985)
‣Input parameters: mh = 126 GeV, mt = 173 GeV
Mode
Top-loop
W-loop
Decay rate
Branching
h → γγ
-1.84
8.38
10.7 keV
0.28 %
h → Zγ
-0.643
12.1
7.12 keV
0.18 %
W and top loop effects
are destructive
with each other.
How these predictions are changed by new physics effects?

33. New physics effects to h→γγ(Z)
‣ Any charged new particle which couples to the Higgs boson
can contribute to the h→ γγ and h → Zγ processes.
(Z)
(Z)
(Z)
Spin 1/2
Spin 0
Spin 1
Ex. Charged Higgs boson,
Squark, Slepton…
Ex. 4th generation fermion,
Chargino…
Ex. W’ boson…
In this talk, we focus on modes with extended Higgs sector,
where new charged scalar bosons are introduced to the SM.

34. Previous works and our work
There are several papers where the
h→γγ mode is studied in an extended Higgs sector.
Posch 2011;
Arhrib, Benbrik, Gaur 2012;
Ferreira, Santos, Sher, Silva 2012
・ 2 Higgs doublet model
Arhrib, Benbrik, Chabab, Moultakae, Rahilib 2012;
Kanemura, Yagyu 2012;
Akeroyd, Moretti 2012
・ Higgs triplet model
・ Zee model (2HDM + charged singlet)
Kanemura, Kasai, Lin, Okada, Tseng, Yuan 2000
We study the h→γγ(Z) more comprehensive way in various extended Higgs sectors.

35. Classes of extended Higgs sectors
Class I : Models with one singly-charged scalar boson SM H±
Ex. 2HDM
Class II : Models with one singly-charged and
one doubly-charged scalar boson
Ex. Higgs triplet model,
Zee-Babu model SM H±
H±±
Class III : Models with two singly-charged scalar bosons
Ex.: Radiative seesaw models
(Zee model,
Kauss-Nasri-Trodden model,
Aoki-Kanemura-Seto model) SM
H1±
H2±

36. List of models ‣ We consider Higgs sectors with additional
SU(2)L singlets (S), doubles (D) and triplets (T).
Class I
Class II
Class III
(Y = 1)
Singlet
(Y = 2)
Doublet
(Y = 1/2)
(Y = 0)
Triplet
(Y = 1)
There are 13 models depending on the # of scalar fields.

37. SM-like Higgs boson X ‣ We assume the SM-like Higgs boson (h):
-The Yukawa coupling (hff) and the gauge coupling (hVV)
is the same as those in the SM. h ・
Production
Decay X
Only h→γγ and h→Zγ decay modes can be modified
significantly. The other decay rates are almost
the same as the SM.
Same as the SM
Modified decay rate directly affects to the number of events.

38. Modified decay rates Points
‣ Decay rates are modified by new contributions from charged scalar bosons:
‣ The Higgs couplings with charged scalars (λSSh) and the
Z boson (gSSZ) can be defined as
Points
1. Decay rate of h→γγ is
enhanced when λSSh is negative.
suppressed when λSSh is positive.
2. Decay rate of h→ Zγ depends on the isospin (I3) of the scalar boson.
Measuring both h→γγ and h→Zγ would be a useful tool to determine the true Higgs sector.

39. Relevant terms in Class I and II
Φ : SM doublet ⊃
: Extra scalar field
1, 2 ⊃

40. Relevant terms in Class III⊃
Mixing angle: =
M1 = M2 = M3
= M ≠
M1 = M2 = M3
= M

41. Results (Class I and Class II)
mH+ = mH++ = 200 GeV
Class I
ΔB (h → X) =
[Br(h → X)NP - Br(h → X)SM]/ Br(h → X)SM
Not allowed by the
vacuum stability bound.
Class II

42. Results (Class I and Class II)
mH+ = mH++ = 200 GeV
Class I
R = Br(h → Zγ)NP/ Br(h → γγ)NP
Not allowed by the
vacuum stability bound.
The h to diphoton decay mode does not depend on the particle content belonging to the same class,
But h to Zgamma mode strongly depends on the particle content, because it has a sensitivity of the isospin of charged scalar bosons.
Typically, in models with large isospin representation fields, the h to gamma Z decay rate is enhanced
Class II

43. Results (Class III) mH1+ = 200 GeV, mH2+ = 300 GeV, M = 308 GeV
ΔB (h → X) =
[Br(h → X)NP - Br(h → X)SM]/ Br(h → X)SM
This black curve shows the prediction in models with two same quantum number fields, while the red curve show the prediction in models with two different quatum number fields.
The maximal value of the prediction around 30% is given at the case with the maximal mixing in these three models.
However, at the same case, minimal prediction is given in these two models.
In the case of these three models, mixing angle dependence is relatively large compare to these two models.
The maximum allowed value is around 30 % in models with two same representation fields, while that is around 15 % in models with two different fields.
These two figures show the mixing angle dependence of the deviation of h to Zgamma decay mode in these three models
And these two models.
The maximal value of the prediction can be given at the maximul mixing case in these three models, while that can be given at theta= pi/2 in these two models.

44. Results (Class III) mH1+ = 200 GeV, mH2+ = 300 GeV, M = 308 GeV
R = Br(h → Zγ)NP/ Br(h → γγ)NP

45. Summary
To know the true Higgs sector → To determine physics beyond the SM.
Direct way : Discovery extra Higgs bosons
Decay of the extra Higgs is important to discriminate each Higgs sector.
-Type-II 2HDM: qq → HA → 4b, Type-X 2HDM: qq → HA → 4τ, 2τ + 2μ
- Decay of H++ in HTM: H++ → l+l+ (Small vΔ), H++ → W+W+ (Large vΔ),
H++ → H+W+ (Large mass splitting).
Indirect way: Precise test of the Higgs couplings (hγγ and hZγ)
　 h → γγ and h → Zγ decay modes are sensitive to the new physics models.　
　　　→ Measuring both modes may be useful.
　　We focused on effects of charged scalar boson which are introduced
from various extended Higgs sectors.
Class I: H±, Class II: H± + H±±, Class III: H1± + H2±
　　When a charged scalar mass is taken to be around 200 GeV, h → γγ
can be enhanced ~ 15 % , ~ 80 % and ~ 30 % in Class I, II and III, respectively
compared with the SM prediction.

46. Scalar loop function

47. Potential in models Class III
In models w/ φSM + S1+ + S2+, φSM + D1 + D2, φSM + T10 + T20 , μ is absent.
In models w/ φSM + D + S, φSM + D + T0, M3 and λ3 are absent.

48. Heavy case (mS = 400 GeV )
Class I
Class II

49. Measurement hZγ coupling at linear colliders
Dubinin, Schreiber, Vologdin, Eur. Phys. J. C30 (2003)
Measurement hZγ coupling at linear colliders
h → Zγ decay process has been analyzed via the vector boson fusion process
at the future linear collider.
mh = 120 GeV, root(s) = 500 GeV, integrated L = 1 ab-1
Accuracy of ΔBR (h → Zγ) is expected to be 48 %
By using polarized beam, this would be improved to be 29 %.

50. Branching ratios of H+, H and A
Next, we discuss the decay branching ratios of H+, H and A.
This figure shows the decay branching ratio of H+ as a function of the v delta.
Similarly to the case of the H++, the H+ to HW+ mode can be dominant in the case of delta m not = 0.
These two figures show the decay branching ratios of H and A as a function of the v delta.
When v delta is large, the mixing between the doublet Higgs and the triplet Higgs becomes strong,
So that the phi to bb mode can be dominant when vdelta greater than MeV.
★ The H+ → f0 W+ mode can be dominant
in the case of Δm ≠ 0.
★ The f0 → bb mode can be dominant
when vΔ > MeV.

51. CP-even Higgs decay in the case with sin(β-α) = 1, mA = mH =150 GeV
Type II (MSSM-like)
Type X
They are decay branching ratio of charged Higgs boson for the same parameter sets.
Tau nu decay mode dominate in the Type-I, II, and X, while cbbar decay mode dominate in only the Type-Y.

52. Type-X 2HDM simulation
Kanemura, Tsumura, Yokoya, PRD 85

53. b→sγ t s b γ W－ H－ Type-II, Y Type-I, X
Barger, Hewett, Phillips PRD 41 (1990)
Here, we consider b to s gamma constraint.
This W boson looped diagram is contribution in the SM, and charged Higgs looped one is THDM contribution.
These Yukawa couplings takes as follows.
The part of proportional to mass of the down-type quark is tanb in the Type-II and Y, while is cotb in the Type-I and X.
Then b to s gamma decay rate can be calculated for the each types at LO.
In the Type-X THDM, destructive interferences occur between the W and the H+ contributions.
Type-I, X