X CPAN DAYS
Salamanca, 29th October 2018
Ana Peñuelas (Instituto de Física Corpuscular, València)
in collaboration with O. Eberhardt and A. Pich
Motivation
Standard Model: Great success but still Strong CP problem
CP-violation Dark Matter (...)
a a
The Two Higgs Doublet Model
Fulfil all precision electroweak tests
New sources of CP-violation
Dark Matter candidates
Axion phenomenology
(...)
Φ
1=
"
G
+√1
2
(v + S
1+ iG
0)
#
, Φ
2=
"
H
+√1
2
(S
2+ iS
3)
#
V = m
211φ
†1φ
1+ m
222φ
†2φ
2− m
212φ
†1φ
2+ φ
†2φ
1+ λ
12
φ
†1φ
12+ λ
22
φ
†2φ
22+ λ
3φ
†1φ
1φ
†2φ
2+ λ
4φ
†1φ
2φ
†2φ
1+ λ
52
φ
†1φ
22+ λ
6φ
†1φ
1φ
†1φ
1+ λ
7φ
†2φ
2φ
†1φ
1+ h.c
The Two-Higgs-Doublet Model
Q
L0(M
d0Φ
1+ Y
d0Φ
2)d
R0→ (d
LM
dd
R+ d
LX
dnon-diagd
R)ϕ
0aFCNC at tree level (very constrained phenomenologically)
Y
uQ
L0(M
d0Φ
1+ Y
d0Φ
2)d
R0→ d
L(M
d+ ς
dM
d)d
Rϕ
0aAlignment in flavour space (A2HDM)
Y
u= ς
u∗M
u, Y
d= ς
dM
d, Y
`= ς
`M
`.
The Two-Higgs-Doublet Model
h H A
= R
S
1S
2S
3
CP-conserving limit
−−−−−−−−−−−→
cos α ˜ sin α ˜ 0
− sin α ˜ cos α ˜ 0
0 0 1
S
1S
2S
3
m
211, m
222, m
212, λ
1, λ
2, λ
3, λ
4→ M
H2, M
A2, M
H2±,
Y
u= ς
uM
u, Y
d= ς
dM
d, Y
`= ς
`M
`.
Parameters of the fit
v ≈ 246 GeV, m
h≈ 125 GeV,
|λ
i| < 10, i = 5, 6, 7, α ˜ ∈ [− π 2 , π
2 ],
ς
u∈ [−3, 3], ς
d∈ [−50, 50], ς
`∈ [−100, 100], M
H2, M
A2, M
H2±∈ [80, 2000]
2GeV
2.
−→ 10 parameters
HEPfit
http://hepfit.roma1.infn.it
h signal strengths
Flavour observables
Unitarity and stability
Electroweak precision observables
Direct searches
The Two-Higgs-Doublet Model – constraints
h signal strengths
Flavour observables
Unitarity and stability
Electroweak precision observables
Direct searches
µ
X= σ(pp → h)Γ(h → X )
σ(pp → h)
SMΓ(h → X )
SMh signal strengths
Flavour observables −→
Unitarity and stability
Electroweak precision observables
Direct searches
b → s γ (g − 2)
µB
s→ µ
+µ
−∆M
BsThe Two-Higgs-Doublet Model – constraints
h signal strengths
Flavour observables
Unitarity and stability
Electroweak precision observables
Direct searches
b → s γ
[Misiak et al. ’15]
b (ςu, ςd) H± (ςu, ςd) s t
γ
(g − 2)
µ→ 2-loop computation
[Cherchiglia, Stöckinger, Stöckinger-
Kim, ’17] → ς
`h signal strengths
Flavour observables
Unitarity and stability
Electroweak precision observables
Direct searches
B
s→ µ
+µ
−[Li, Lu, Pich, ’14]
∆M
Bs[Jung, Pich, Tuzón, ’06]
s
(ς
u, ς
d) H
±(ς
u, ς
d), (ς
`) b, µ b
t t, ν
(ς
u, ς
d) H
±(ς
u, ς
d), (ς
`)
s, µ
The Two-Higgs-Doublet Model – constraints
h signal strengths
Flavour observables
Unitarity and stability
Electroweak precision observables
Direct searches
CKM fits: K
0L→ π`ν, D
s→ µν, B
0− B ¯
0...
assume SM
¯ s V
tsW
±V
tbb ¯ b
t t
V
tbW
±V
tss
Pre-fit to CKM parameters
V
ud: 0
+→ 0
+transitions [Hardy, Towner, ’14]
V
ub, V
cb: b → q`ν, q = u, c exclusive +
h signal strengths
Flavour observables
Unitarity and stability
Electroweak precision observables
Direct searches
P (φ
aφ
b→ φ
cφ
d) < 1
→ At LO a
j(0)2<
14λi
φa
φb
λi
φc
φd
[Ginzburg, I. P. Ivanov, ’05]
Stability = potential bounded from below
↓ bounds on λ
i[Barroso, Ferreira, Ivanov, Santos ’13]
The Two-Higgs-Doublet Model – constraints
h signal strengths
Flavour observables
Unitarity and stability
Electroweak precision observables
Direct searches
S, T, U: Oblique parameters
V
φi
V
[Haber, O’Neil, ’10]
R
b≡
Γ(Z→hadrons)Γ(Z→bb)¯Z H±
(ςu, ςd) b
b¯
h signal strengths
Flavour observables
Unitarity and stability
Electroweak precision observables
Direct searches
Results-h signal strengths
|˜ α| < 0.0027 h = cos ˜ α S
1+ sin ˜ α S
2H = − sin ˜ α S
1+ cos ˜ α S
20.2 0.4 0.6 0.8 1.0
68.3% region 95% region
Vertex:
2ςvimi2 0 2
u
50 25 0 25 50
d
0.02 0.01 0.00 0.01 0.02
100
50
0
50
100
Results-flavour
Allowed at 95%
|ς
u||ς
d| < 6 , |ς
u| < 1.8
40 20 0 20 40
d
100 75 50 25 0 25 50 75 100
l
100 75 50 25 0 25 50 75 100
l
MH± ≤0.0009−M
H± , M
H± ≤0.0134− M
H±
qd
2 0 2
u
50 25 0 25 50
d
250 500 750 1000 1250 1500 1750 2000
M H
±(GeV)
100
50
0
50
100
Results-theory
Allowed at 95%
|M
H− M
A| ≤ 200 GeV,
|M
H− M
H±| ≤ 180 GeV ,
|M
A− M
H±| ≤ 160 GeV
M H (GeV)
80 1000 2000
M A (G eV )
M H (GeV)
80 1000 2000
M H
±(G eV )
1000 2000
M H
±(G eV )
5.0 2.5 0.0 2.5 5.0
H 4 H 5
5 0 5
H3 5.0
2.5 0.0 2.5 5.0 H 6
5 0 5
H3
H 7
Results-Direct searches
Allowed at 95%
2 0 2
u
50 25 0 25 50
d
1.5 1.0 0.5 0.0 0.5 1.0 1.5
100 50
0
50
100
Bounds on:
|˜ α| < 0.015 at 68.4 % and |˜ α| < 0.0027 at 95 %
|ς
u||ς
d| ≤ 6 at 95 %
|ς
u| < 1.8 at at 95 %
|M
H− M
A| ≤ 200 GeV
|M
H− M
H±| ≤ 180 GeV
|M
A− M
H±| ≤ 160 GeV Constraints on the planes
ς
i− ς
jς
i− M
H±λ
i− λ
jA2HDM
Model fulfilling all experimental+theoretical bounds
Different constraints → constrain different planes/directions Future plans
Combined fit Increase statistics
Include more flavour observables
Generalize to the non-CP conserving limit
Fit Iterations Chains Time
Strengths 10
88 51h
Flavour 10
68 7h
Theory 10
88 17h
HEPfit
C++ open source
Bayesian statistical analysis: Bayesian Analysis Toolkit (BAT)
r
ff= cos ˜ α + ς
fsin ˜ α, r
VV= cos ˜ α,
r
γγ=
P
f
r
ffN
CfQ
f2F (x
f) + G(x
W) + C
H±2
P
f
N
CfQ
f2F(x
f) + G(x
W)
, r
gg= | P
f
r
ffF(x
f)|
| P
f
F(x
f)| .
Results-theoretical
[Jurˆ ciukonis, Lavoura, 2018]
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
H 1
95% probability. Theoretical constraints
5.0 2.5 0.0 2.5 5.0 H 4
95% CL. Theoretical constraints
Re
H 5
5 0 5
H3 5.0
2.5 0.0 2.5 5.0
Re
H 6
5 0 5
H3
Re
H 7
Results-flavour
[Jurˆ ciukonis, Lavoura, 2018]
2 0 2
u
50 25 0 25 50
d
0
50
100
Yukawa Lagrangian
LY=−1 v
d¯LMddR+ ¯uLMuuR+ ¯`LMl`R
−
N
X
a=2
1 v
(2N−1 X
i
Riaϕ0a
d¯LYd(a)dR+ ¯uRYu(a)†uL+ ¯`LY`(a)`R
+
√ 2 v Ha+
¯
uLVCKMYd(a)dR−u¯RYu(a)†VCKMdL+ ¯νLY`(a)`R
)
+h.c. ,
↓
Natural flavour conservation
↓
Flavour alignment
Results-combined
2 0 2
u
50 25 0 25 50
d
100
50
0
50
100
2.5 0.0 2.5 40
20 0 20 40
d
2.5 0.0 2.5 100
75 50 25 0 25 50 75
l
50 0 50
100 75 50 25 0 25 50 75
l