Fingerprinting of the Higgs boson couplings
as a probe of new physics models
Kei Yagyu (National Central U.)
The 11th LHC Physics Monthly Meeting,
KIAS, Feb. 18, 2014
1
Congratulation!
이 상화
2
Figure Skating (20 th and 21st)
김 연아
浅田 真央
3
Minimal
(1 doublet)
Explained
EW data,
Flavor, …
126 GeV Higgs
4
Extended Higgs sectors
Minimal
(1 doublet)
Extra
Singlets
Doublets
Triplets…
Explained
EW data,
Flavor, …
126 GeV Higgs
5
Beyond the SM
Neutrino mass, Dark matter and Baryon asymmetry
Introduce
Extended Higgs sectors
Minimal
(1 doublet)
Extra
Singlets
Doublets
Triplets…
Explained
EW data,
Flavor, …
126 GeV Higgs
6
Beyond the SM
Neutrino mass, Dark matter and Baryon asymmetry
Determine
Extended Higgs sectors
Minimal
(1 doublet)
Extra
Singlets
Doublets
Triplets…
Determine
EW data,
Flavor, …
126 GeV Higgs
Higgs prop.
7
Beyond the SM
Determine
Extended Higgs sectors
Minimal
(1 doublet)
Extra
Singlets
Doublets
Triplets…
Determine
EW data,
Flavor, …
126 GeV Higgs
Bottom up Approach!
Neutrino mass, Dark matter and Baryon asymmetry
Higgs prop.
8
Bottom up Approach
1. Direct search
2. Indirect search
Measuring effects
Energy
on the 126 GeV Higgs boson
Discovery
Energy
126 GeV
h
H++, H+,
H, A, …
126 GeV
h
H++,
H+,
H,
A, ...
Studying both ways is important to determine
the structure of the Higgs sector.
9
Bottom up Approach
1. Direct search
2. Indirect search
Measuring effects
Energy
on the 126 GeV Higgs boson
Discovery
Energy
126 GeV
h
H++, H+,
H, A, …
126 GeV
h
H++,
H+,
H,
A, ...
Studying both ways is important to determine
the structure of the Higgs sector.
10
Indirect Search
Indirect search = Precision test of Higgs couplings
 Patterns of deviation in various Higgs couplings strongly
depend on the structure of the Higgs sector.
Experiments
Theory
hVV
Minimal
hbb
Singlet Models
hττ
2HDMs
Compare
etc…
hcc
hγγ
Triplet Models
hhh
Make a “Fingerprint” from precise measurements.
11
Higgs coupling measurements
ILC, TDR
ILC, Higgs White Paper, arXiv: 1310.0763
(300/fb)
The hZZ coupling can be measured by 1 % accuracy
at the ILC(250) !
12
Higgs coupling measurements
ILC, TDR
ILC, Higgs White Paper, arXiv: 1310.0763
(300/fb)
The hVV and hff couplings can be measured by 1 % accuracy
at the ILC(500) !!
13
Higgs coupling measurements
ILC, TDR
ILC, Higgs White Paper, arXiv: 1310.0763
(300/fb)
The hVV and hff couplings can be measured by 1 % accuracy
at the ILC(500) !!
14
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
Basic Constraints
There are two guidelines to restrict Higgs sectors.
1. Electroweak rho parameter
ρexp = 1.0004
+0.0003
-0.0004
Models with ρtree = 1 seems to be a natural choice.
Satisfy the relation
Alignment of (exotic) VEVs
T
Y
1
0
1/2
1/2
3
2
…
…
Ex. Model with doublet (Y=1/2) + triplet (Y=1) + triplet (Y=0)
(Georgi-Machacek model)
if
16
Basic Constraints
There are two guidelines to restrict Higgs sectors.
2. Flavor Changing Neutral Current (FCNC)
Tree level FCNC process should be absent.
In general, multi-doublet extensions cause FCNC at the tree level
B0
Φ0
B0
17
Basic Constraints
There are two guidelines to restrict Higgs sectors.
2. Flavor Changing Neutral Current (FCNC)
Tree level FCNC process should be absent.
In general, multi-doublet extensions cause FCNC at the tree level
B0
Φ0
B0
Only one Higgs doublet couples
to each fermion.
18
Simple Extended Higgs Sectors
We consider the following simple Higgs sectors;
(with ρtree = 1 and no tree level FCNC)
1. Φ + S (Singlet)
2. Φ + D (Doublet)
3. Φ + Δ (Triplets or larger)
[GM model, Septet model]
Hisano, Tsumura, PRD87 (2013)
Kanemura, Kikuchi, KY, PRD88 (2013)
19
Two mixing angles
 Mixing between CP-even states
 VEVs
T: isospin, Y:hypercharge
where
20
Deviations in hff and hVV
 Yukawa
f
α
Φ
f
β
Yf = mf /<Φ>
 Gauge
V
<Φ>
V
β
α
Φ
φ
<φ>
<φ>
V
φ
V
21
Higgs Singlet Model (φ=S)
 Yukawa
f
Φ
f
★ The singlet VEV
α
S
does not contribute
to the EWSB.
<S>
Yf = mf /<Φ>
→ β=0 (<Φ>=246 GeV)
★ The hff and hVV
couplings are
 Gauge
V
<Φ>
α
Φ
V
<S>
V
universally suppressed.
S
V
22
Two Higgs Doublet Model (φ=D)
 Yukawa
f
α
Φ (D)
Yf = mf /<Φ (D)>
f
★ There are 2 patterns in κf
D (Φ)
β
<D (Φ)>
for each fermion f.
★ξ=1
 Gauge
β
<Φ>
V
V
Φ
V
<D>
α
D
V
23
Model with a triplet (or higher) (φ=Δ)
 Yukawa
f
α
Φ
f
★ The hff couplings are
Yf = mf /<Φ>
universally suppressed.
Δ
β
★ ξ factor can be larger
<Δ>
than unity.
→ κV > 1
Ex.
 Gauge
V
<Φ>
α
Φ
V
β
GM model: ξ = 2*sqrt(6)/3
<Δ>
V
Septet model : ξ = 4
Δ
V
24
SM
25
κF’
SM
26
κF’
SM
κF = κF’
27
κF’
SM
κF = κF’
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
Tau vs Bottom
-π/4 < α < +π/4
0.1 < tanβ < 100
Singlet
2HDM (Type-I)
Georgi-Machacek Model
2HDM (Type-II)
2HDM (Type-X)
2HDM (Type-Y)
30
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
S. Kanemura, M. Kikuchi, KY, appear in PLB,
arXiv: 1401.0515 [hep-ph]
 Summery
31
2HDMs
In general, Yukawa Lagrangian is given by
To avoid the tree level FCNC, one of the Yukawa couplings
should be forbidden.
Z2 symmetry (softly-broken) Glashow, Weinberg, PRD15 (1977)
Z2 symmetry (unbroken) Barbieri, Hall, Rychkov, PRD74 (2006)
S3 symmetry Kajiyama, Okada, KY, arXiv:1309.6234 [hep-ph]
U(1) symmetry Ko, Omura, Yu, JHEP1201 (2012)
…
32
2HDMs with the softly-broken Z2 sym.
In general, Yukawa Lagrangian is given by
To avoid the tree level FCNC, one of the Yukawa couplings
should be forbidden.
Z2 symmetry (softly-broken) Glashow, Weinberg, PRD15 (1977)
Z2 symmetry (unbroken) Barbieri, Hall, Rychkov, PRD74 (2006)
S3 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.
33
Four Yukawa Interactions
Under the Z2 symmetry, two doublets are transformed as
Φ1 → +Φ1 and Φ2 → -Φ2.
Type-I
Type-II (MSSM)
Φ２
Φ２
u
e
u
d
Φ１
e
Barger, Hewett, Phillips (1990), Grossman (1994)
Aoki, Kanemura, Tsumura, KY (2008)
d
Type-X
(Leptophilic)
Type-Y
(Flipped)
Φ２
Φ１
Φ２
u
d
e
u
e
d Φ１
34
Mass Eigenstates
In the Higgs basis, two doublets can be parameterized as:
tanβ = <Φ2>/<Φ1>
NG bosons
CP-even Higgs
Charged Higgs
CP-odd Higgs
SM-like Higgs boson w/126 GeV
35
Yukawa/Gauge Interaction
V
= (SM) × sin(β-α)
h
V
ξu
ξd
ξe
cotβ
cotβ
cotβ
Type-II cotβ
-tanβ
-tanβ
Type-X
cotβ
cotβ
-tanβ
Type-Y
cotβ
-tanβ
cotβ
Type-I
f
= (SM)
h
f
× [sin(β-α)+ξf cos(β-α)]
36
Higgs Potential
 The Higgs potential under the softly-broken Z2 sym. and CP-invariance
 We have 8 parameters in the potential. They can be interpreted by
v (=246 GeV), mh (=126 GeV),
mH, mA, mH+, sin(β-α), tanβ, and M2
 Mass formulae with sin(β-α) ~1
mh2 ~ λv2, mΦ2 ~ M2 + λv2
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 M2 (=mΦ2) → ∞
[mΦ2 ~ M2 + λv2]
Decoupling limit can be taken
only when the SM-like limit is taken.
38
Decoupling/SM-like Limit
10% dev.
cos(β-α) > 0
cos(β-α) < 0
δ=
1% dev.
0.1% dev.
(mH = mA = mH+= M =)
39
Decoupling/SM-like Limit
10% dev.
κV = sin(β-α) → 1
δ=
cos(β-α) > 0
cos(β-α) < 0
1% dev.
0.1% dev.
(mH = mA = mH+= M =)
40
Decoupling/SM-like Limit
10% dev.
cos(β-α) > 0
cos(β-α) < 0
δ=
1% dev.
0.1% dev.
(mH = mA = mH+= M =)
41
Patterns of Deviation in hff Couplings
 If κV ≠ 1 is found, several patterns of deviation in hff appear.
f
= (SM) × [sin(β-α) + ξf cos(β-α)]
h
(SM) × [sin(β-α) + cotβ cos(β-α)]
=
f
δ = 1 - sin(β-α)
(SM) × [sin(β-α) - tanβ cos(β-α)]
(SM) ×
For cos(β-α) > 0
~
δ≪1
Type-I
cotβ
u
d
e
Type-II
cotβ
u
d
cos(β-α) < 0
(SM) ×
Type-X
tanβ
e
Type-Y
cotβ
tanβ
cotβ
u
e
u
d
e
d tanβ
42
Patterns of Deviation in hff Couplings
 If κV ≠ 1 is found, several patterns of deviation in hff appear.
f
= (SM) × [sin(β-α) + ξf cos(β-α)]
h
(SM) × [sin(β-α) + cotβ cos(β-α)]
=
f
δ = 1 - sin(β-α)
(SM) × [sin(β-α) - tanβ cos(β-α)]
(SM) ×
For cos(β-α) > 0
~
δ≪1
Type-I
cotβ
u
d
e
Type-II
cotβ
u
d
cos(β-α) < 0
(SM) ×
Type-X
tanβ
e
Type-Y
cotβ
tanβ
cotβ
u
e
u
e
d
tanβ
d
43
Bottom vs Tau
κV2 = 0.99, 0.95,
(δ ~ 0.005, 0.02)
cos(β-α) < 0
44
Radiative Corrections
• 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!
1-loop level
45
Radiative Corrections in the 2HDMs
 There are papers for 1-loop corrections to
the Higgs boson couplings in 2HDMs.
hhh
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).
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
Decoupling theorem
Appelquist, Carazzone (1975)
 NP loop effects to the low energy obs. vanish when new particles are heavy.
SM
SM
NP+SM
SM
1/Mn → 0 (M → ∞)
SM
SM
M→∞
SM
SM
Violation of the decoupling theorem
 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.,
Top mass：mt = ytv
Scalar boson mass：mφ2 = λv2 + M2
(with λv2 > M2 )
47
The hhh coupling @1-loop in the 2HDM
Φ = H, A, H±
Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558 (2003)
48
The hhh coupling @1-loop in the 2HDM
Φ = H, A, H±
Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558 (2003)
0
In the case with M2 >> λv2,
we can see the decoupling
behavior.
49
The hhh coupling @1-loop in the 2HDM
Φ = H, A, H±
Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558 (2003)
~1
In the case with M2 < λv2,
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
Kanemura, Okada, Senaha, Yuan, PRD70 (2004).
 CP-even Higgs sector and mixing angle β
 The VEV
52
On-shell Renormalization Conditions
=0
f
f
f
f
p2=mf2
=0
p2=mf2
δmf and δZVf
h
h
=0
p2 =mh2
h
H
=
h
p2=mh2
H
=0
p2=mH2
δZh, δα and δCh
The counter term δv
G0
A
=
p2=mZ2
G0
A
=0
p2=mA2
is determined from the
EW on-shell RCs.
Hollik, Fortsch. Phys. 38, 165 (1990).
δβ (and δCA)
53
Decoupling
[sin(β-α)=1, mH+=mA=mH (=mΦ) and mΦ2-M2 = (300 GeV)2]
Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515
tanβ = 1
tanβ = 3
SM
54
Nondecoupling
[sin(β-α)=1, mH+=mA=mH (=mΦ) and M2 = 0]
Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515
55
Nondecoupling
[sin(β-α)=1, mH+=mA=mH (=mΦ) and M2 = 0]
Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515
56
Fingerprinting at the tree level
Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515
 cos(β-α) < 0,
 tanβ = 1, 2, 3 and 4,
57
Fingerprinting at the 1-loop level
Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515
 cos(β-α) < 0,
 tanβ = 1, 2, 3 and 4,
 mH+ = mA = mH (=mΦ),
 100 GeV < mΦ < 1 TeV,
 0 < M < mΦ,
 Unitarity + Vacuum stab.
58
Fingerprinting at the 1-loop level
Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515
 cos(β-α) < 0,
 tanβ: Scanned
 mH+ = mA = mH (=mΦ),
 100 GeV < mΦ < 1 TeV,
 0 < M < mΦ,
 Unitarity + Vacuum stab.
59
Fingerprinting at the 1-loop level
Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515
 cos(β-α) < 0,
 tanβ: Scanned
 mH+ = mA = mH (=mΦ),
 100 GeV < mΦ < 1 TeV,
 0 < M < mΦ,
 Unitarity + Vacuum stab.
60
One-loop corrected hZZ coupling
Kanemura, Okada, Senaha, Yuan, PRD70 (2004).
Tanβ = 2,
mΦ = 300 GeV
1 - sin2(β - α)
Even taking the maximal nondecoupling case (M2=0),
the amount of correction is less than 1%.
61
Summary
 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
→ κf and κV are universally suppressed.
2. Two Higgs doublet models → 4 patterns in κf’s.
3. Triplet models
→ κf are universally suppressed and κV 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).
62
63
Vacuum stability + Unitarity
64
Unitarity bound for the Singlet Model
Kang, Park, arXiv:1306.6713 [Singlet]
65
Gauge vs Yukawa
-π/4 < α < +π/4
0.1 < tanβ < 100
Unitarity const.
w/ 300 GeV.
Singlet Model
2HDM (Type-I)
Georgi-Machacek Model
[ξ = 2*Sqrt(6)/3]
Kang, Park, arXiv:1306.6713 [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
Unitarity const.
w/ 500 GeV.
Singlet Model
2HDM (Type-I)
Georgi-Machacek Model
[ξ = 2*Sqrt(6)/3]
Kang, Park, arXiv:1306.6713 [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
On-shell Renormalization Scheme
Parameters shift: g → g + δg,
g’ → g’ + δg’,
Wμ → ZW1/2 Wμ ,
2-point
function
= IPI diagram
+
Counter term
v → v + δv,
Bμ → ZB1/2 Bμ
3-point
function = IPI diagram + Counter term
73
Higgs coupling measurements
Peskin, 1207.2516[hep-ph]
LHC:
14 TeV, 300 fb-1
ILC1:
250 GeV, 250 fb-1
ILC:
500 GeV, 500 fb-1
ILCTeV:
1 TeV, 1000 fb-1
74
Signal Significance @125 GeV
Obs. (Exp.)
ATLAS
γγ
7+8TeV, ~25/fb
CMS
7.4σ (4.3σ)
3.2σ (4.2σ)
[CONF-2013-012]
[PAS-HIG-13-1]
ZZ*
→4l
6.6σ (4.4σ)
6.7σ (7.1σ)
[CONF-2013-013]
[PAS-HIG-13-2]
WW*
→lvlv
3.8σ (3.8σ)
4.0σ (5.1σ)
[CONF-2013-030]
[PAS-HIG-13-3]
bb
No excess
2.1σ（2.2σ）
1.4 (1.3)×SM exc.
[PAS-HIG-13-012]
[CONF-2013-079]
ττ
Spin 1 is excluded
Higgs mechanism
Yukawa?
4.1σ (3.2σ)
2.9σ (2.6σ)
[CONF-2012-160]
[PAS-HIG-13-004]
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