Higgs, Supersymmetry, and CP Violation
Jae Sik Lee
National Center for Theoretical Sciences, Hsinchu, TAIWAN
♠ Contents
♠ The 1st part: Introduction to
Higgs, Supersymmetry, CP Violation and the LHC
... Please don’t be too picky
♠ The 2nd part: My works on manifestations of
CP Violation through the Supersymmetric Higgs sector
at the LHC and other low-energy experiments
... Please don’t feel too sleepy
♠ the 1st part
st
the 1 part
♠ Higgs (1/5)
• Why Particles Physics?
... to find answers to the Eternal Questions of
”What is the world made of?”
and
”What holds it together?”
The Particle Adventure
the fundamentals of matter and force
http://particleadventure.org/particleadventure/
♠ Higgs (2/5)
up
u
d
νe
e
c
s
νµ
µ
t
b
ντ
τ
γ
g
charm
top
photon
down
strange
bottom
gluon
electron neutrino
muon neutrino
tau neutrino
Z boson
electron
I
muon
II
tau
III
Three Generations of Matter
Z
W
W boson
Force Carriers
Leptons Quarks
• Answers to the Questions in 2011: Standard Model
They are all Massive except γ and g
The
BIG
question is :
How do they become massive?
♠ Higgs (3/5)
• Spontaneous breaking of Electroweak symmetry
Y. Nambu, PRL4(1960)380 Nobel Prize
2008
We are NOT living in ”True Void” ⇒ The ”Vacuum” is filled with Nonvanishing
Field Strength of a scalar field called a Higgs boson : hHi0 6= 0
Yukawa interactions ⇒ ml and mq
Gauge interactions ⇒ MW and MZ
∗ Something else may be needed for mν
♠ Higgs (4/5)
• Status of the SM Higgs:
SM
≥ 114.4 GeV (95 % C.L.)
– LEP bound: MH
ADLO, arXiv:hep-ex/0306033
SM <
– Electroweak precision data: MH
∼ 185 GeV (95 % C.L.)
ACDDLOS, arXiv:0811.4682[hep-ex]
6
mLimit = 154 GeV
July 2008
Theory uncertainty
∆α(5)
had =
5
0.02758±0.00035
0.02749±0.00012
incl. low Q2 data
∆χ
2
4
3
2
1
0
Excluded
30
Preliminary
100
mH [GeV]
300
direct-search limit included
♠ Higgs (4′/5)
• Status of the SM Higgs: ... continued
– Tevatron exclusion:
arXiv:1007.4587[hep-ex]
SM <
158 GeV <
∼ MH ∼ 175 GeV (95 % C.L.)
95% CL Limit/SM
Tevatron Run II Preliminary, <L> = 5.9 fb
LEP Exclusion
10
1
Expected
Observed
±1σ Expected
±2σ Expected
-1
Tevatron
Exclusion
SM=1
Tevatron Exclusion
July 19, 2010
100 110 120 130 140 150 160 170 180 190 200
2
mH(GeV/c )
CDF/D0,
♠ Higgs: (4′′/5)
12
8
6
G fitter
Tevatron exclusion at 95% CL
10
4
2
0
100
Gfitter, arXiv:0811.0009
150
SM
Jul 10
LEP exclusion at 95% CL
∆χ 2
• Status of the SM Higgs: combining all...
3σ
2σ
Theory uncertainty
Fit including theory errors
Fit excluding theory errors
1σ
200
250
300
MH [GeV]
We anticipate the SM Higgs boson lighter than ∼ 200 GeV
♠ Higgs (5/5)
Higgs = the God particle ?
Leon Lederman, The God Particle: If the Universe Is the
Answer, What Is the Question?
• elusive ...
• controlling behind indirectly...
and ...
causing conceptual problems ...
♠ Supersymmetry (1/4)
• The Naturalness Problem
2
MH
∼ m0
2
Λ2
19
2
with
−
Λ
∼
10
GeV
and
M
∼
10
GeV
H
2
16π
P ≪ a thunderbolt ⊗ a lottery ticket
Isn’t it natural to
assume
there is something ?
♠ Supersymmetry (2/4)
• Introducing Supersymmetry
2
2
2
δMH
∼ −ւ
Λ2 (Particles) + ր
Λ2 (”S”Particles) + MSUSY
log(Λ2/MSUSY
)
MSUSY ∼ O(1) TeV
Great Discoveries at the LHC !
♠ Supersymmetry (3/4)
• Support for the existence of ”S”Particles (I)
1/αi
1/αi
Unification of the Coupling Constants
in the SM and the minimal MSSM
60
60
50
50
40
40
30
30
20
20
10
10
0
0
5
10
15
10
log Q
0
1/α1
MSSM
1/α2
1/α3
0
5
10
15
10
log Q
♠ Supersymmetry (4/4)
• Support for the existence of ”S”Particles (II)
C. L. Bennett et al., “First Year WMAP Observations:
Preliminary Maps and Basic Results,”
Astrophys. J. Suppl. 148 (2003) 1 [arXiv:astro-ph/0302207];
M. Tegmark et al. [SDSS Collaboration],
“Cosmological parameters from SDSS and WMAP,”
Phys. Rev. D 69 (2004) 103501 [arXiv:astro-ph/0310723];
P. Gondolo [arXiv:hep-ph/0501134]
ΩΛ = 0.72 ± 0.08
Ωm = 0.27 ± 0.016
Ωb
= 0.0448 ± 0.0018
=
ΩCDM = 0.226 ± 0.0016
CDM = Lightest Supersymmetric Particle ?
♠ CP violation (1/4)
• What is CP Violation?:
If Nature treated
Left-handed particle moving right
Right-handed antiparticle moving left
differently, we are saying
CP is violated
http://universe-review.ca
and
♠ CP violation (2/4)
• Why CP Violation?: ⇒ There IS CP Violation!
η
Phys. 49 (1973) 652 Nobel Prize 2008
γ
1
β
0.5
εK
∆md
∆md
∆ms
V ub
V cb
0
sin(2β+γ )
α
-0.5
-1
-1
-0.5
0
0.5
1
ρ
M. Kobayashi and T. Maskawa, Prog. Theor.
♠ CP violation (3/4)
• Then, who ordered ”more” CP violation beyond the SM CKM phase?
A. D. Sakharov,
JETP Letters 5(1967)24
CP violation in the SM is too weak to explain the matter dominance of the Universe J. Cline,
arXiv:hep-ph/0609145
The matter-dominated Universe did!
♠ CP violation (4/4)
• Even the minimal SUSY model contains many possible sources of CP violation:
– Gaugino mass terms: 3 ⊕ 3 = 6
1
fW
f + M1 B
eB
e + h.c.)
−Lsoft ⊃ (M3 gege + M2 W
2
– Trilinear a terms af ij ≡ hf ij · Af ij : 3 × (3 ⊕ 6 ⊕ 9) = 54
e 2 − de∗R ad QH
e 1 − ee∗R ae LH
e 1 + h.c.)
−Lsoft ⊃ (e
u∗R au QH
– Sfermion mass terms: 5 × (3 ⊕ 3 ⊕ 3) = 45
∗
2
e∗ M2 deR + ee∗ M2 eeR
e+L
e † M2 L
e+u
e † M2 Q
e
−Lsoft ⊃ Q
M
u
e
+
d
R
R
R
R
e
e
e
e
e
u
e
Q
L
d
1 KM phase (SM) =⇒ 1 + 45 (Minimal SUSY Model)
♠ LHC (1/6)
•
LHC = the Large Hadron Collider
♠ LHC (1′/6)
•
LHC = the Large Hadron Collider
“Human beings can’t see
anything without wanting to
destroy it, Lyra, That’s original
sin. And I’m going to destroy it.”
... Lord Asriel
HIS DARK MATERIALS trilogy #1
♠ LHC (2/6)
• Two protons collide with a kinetic energy of 14 TeV
1 GeV ≃ a proton mass
• then the two protons are destroyed to disappear and we will see something ...
♠ LHC (3/6)
• Past and present ...
1989
1997
2003
2008
:
:
:
:
R&D starts
Construction starts
Underground installation starts
Installation completed
11 Sep 2008 : First beam circulated
20 Sep 2008 : Magnet failures ...
LHC.JPG
√
23 Nov 2009 : First collisions at √ s = 900 GeV
8 Dec 2009 : First collisions at √s = 2.36 TeV
30 Mar 2010 : First collisions at s = 7 TeV
From Junichi Kanzaki’s talk @ KEKPH2010
♠ LHC (3′/6)
♠ LHC (4/6)
• ... and near/far future of the LHC
2010 ∼ 2011 : 7 TeV (3.5+3.5 TeV) runs until 1 fb−1
LHC 1/2
⇒ For SUSY searches with 35 pb−1, see next page
2012 ∼ 2012 : Shutdown for repairing to achieve 7 (6.5) TeV/beam collisions
2013 ∼ 2014 : Go to 7 (6.5) + 7 (6.5) TeV runs to get ∼ 10 fb−1
LHC
2015 ∼ 202? : accumulate 3000 fb−1 with 250 ∼ 300 fb−1 per year
again, from Junichi Kanzaki’s talk @ KEKPH2010, or
LHC Performance Workshop - Chamonix 2010 (Jan)
♠ Initial SUSY searches with 35 pb−1 at the LHC
• CMS (jets + missing ET ; left) and ATLAS (lepton + jets + missing ET ; right)
m1/2 [GeV]
CMS, PLB698(2011)196,2011, arXiv:1101.1628 [hep-ex] and ATLAS, arXiv:1102.2357 [hep-ex]
400
MSUGRA/CMSSM: tanβ = 3, A = 0, µ>0
0
ATLAS
350
int
L = 35 pb-1, s=7 TeV
Observed limit 95% CL
Median expected limit
1 lepton, ≥3 jets
Expected limit ± 1σ
300
CMS jets (αT), 35 pb-1
~±
LEP2 l
±
LEP2 χ∼
1
± 0
D0 χ∼ , χ∼
~
g (700 GeV)
1
250
~
g (600 GeV)
200
2
D0 ~g, ~q, µ<0, 2.1 fb-1
CDF ~g, ~q, tanβ=5, 2 fb-1
~
g (500 GeV)
~
g (400 GeV)
150
~
q (400 GeV)
100
200
300
400
~
~
q (500 GeV) q (600 GeV)
500
600
~
q (700 GeV)
700
800 900
m0 [GeV]
ATLAS, more stringent ...
♠ LHC (4′/6)
• ... and near/far future of the LHC
2010 ∼ 2011 : 7 TeV (3.5+3.5 TeV) runs until 1 fb−1
LHC 1/2
2012 ∼ 2012 : Shutdown for repairing to achieve 7 (6.5) TeV/beam collisions
2013 ∼ 2014 : Go to 7 (6.5) + 7 (6.5) TeV runs to get ∼ 10 fb−1
LHC
2015 ∼ 202? : accumulate 3000 fb−1 with 250 ∼ 300 fb−1 per year
again, from Junichi Kanzaki’s talk @ KEKPH2010, or
LHC Performance Workshop - Chamonix 2010 (Jan)
♠ LHC (5/6)
• ... and near/far future of the LHC: ... continued
3000 fb−1 ≈ 2,400,000,000 tt̄ pairs : Top factory
≈ 100,000,000 130 GeV SM Higgs bosons
≈ 3,000,000 O(1) TeV gluinos + squarks
≈ 300,000 O(1) TeV charginos + neutralinos
♠ LHC (6/6)
Higgs
Top
• ... and near/far future of the LHC: ... continued
DM
SUSY
3000 fb−1 ≈ 2,400,000,000 tt̄ pairs : Top factory
≈ 100,000,000 130 GeV SM Higgs bosons
≈ 3,000,000 O(1) TeV gluinos + squarks
≈ 300,000 O(1) TeV charginos + neutralinos
Great Expectations at the LHC!
♠ the 2nd part
the 2
nd
part
♠ Preliminary (1/4)
• The Nobel Prize in Physics 2008: ”Passion for symmetry” (broken?)
♠ Preliminary (2/4)
• My works aim at ...:
♠ Preliminary (3/4)
• Introducing SUSY =⇒ Introducing lots of additional CP phases ! :
1 KM phase (SM) =⇒ 1 + 45 (Minimal SUSY Model)
My Question:
How does the SUSY CP violation manifest itself through the Higgs sector ?
more specifically,
Where to find it? and Why through Higgs sector?
♠ Preliminary (4/4)
•
Where to find it?
Colliders : LHC
8
< SM Higgs
M SSM Higgs
:
CP V Signatures
B-meson Obsrvables
8
+ −
>
< ∆MBd,s , Bs → µ µ ,
B → τ ν , B → Xsγ ,
>
: ···
Dark Matter
˘
Electric Dipole Moments
http://www.er.doe.gov/hep/vision/index.shtml
χχ → γ , p̄ , etc
♠ Preliminary (4′/4)
•
Why through Higgs sector?
– Experimental Side: LHC
∗ Higgs boson will be searched most intensively
∗ Higgs boson will be studied most extensively
– Theoretical Side: Quantum sensitivity
∗ Large quantum correction
∗ Resonant enhancement
♠ CPsuperH
• Tool: CPsuperH : △ RG-improved effective potential approach
– For
experimentalists
as
well
as
phenomenologists who are exploring the
MSSM Higgs sector both in CP-conserving
and CP-violating cases V. M. Abazov et al. [D0
Collaboration], “Search for neutral supersymmetric Higgs
bosons in multijet events at s**(1/2) = 1.96-TeV,” Phys.
Rev. Lett. 95 (2005) 151801 [arXiv:hep-ex/0504018];
A. Abulencia et al. [CDF Collaboration], “Search for charged
Higgs bosons from top quark decays in pp̄ collisions at
√
s = 1.96-TeV,” Phys. Rev. Lett. 96 (2006) 042003
[arXiv:hep-ex/0510065].
– Consistent computational tool for both
Energy- and Intensity-Frontier experiments
including several B observables and EDMs
♠ Where to find it ?
II-A
Colliders
Colliders : LHC
8
< SM Higgs
M SSM Higgs
:
CP V Signatures
B-meson Obsrvables
8
+ −
>
< ∆MBd,s , Bs → µ µ ,
B → τ ν , B → Xsγ ,
>
: ···
Dark Matter
˘
Electric Dipole Moments
http://www.er.doe.gov/hep/vision/index.shtml
χχ → γ , p̄ , etc
♠ SM Higgs (1/2)
expected significance
• LHC Discovery Significance of the SM Higgs
• H → ττ
18
16
Combined
(*)
ZZ → 4l
γγ
ATLAS
-1
14
L = 10 fb
• H → γγ
ττ
WW0j → eν µν
WW2j → eν µν
12
⊲ H → W W ∗ → lνlν (GF)
10
⊲ H → W W ∗ → lνlν (VBF)
8
6
2 H → ZZ (∗) → 4 l
4
2
0
100
ATLAS TDR, arXiv:0901.0512[hep-ex]
120
140
160
180
200
220
mH (GeV)
The W W channel plays a dominant
<
role for 130 GeV <
∼ MH ∼ 190 GeV !
♠ SM Higgs (2/2)
W+jets
45
WW
40
tt
Signal
Pseudodata
35
30
25
20
ATLAS
15
∫
10
5
0
0
100
200
300
400
End point
Number of events / 8 GeV / 10 fb-1
Events / ( 10 )
• The 2 missing neutrinos: Transverse mass vs. MAOS Higgs mass
300
SM
MH
= 150 GeV
250
200
150
100
-1
L dt=10 fb
500
600
MT(GeV)
50
0
120
140
160
180
200
220
240
260
280
mmaos
[GeV]
H
Mass peak
K. Choi, S. Choi, JSL, C.B. Park, PRD80 (2009) 073010;
K. Choi, JSL, C.B. Park, arXiv:1008.2690 [hep-ph], to appear in PRD
♠ MSSM Higgs (1/2)
• LEP Limits on the MSSM Higgs:
A. Djouadi, hep-ph/0503173 and references there in: P. Bechtle,
CPNSH Report, CERN-2006-009, hep-ph/0608079; ADLO, hep-ex/0602042, Combined results with FeynHiggs
tanβ
CP Conserving
mh°-max
10
Excluded
by LEP
1
Theoretically
Inaccessible
0
20
40
60
80 100 120 140
mh° (GeV/c2)
MH1 & 90 GeV ?
MH1 <
∼ 10 GeV !
♠ MSSM Higgs (2/2)
• LHC Discovery of the MSSM Higgs:
ATLAS TDR(1999); M. Schumacher, CPNSH Report, CERN-
2006-009, hep-ph/0608079
CP Conserving
CP Violating
tanβ
ATLAS preliminary
30
20
10
9
8
7
6
5
4
3
2
theoretically inaccessible
1
No Lose ?
0
20
40
60
80
100
No Higgs !
120
140
MH1 (GeV)
♠ b-quark Fusion (1/2)
• Strong dependence of Higgs-boson production via b-quark fusion on CP phases:
CPX
Scenario with Φ3 = 0◦ or Φ3 = 180◦ and MH1 = 115 GeV. F. Borzumati and JSL, PLB595(2004)347 and
PLB641(2006)486
∗ Solid: Φ3 = 180◦ and Dashed: Φ3 = 0◦
∗ Around ΦAµ = 100◦, MH2 − MH1 ≃ 3 GeV =⇒ Distinguishable ?
♠ b-quark Fusion (2/2)
• Invariant mass distribution when Higgs bosons decay into two γ’s and/or µ+µ−
At the LHC, the experimental resolution δMγγ ∼ 1 GeV and δMµµ ∼ 3 GeV
ATLAS TDR, Vol 2, CERN-LHCC-99-15, ATLAS-TDR-15 (1999); CMS Physics TDR, Volume II, CERN-LHCC2006-021, 25 June 2006
H1,2 → γγ
One peak
H1,2 → µ+µ−
T wo peaks
♠ CP Asymmetries (1/3)
• CP asymmetry in Higgs decays in the tau leptons :
J.
Ellis,
JSL
and
A.
D71(2005)075007
W+
τ+
Hi
W
Hj
τ−
−
σRR
ACP =
σRR − σLL
σRR + σLL
with
(
σLL
σRR ≡ σ(pp → H → τR+ τR−X)
σLL ≡ σ(pp → H → τL+ τL−X)
Pilaftsis,
♠ CP Asymmetries (2/3)
• Resonant transitions between Higgs bosons enhance the asymmetry!:
Hi
Hj
i 6= j
≃
Hi
Hi
when ∆MH ≃ ΓH
The neutral Higgs bosons should not be treated separately !
J. Ellis, JSL and A. Pilaftsis, D70(2004)075010
♠ CP Asymmetries (3/3)
W
WW
• Integrated CP asymmetry AW
CP with σtot > 0.2 pb:
1
0.75
Φ3 = − 10
o
WW
ACP
1
0.75
0.5
0.5
0.25
0.25
0
0
-0.25
-0.25
-0.5
-0.5
-0.75
-0.75
-1
-100
0
100
-1
ΦA [ ]
o
Φ3 = − 90o
WW
ACP
-100
0
100
ΦA [ o ]
CP asymmetry is large over the whole ranges of CP phases !
♠ Diffraction (1/3)
• Diffraction is a process with a t-channel exchange leading to a Large Rapidity Gap
M. Arneodo, M. Diehl, hep-ph/0511047
The differential cross section
dσ (pp → pp) dt
elastic
has a resemblance to the
diffraction pattern in optics:
I(θ)
λ
I(θ)
θ
λ /2Ro
Ro
θ
♠ Diffraction (2/3)
• Exclusive double diffractive process
p1
s →
p2
p′1
ga
Hi ⊕ Hj
gb
(M , y)
p′2
f
√
† M 2 = s − 2 s(E1′ + E2′ ) + (p′1 + p′2)2
⇒ δM ∼ 1 GeV !
f¯
† Clean environment due to the large
rapidity gap
Outgoing protons remain intact & scatter
through small angles with p⊥ ≪ 1 GeV
A. De Roeck, et al., EPJC25 (2002) 391; M. Boonekamp,
et al., PLB598 (2004) 243; K. A. Assamagan et al. hepph/0406152; B. E. Cox, hep-ph/0409144, hep-ph/0501064;
J. Ellis, JSL and A. Pilaftsis, D71(2005)075007
B.E. Cox∗ , J.R. Forshaw, JSL, J.W. Monk∗ and A. Pilaftsis,
∗ Need TOTEM/ATLASFP detectors
PRD68 (2003) 075004; V.A. Khoze, A.D. Martin and M.G.
Ryskin, EPJC34 (2004) 327
♠ Diffraction (3/3)
CP
a
τ
• pp → pHip ; Hi → τ +τ −
(ΦA , Φ3) = (90◦ , −90◦) (ΦA , Φ3) = (90◦ , −10◦)
1
0.8
y=0
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
Invariant mass distribution can be studied !
-0.8
-1
116
118
120
122
124
126
128
130
M [ GeV ]
♠ Beyond the Minimal SUSY Model (1/2)
• The µ problem
J. E. Kim and H. P. Nilles, Phys. Lett. B 138, 150 (1984)
µ H1H2
200
−→
S H1H2
More Higgs bosons and more CP violation !
1
150
100
10-1
50
0
10-2
-50
-100
10-3
400 450 500 550 600 650 700 750 800
400 450 500 550 600 650 700 750 800
K. Cheung, T. J. Hou, JSL and E. Senaha, PRD82(2010)075007
♠ Beyond the Minimal SUSY Model (2/2)
• We are working on ...
– Constraints from EDMs on the new CP violation
– ElectroWeak Phase Transitions
– New CP-phase driven baryogenesis
– B- and K-meson observables
– Collider signatures of the light Higgs bosons
– Higgs Inflation(?)
– etc
♠ Summary (LHC)
• Phases of the LHC :
I
(2013 ∼ 2014) :
LHC with L ∼ 10 fb−1
SM Higgs Discovery,
Non-SM-like Higgs decays and productions, Multiple Higgs peaks
II
(2015 ∼ 2016) :
LHC with L ∼ 300 fb−1
I ⊕ Strongly-coupled Higgs, CP asymmetries, Final-state spin-spin correlations
III
(2017 ∼ 202?) :
LHC with L ≫ 300 fb−1
I ⊕ II ⊕ Exotic Higgs productions
♠ Conclusions and Future Prospects
• Spontaneous breaking of the electroweak symmetry may be responsible for the
masses of SM particles
• Supersymmetry may stabilize the Higgs-boson masses against the Quantum
corrections
• The additional CP phases in the models extended by Supersymmetry may explain
the matter dominance of the Universe
• The Supersymmetric CP phases may manifest themselves through the Higgs sector
in Energy-, Intensity-, and Cosmic-Frontier experiments
• The LHC is to give definite answers to these may’s
♠ Where to find it ?
II-B
B-meson Observables
Colliders

LEP Holes
LHC Signatures
B-meson Obsrvables
8
+ −
>
< ∆MBd,s , Bs → µ µ ,
B → τ ν , B → Xsγ ,
>
: ···
Dark Matter
˘
Electric Dipole Moments
http://www.er.doe.gov/hep/vision/index.shtml
χχ → γ , p̄ , etc
♠ B Observables (1/4)
• Higgs-mediated B-meson mixing and rare decays: LHCb and SuperB
J. Ellis, JSL and
A. Pilaftsis, PRD76(2007)115011
d H
−Leff
=
g
cd gL ¯ PL d Hi + h.c.
dM
Hidd
2MW
−1
†
L
gH
∝
V
¯
CKM [1 + tan β ∆d ]
i dd
Φ†1,2
Φ†1,2
∆d[ΦCP] :
ej
Q
QjL
×
g̃
VCKM
ei
D
diR
ek
U
×
el
Q
QjL He u He d
diR QjL
×
ej
Q
fi
W
e
B
×
ed
eu H
H
Φ†2
diR
Non-universal Quantum interactions inducing the mixing and rare decays !
♠ B Observables (2/4)
ΦM = 180
o
10
-2
ΦM = 0
10
10
10
ΦM = 180
o
-1
MEASURED
SUSY
-1
10 2
EXP
MEASURED
10
∆ MBs
∆ MBd
SUSY
10
EXP
[ ps ]
1
-1
[ ps ]
SUSY
• ∆MBSUSY
and
∆M
as functions of tan β(MSUSY ) for three values of ΦM ≡
B
s
d
fL,E = 200 GeV and ΦGUT = 0◦
Φ1 = Φ2 = Φ3 SPS1a-like scenario M
A
o
-3
ΦM = 90
ΦM = 0
1
-4
ΦM = 90
o
-5
10
20
30
GUT
ΦA =
40
o
0
10
50
o
GUT
ΦA =
-1
10
20
tanβ
Strong CP phase dependence
30
40
o
0o
50
tanβ
♠ B Observables (3/4)
10
RBτν
B(BS → µµ) x 10
7
• B(B̄s0 → µ+µ−) and the ratio RBτ ν as functions of tan β(MSUSY ) for three values
fL,E = 200 GeV and ΦGUT = 0◦
of ΦM ≡ Φ1 = Φ2 = Φ3 SPS1a-like scenario M
A
GUT
ΦA = 0o
ΦM = 90
EXP
1
UPPER
EXP (1 σ)
o
10
o
-1
ΦM = 180
o
-1
10
-2
GUT
ΦM = 180
o
-2
10
20
o
1
SM
10
ΦM = 90
(90 %)
ΦM = 0
10
10
30
40
50
10
-3
10
ΦM = 0
ΦA = 0o
20
tanβ
Strong CP phase dependence
30
40
50
tanβ
o
♠ B Observables (4/4)
ACP [ % ]
B ( b → s γ ) x 10
4
• B(B → Xsγ) and Adir
CP (B → Xs γ) as functions of ΦM for four values of
fL,E = 200 GeV and ΦGUT = 0◦
tan β(MSUSY ) = 10 , 20 , 30 , 40 SPS1a-like scenario M
A
tanβ = 40
30
10
20
6
GUT
ΦA = 0
o
4
2
10
0
-2
EXP ( 2 σ )
-4
GUT
ΦA =
1
0
100
❏
o
0
200
EXP
Bb → s γ
-6
300
0
100
ΦM [ ]
o
Strong CP phase dependence
200
300
ΦM [ ]
o
♠ Where to find it ?
II-C
EDMs
Colliders

LEP Holes
LHC Signatures
B-meson Obsrvables
8
+ −
>
< ∆MBd,s , Bs → µ µ ,
B → τ ν , B → Xsγ ,
>
: ···
Dark Matter
˘
Electric Dipole Moments
http://www.er.doe.gov/hep/vision/index.shtml
χχ → γ , p̄ , etc
♠ EDMs (1/4)
• Electric Dipole Moments (EDMs): T violation ⇒ CP violation (under CPT )
H
|dTl| < 9 × 10−25 e cm ,
EDM
= −d E · ŝ
|dHg | < 3.1 × 10−29 e cm ,
|dn| < 3 × 10−26 e cm
B. C. Regan, E. D. Commins, C. J. Schmidt and D. DeMille, PRL88 (2002) 071805; W. C. Griffith, M. D. Swallows,
T. H. Loftus, M. V. Romalis, B. R. Heckel and E. N. Fortson, PRL102 (2009) 101601; C. A. Baker et al., PRL97
(2006) 131801
– No large CP phases? -No! But, one needs to introduce some hierarchy between
first two and third generations and/or some moderate tuning among parameters
♠ EDMs (2/4)
• EDM constraints and cancellation:
CPX Scenario with ΦA
t,b
= Φ3 = 90◦, ΦA
u,d,c,s
= 0◦
tan β = 5, MH ± = 300 GeV, |M2 | = 2|M1 | = 100 GeV, and MSUSY = 0.5 TeV The hierarchy factor ρ:
= ρ MX̃ with X = Q = U = D = L = E J. Ellis, JSL and A. Pilaftsis, JHEP08(2008)049
2
| dn / d
10
1
10
-1
10
10
10
10
|
o
2
10
10
10
( Φ1 , Φ2 ) = (0 , 90 )
o
( Φ1 , Φ2 ) = (0 , 90 )
o
o
-25
χ
±
-26
-1
ρ
|
-24
0
H
10
10
10
10
( Φ1 , Φ2 ) = (0 , 90 )
o
o
2
d
-28
G
1
10
ρ
10
10
10
10
10
E
d u,d
-1
10
10
1
10
-1
1
10
1
0
2
ρ
3
C
χ
o
10
10
d u,d
-27
3
1
1
| dn / d
10
( Φ1 , Φ2 ) = (0 , 90 )
o
EXP
| dEe | [ e cm ]
10
3
1
1
10
10
| dCd | [ cm ]
EXP
| dTl / d
10
o
EXP
( Φ1 , Φ2 ) = (0 , 90 )
o
| dHg / d
3
3
|
10
|
1,2
EXP
MX̃
ρ
-23
10
ρ
( Φ1 , Φ2 ) = (0 , 90 )
o
o
-24
0
H
-25
~
χ
-26
χ
-27
g
±
0
-28
1
10
ρ
♠ EDMs (3/4)
• Analytic determination of the cancellation regions: EDM-free
Optimal direction J. Ellis, JSL and A. Pilaftsis, JHEP10(2010)049
EDM vector
directions
and
An Observable vector
Φ = E × (O × E)
An Optimal direction
CP-phase space
Subspace of EDM-free directions
♠ EDMs (4/4)
• Optimal direction : the higher-dimensional generalization with N CP phases and
n EDM constraints
(1)
Φα = ǫαβ1···βnγ1···γ
N −n−1
(n)
E β1 · · · E βn B γ1···γN −n−1
where (N -n-1)-dimensional B form is
B γ1···γN −n−1 = ǫγ1···γ
N −n−1 σβ1 ···βn
(1)
(n)
Oσ E β1 · · · E βn
♠ Where to find it ?
II-D
Dark Matter
Colliders

LEP Holes
LHC Signatures
B-meson Obsrvables
8
+ −
>
< ∆MBd,s , Bs → µ µ ,
B → τ ν , B → Xsγ ,
>
: ···
Dark Matter
˘
Electric Dipole Moments
http://www.er.doe.gov/hep/vision/index.shtml
χχ → γ , p̄ , etc
♠ Dark Matter (1/1)
• LEP Holes ⇒ Very light 7.5 GeV Higgs signals through the inclusive process
χχ → H → γ , p̄ JSL and S. Scopel, Phys. Rev. D 75 (2007) 075001 [arXiv:hep-ph/0701221]
♠ MAÔS momenta of the missing neutrinos (1/2)
• MAÔS = M T 2-Assisted On-shell Scheme:
H → W (p + k) W (q + l) → l(p) ν(k) l′(q) ν ′(l)
(MH2 )MAÔS = (p + k MAÔS + q + lMAÔS)2
ÔS
= −qT
kMA
T
ÔS
k MA
L
=
ÔS
and lMA
= −pT
T
ÔS
|kMA
|
T
|pT | pL ,
ÔS
lMA
L
=
ÔS
|lMA
|
T
|qT | q L
♠ MAÔS momenta of the missing neutrinos (2/2)
• Is the modified MAÔS scheme working well?:
MH = 140 GeV
MH = 180 GeV
∆ kT
∆ kL (modified)
∆ kL (original)
14000
12000
Number of events
Number of events
18000
16000
∆ kT
∆ kL (modified)
∆ kL (original)
16000
14000
12000
10000
10000
8000
8000
6000
6000
4000
4000
2000
2000
0
-300
-200
-100
0
100
200
300
∆ k T, L [GeV]
0
-300
-200
-100
0
100
200
300
∆ k T, L [GeV]
♠ MT 2: 1/2
• Transverse Mass MT :
V (p)
p
p = ( mV 2 + |pT |2 + p2L , pT , pL)
µ
p
k = ( mχ2 + |kT |2 + k 2L , kT , k L)
µ
X
χ(k)
2
2
2
MX = mV + mχ + 2
2
2
2
MT = mV + mχ + 2
p
p
kT = p/T (fully determined)
p
mV 2 + |pT |2 + p2L mχ2 + |kT |2 + k 2L − pT · kT − pLk L
mV 2 + |pT |2
p
mχ2 + |kT |2
MT ≤ MX
− pT · kT
♠ MT 2: 2/2
• ... then MT 2 ?: Generalization of MT when there are 2 missing particles
V (p)
X(1)
X(2)
χ(k)
χ(l)
V (q)
kT + lT = p/T
Only determined are ...
the 2 among the 4 unknown degrees of freedom !
... but we know:
(1)
(2)
true
max{MT , MT }(ktrue
T , lT ) ≤ MX
♠ MT 2: 2′/2
• ... then MT 2 ?: Generalization of MT when there are 2 missing particles
kT + lT = p/T
Only determined are ...
the 2 among the 4 unknown degrees of freedom !
... but we know:
(1)
(2)
true
max{MT , MT }(ktrue
T , lT ) ≤ MX
(1)
(2)
(1)
(2)
min
true true
max{MT , MT }(kmin
T , lT ) ≤ max{MT , MT }(kT , lT ) ≤ MX
oi
h
n
(2)
(1)
≤ MX
MT 2 ≡ minkT +lT =p/T max MT , MT
♠ AFB at the Tevatron: 1/2
• q q̄ → tt̄ and AFB at the Tevatron
AFB ≡
Shabamina(Blois2010)
Nt(cos θ ≥ 0) − Nt̄(cos θ ≥ 0)
= (0.15 ± 0.05 ± 0.024)
Nt(cos θ ≥ 0) + Nt̄(cos θ ≥ 0)
Pertinent ∼ 2σ deviation !
♠ AFB at the Tevatron: 2/2
• Effective Lagrangian approach to explain the anomaly
D.-W. Jung, P. Ko, JSL, S.-h. Nam,
PLB691(2010)238; D.-W. Jung, P. Ko, JSL, arXiv:1012.0102 [hep-ph]
gs2 AB
L6 = 2 C8q (q̄AT aγµqA)(t̄B T aγ µtB )
Λ
6
0.5
09
g 8t
)=
V
1
0.
=
FB
0.
21
=
DFB
2
FB
)=
A
2
2
/m
-1
0
L
g 8q
-0.1
L
g 8t
-2
V
2
)=
IV
/m
(Λ
V
I
2
L
g 8t
2
/m
pb
0.1
0
(Λ
L
2
pb
(Λ
A
L
g 8q
L
98
0.2
g 8t
7.
02
7.
C2 (1 TeV/Λ)2
L
L
=
0.3
=
II
g 8q
σ
σ
2
g 8q
0.4
4
2
/m
-2
)=
V
-0.3
2
-4
(Λ
-0.2
III
-0.4
-6
-6
LL
RR
,
+ C8q
C1 ≡ C8q
-4
-2
0
2
2
C1 (1 TeV/Λ)
4
6
RL
LR
,
+ C8q
C2 ≡ C8q
-0.5
-0.5 -0.4 -0.3 -0.2 -0.1
0
0.1 0.2 0.3 0.4 0.5
D
RL
LR
LL
RR
)
− C8q
) ± (C8q
− C8q
D , DFB ∝ (C8q
♠ Backup
• CPX Scenario:
2
Recall CPV mixing ∝ ℑm(Af µ)/MSUSY
MQ̃3 = MŨ3 = MD̃3 = ML̃3 = MẼ3 = MSUSY
|µ| = 4 MSUSY , |At,b,τ | = 2 MSUSY
|M3| = 1 TeV
Varying parameters are :
pole
tan β , MH
± , MSUSY
(Φµ) , ΦAt , ΦAb , ΦAτ , Φ3
*
*
M1 and M2
For simplicity, common ΦA
♠ Backup
pole
• Large tan β and MH
± ∼ 150 GeV ⇒ Trimixing scenario
J. Ellis, JSL and A. Pilaftsis,
PRD70(2004)075010, PRD71(2005)075007, PRD72(2005)095006, and NPB718(2005)247
pole
tan β = 50, MH
± = 155 GeV,
MQ̃3 = MŨ3 = MD̃3 = ML̃3 = MẼ3 = 0.5 TeV,
|µ| = 0.5 TeV, |At,b,τ | = 1 TeV, |M1,2| = 0.3 TeV, |M3| = 1 TeV,
Φµ = 0◦, Φ1,2 = 0◦ .
For ΦAt ,Ab,Aτ = 90◦ and Φ3 = −90◦, we have (in GeV)
MH1 = 117.6, MH2 = 118.7, MH3 = 122.6,
ΓH1 = 1.48,
ΓH2 = 8.12,
ΓH3 = 8.21.
All Higgs bosons are nearly degenerate with Γi & ∆MH !
♠ Backup
• SPS1a-like scenario
–
–
–
–
At
At
At
At
MZ : Three gauge couplings α1(MZ ), α2(MZ ), and α3(MZ )
mpole
: Quark and Lepton masses mq,l (mpole
) and VCKM(mpole
)
t
t
t
MSUSY : tan β(MSUSY )
MMFV = MGUT: 19 MCPMFV Parameters
iΦ
2
2
fQ,U,D,L,E
|M1,2,3| ei Φ1,2,3 , |Au,d,e| e Au,d,e , M
, MH
u,d
Specifically, we have taken the parameter set:
|M1,2,3| = 250 GeV
2
2
2 f2 f2
fQ
fL2 =M
fE2 = (100 GeV)2
MH
=M
=
=
=
=
M
M
M
M
H
U
D
u
d
|Au| = |Ad| = |Ae| = 100 GeV
This parameter set is equivalent to SPS1a when ΦA
u,d,e
tan β = 10
pole
= 180◦ and Φ1,2,3 = 0◦ if MSUSY = mt
and
♠ Backup
• The B-meson observables strike against CPX!: B(Bs → µ+µ−) (95 %), B(B →
Xsγ) (2 σ), RBτ ν (1 σ), Υ(1S) → H1γ CPX scenario with ΦA = Φ3 = 90◦ and MSUSY = 0.5
ρ=1
50
45
tan β
tan β
TeV JSL, M. Carena, J. Ellis, A. Pilaftsis, C.E.M. Wagner, arXiv:0712.2360; JSL and S. Scopel, PRD75(2007)075001
B(b → sγ)
40
50
45
40
Υ → H1 γ
35
ρ = 10
35
30
30
25
25
B(Bs → µµ)
20
20
RBτν
15
15
10
10
5
5
0
20
40
60
80
100
120
MH1 [ GeV ]
0
20
40
60
80
100
120
MH1 [ GeV ]
The CPX scenario excluded ? ... flavour-mixing terms