higgs, supersymmetry, and cp violation jae sik lee · higgs, supersymmetry, and cp violation jae...

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

the 1st

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 Adventurethe fundamentals of matter and force

http://particleadventure.org/particleadventure/

♠ Higgs (2/5)

• Answers to the Questions in 2011: Standard Model

Fo

rce C

arr

iersWZ

gγ

W boson

Z boson

gluon

photon

Lep

ton

s

e µ τν ν νe µ τ

electron muon tau

electron neutrino muon neutrino tau neutrino

Qu

ark

s

d s bu c t

down strange bottom

up charm top

I II IIIThree Generations of Matter

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 : 〈H〉0 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:

– LEP bound: MSMH ≥ 114.4 GeV (95 % C.L.) ADLO, arXiv:hep-ex/0306033

– Electroweak precision data: MSMH

<∼ 185 GeV (95 % C.L.) direct-search limit included

ACDDLOS, arXiv:0811.4682[hep-ex]

0

1

2

3

4

5

6

10030 300

mH [GeV]

∆χ2

Excluded Preliminary

∆αhad =∆α(5)

0.02758±0.00035

0.02749±0.00012

incl. low Q2 data

Theory uncertaintyJuly 2008 mLimit = 154 GeV

♠ Higgs (4′/5)

• Status of the SM Higgs: ... continued

– Tevatron exclusion: 158 GeV <∼ MSMH

<∼ 175 GeV (95 % C.L.) CDF/D0,

arXiv:1007.4587[hep-ex]

1

10

100 110 120 130 140 150 160 170 180 190 200

1

10

mH(GeV/c2)

95%

CL

Lim

it/SM

Tevatron Run II Preliminary, <L> = 5.9 fb-1

ExpectedObserved±1σ Expected±2σ Expected

LEP Exclusion TevatronExclusion

SM=1

Tevatron Exclusion July 19, 2010

♠ Higgs: (4′′/5)

• Status of the SM Higgs: combining all... Gfitter, arXiv:0811.0009

[GeV]HM

100 150 200 250 300

2 χ∆

0

2

4

6

8

10

12

LEP

excl

usio

n at

95%

CL

Teva

tron

exc

lusi

on a

t 95%

CL

σ1

σ2

σ3

Theory uncertaintyFit including theory errorsFit excluding theory errors

[GeV]HM

100 150 200 250 300

2 χ∆

0

2

4

6

8

10

12

G fitter SM

Jul 10

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

M2H ∼ m0

2 − Λ2

16π2with Λ ∼ 1019 GeV and MH ∼ 102 GeV

P ≪ a thunderbolt ⊗ a lottery ticket

Isn’t it natural to

assumethere is something ?


• Introducing Supersymmetry

δM2H ∼ −Λ2ւ (Particles) + Λ2ր (”S”Particles) + M2

SUSY log(Λ2/M2SUSY)

MSUSY ∼ O(1) TeV

Great Discoveries at the LHC !


• Support for the existence of ”S”Particles (I)

10log Q

1/α i

1/α1

1/α2

1/α3

MSSM

10log Q

1/α i

Unification of the Coupling Constants in the SM and the minimal MSSM

0

10

20

30

40

50

60

0 5 10 150

10

20

30

40

50

60

0 5 10 15


• 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 ± 0.0018ΩCDM = 0.226 ± 0.0016

CDM = Lightest Supersymmetric Particle ?

♠ CP violation (1/4)

• What is CP Violation?:

http://universe-review.ca

If Nature treated

Left-handed particle moving right and

Right-handed antiparticle moving left

differently, we are saying

CP is violated


• Why CP Violation?: ⇒ There IS CP Violation! M. Kobayashi and T. Maskawa, Prog. Theor.

Phys. 49 (1973) 652 Nobel Prize 2008

ρ-1 -0.5 0 0.5 1

η

-1

-0.5

0

0.5

1γ

β

α

)γ+βsin(2

sm∆dm∆ dm∆

Kε

cbVubV

ρ-1 -0.5 0 0.5 1

η

-1

-0.5

0

0.5

1


• 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!


• Even the minimal SUSY model contains many possible sources of CP violation:

– Gaugino mass terms: 3 ⊕ 3 = 6

−Lsoft ⊃1

2(M3 gg + M2 WW + M1 BB + h.c.)

– Trilinear a terms af ij ≡ hf ij · Af ij: 3 × (3 ⊕ 6 ⊕ 9) = 54

−Lsoft ⊃ (u∗R au QH2 − d∗

R ad QH1 − e∗R ae LH1 + h.c.)

– Sfermion mass terms: 5 × (3 ⊕ 3 ⊕ 3) = 45

−Lsoft ⊃ Q† M2eQ Q + L† M2

eL L + u∗R M2

eu uR + d∗R M2

ed dR + e∗R M2ee eR

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 seeanything without wanting todestroy it, Lyra, That’s originalsin. 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 : R&D starts1997 : Construction starts2003 : Underground installation starts2008 : Installation completed

11 Sep 2008 : First beam circulated20 Sep 2008 : Magnet failures ...

23 Nov 2009 : First collisions at√

s = 900 GeV8 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.JPG

♠ 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)CMS, PLB698(2011)196,2011, arXiv:1101.1628 [hep-ex] and ATLAS, arXiv:1102.2357 [hep-ex]

[GeV]0m100 200 300 400 500 600 700 800 900

[G

eV

]1

/2m

150

200

250

300

350

400

(400 GeV)q~ (500 GeV)q~ (600 GeV)q~ (700 GeV)q~

(400 GeV)g~

(500 GeV)g~

(600 GeV)g~

(700 GeV)g~

>0µ= 0, 0

= 3, AβMSUGRA/CMSSM: tan

=7 TeVs, -1 = 35 pbintL

3 jets≥1 lepton,

ATLAS Observed limit 95% CL

Median expected limit

σ1±Expected limit -1), 35 pb

TαCMS jets (

± l~

LEP2

1

±χ∼LEP2

2

0χ∼, 1

±χ∼D0 -1<0, 2.1 fbµ, q~, g~D0

-1=5, 2 fbβ, tanq~, g~CDF

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 tt 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)

• ... and near/far future of the LHC: ... continued

3000 fb−1 ≈ 2,400,000,000 tt 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

Top

Higgs

SUSY

DM

Great Expectations at the LHC!

♠ the 2nd part

the 2nd part

♠ Preliminary (1/4)

• The Nobel Prize in Physics 2008: ”Passion for symmetry” (broken?)


• My works aim at ...:


• 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?


• Where to find it?

http://www.er.doe.gov/hep/vision/index.shtml

Colliders : LHC

8<:

SM Higgs

MSSM Higgs

CPV SignaturesB-meson Obsrvables

8><>:

∆MBd,s, Bs → µ+µ− ,

B → τν , B → Xsγ ,

· · ·

Electric Dipole Moments

Dark Matter

˘χχ → γ , p , 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 asphenomenologists who are exploring theMSSM Higgs sector both in CP-conservingand 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 pp collisions at√

s = 1.96-TeV,” Phys. Rev. Lett. 96 (2006) 042003

[arXiv:hep-ex/0510065].

– Consistent computational tool for bothEnergy- and Intensity-Frontier experimentsincluding several B observables and EDMs

♠ Where to find it ?

II-A Colliders


Colliders : LHC

8<:

SM Higgs

MSSM Higgs

CPV SignaturesB-meson Obsrvables

8><>:


B → τν , B → Xsγ ,

· · ·


Dark Matter


♠ SM Higgs (1/2)

• LHC Discovery Significance of the SM Higgs ATLAS TDR, arXiv:0901.0512[hep-ex]

(GeV)Hm

100 120 140 160 180 200 220

exp

ect

ed

sig

nifi

can

ce

0

2

4

6

8

10

12

14

16

18

Combined 4l→

(*)ZZ

γ γτ τ

νµν e→WW0j νµν e→WW2j

ATLAS-1L = 10 fb

• H → ττ

• H → γγ

⊲ H → WW ∗ → lνlν (GF)

⊲ H → WW ∗ → lνlν (VBF)

2 H → ZZ(∗) → 4 l

The WW channel plays a dominant

role for 130 GeV <∼ MH<∼ 190 GeV !

♠ SM Higgs (2/2)

• The 2 missing neutrinos: Transverse mass vs. MAOS Higgs mass

(GeV)TM0 100 200 300 400 500 600

Eve

nts

/ (

10

)

0

5

10

15

20

25

30

35

40

45

(GeV)TM0 100 200 300 400 500 600

Eve

nts

/ (

10

)

0

5

10

15

20

25

30

35

40

45W+jets

WW

ttSignal

Pseudodata

ATLAS-1 L dt=10 fb∫

[GeV]maosHm

120 140 160 180 200 220 240 260 280-1

Nu

mb

er

of e

ven

ts / 8

Ge

V / 1

0 fb

0

50

100

150

200

250

300

MSMH = 150 GeV

End point 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

CP Conserving

1

10

0 20 40 60 80 100 120 140

1

10

mh° (GeV/c2)

tanβ

Excludedby LEP

TheoreticallyInaccessible

mh°-max

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

1

2

3

4

5

6789

10

20

30

0 20 40 60 80 100 120 140

MH1 (GeV)

tanβ

ATLAS preliminary

theoretically inaccessible

No Lose ? No Higgs !

♠ 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 GeVATLAS TDR, Vol 2, CERN-LHCC-99-15, ATLAS-TDR-15 (1999); CMS Physics TDR, Volume II, CERN-LHCC-

2006-021, 25 June 2006

H1,2 → γγ H1,2 → µ+µ−

One peak Two peaks

♠ CP Asymmetries (1/3)

• CP asymmetry in Higgs decays in the tau leptons : J. Ellis, JSL and A. Pilaftsis,

D71(2005)075007

W+

W−

Hi Hj

τ+

τ−

σRR σLL

ACP =σRR − σLL

σRR + σLLwith

σRR ≡ σ(pp → H → τ+

R τ−R X)

σLL ≡ σ(pp → H → τ+L τ−

L X)


• 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


• Integrated CP asymmetry AWWCP with σWW

tot > 0.2 pb:

ΦA [ o ]

ACPWW Φ3 = − 10o

ΦA [ o ]

ACPWW Φ3 = − 90o

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

-100 0 100-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

-100 0 100

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 GapM. Arneodo, M. Diehl, hep-ph/0511047

The differential cross section

dσ (pp → pp)

d t

∣∣∣∣elastic

has a resemblance to thediffraction pattern in optics:

oR

θ

I (θ)

λ /2Ro

I (θ)

θ

λ


• Exclusive double diffractive process

f

f

p1

p2

p′1

p′2

ga

gb

Hi ⊕ Hjs →

(M , y)

Outgoing protons remain intact & scatter

through small angles with p⊥ ≪ 1 GeV

J. Ellis, JSL and A. Pilaftsis, D71(2005)075007

∗ Need TOTEM/ATLASFP detectors

† M2 = s − 2√

s(E′1 + E′

2) + (p′1 + p′2)2

⇒ δM ∼ 1 GeV !

† Clean environment due to the largerapidity gap

A. De Roeck, et al., EPJC25 (2002) 391; M. Boonekamp,

et al., PLB598 (2004) 243; K. A. Assamagan et al. hep-

ph/0406152; B. E. Cox, hep-ph/0409144, hep-ph/0501064;

B.E. Cox∗, J.R. Forshaw, JSL, J.W. Monk∗ and A. Pilaftsis,

PRD68 (2003) 075004; V.A. Khoze, A.D. Martin and M.G.

Ryskin, EPJC34 (2004) 327


• pp → pHip ; Hi → τ+τ− (ΦA , Φ3) = (90 ,−90) (ΦA ,Φ3) = (90 ,−10)

M [ GeV ]

aC

P

τ

y = 0

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

116 118 120 122 124 126 128 130

Invariant mass distribution can be studied !

♠ Beyond the Minimal SUSY Model (1/2)

• The µ problem J. E. Kim and H. P. Nilles, Phys. Lett. B 138, 150 (1984)

µH1H2 −→ S H1H2 More Higgs bosons and more CP violation !

-100

-50

0

50

100

150

200

400 450 500 550 600 650 700 750 800

10-3

10-2

10-1

1

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 themasses of SM particles

• Supersymmetry may stabilize the Higgs-boson masses against the Quantumcorrections

• The additional CP phases in the models extended by Supersymmetry may explainthe matter dominance of the Universe

• The Supersymmetric CP phases may manifest themselves through the Higgs sectorin Energy-, Intensity-, and Cosmic-Frontier experiments

• The LHC is to give definite answers to these may’s


II-B B-meson Observables


Colliders

LEP Holes

LHC Signatures

B-meson Obsrvables

8><>:


B → τν , B → Xsγ ,

· · ·


Dark Matter


♠ B Observables (1/4)

• Higgs-mediated B-meson mixing and rare decays: LHCb and SuperB J. Ellis, JSL and

A. Pilaftsis, PRD76(2007)115011

(−Ld

eff

)H=

g

2MWd Md gL

Hidd PL dHi + h.c.

gLHidd ∝ V †

CKM [1 + tanβ ∆d]−1

VCKM

×QjL diRg

Φ†1,2

Qj Di

×QjL diReHu eHd

Φ†1,2

Uk Ql

× ×QjL diRfW i

eB

eHu eHd

Qj

Φ†2

∆d[ΦCP] :

Non-universal Quantum interactions inducing the mixing and rare decays !


• ∆MSUSYBd

and ∆MSUSYBs

as functions of tanβ(MSUSY) for three values of ΦM ≡Φ1 = Φ2 = Φ3 SPS1a-like scenario fML,E = 200 GeV and ΦGUT

A = 0

tanβ

∆ M

Bd S

US

Y [ ps

-1 ]

EXPMEASURED

ΦM = 0o

ΦM = 90o

ΦM = 180o

ΦA GUT

= 0o

tanβ

∆ M

Bs S

US

Y [ ps

-1 ]

EXPMEASURED

ΦM = 0o

ΦM = 90o

ΦM = 180o

ΦA GUT

= 0o

10-5

10-4

10-3

10-2

10-1

1

10 20 30 40 50

10-1

1

10

10 2

10 20 30 40 50

Strong CP phase dependence


• B(B0s → µ+µ−) and the ratio RBτν as functions of tanβ(MSUSY) for three values

of ΦM ≡ Φ1 = Φ2 = Φ3 SPS1a-like scenario fML,E = 200 GeV and ΦGUTA = 0

tanβ

B(B

S →

µµ)

x 1

07

EXPUPPER (90 %)

SM

ΦM = 0o

ΦM = 90o

ΦM = 180o

ΦA GUT

= 0o

tanβ

RB

τν

EXP (1 σ)

ΦM = 180o

ΦM = 90o

ΦM = 0oΦA

GUT = 0o

10-2

10-1

1

10

10 20 30 40 5010

-3

10-2

10-1

1

10

10 20 30 40 50



• B(B → Xsγ) and AdirCP(B → Xsγ) as functions of ΦM for four values of

tanβ(MSUSY) = 10 , 20 , 30 , 40 SPS1a-like scenario fML,E = 200 GeV and ΦGUTA = 0

ΦM [ o ]

B (

b →

s γ

) x 1

04

EXP ( 2 σ )

tanβ = 40

30

20

10

ΦA GUT

= 0o

ΦM [ o ]

AC

P [ %

] B

EXP

b → s γ

ΦA GUT

= 0o

1

10

0 100 200 300

-6

-4

-2

0

2

4

6

0 100 200 300



II-C EDMs


Colliders

LEP Holes

LHC Signatures

B-meson Obsrvables

8><>:


B → τν , B → Xsγ ,

· · ·


Dark Matter


♠ EDMs (1/4)

• Electric Dipole Moments (EDMs): T violation ⇒ CP violation (under CPT )

HEDM = −d E · s

|dTl| < 9 × 10−25 e cm , |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 betweenfirst two and third generations and/or some moderate tuning among parameters

♠ EDMs (2/4)

• EDM constraints and cancellation: CPX Scenario with ΦAt,b= Φ3 = 90, ΦAu,d,c,s

= 0

tan β = 5, MH± = 300 GeV, |M2| = 2|M1| = 100 GeV, and MSUSY = 0.5 TeV The hierarchy factor ρ:

MX1,2

= ρ MX3

with X = Q = U = D = L = E J. Ellis, JSL and A. Pilaftsis, JHEP08(2008)049

ρ

| dTl

/ dEX

P |

( Φ1 , Φ2 ) = (0o, 90o)

ρ

| dn / d

EXP |

( Φ1 , Φ2 ) = (0o, 90o)

ρ

| dHg

/ dEX

P |

( Φ1 , Φ2 ) = (0o, 90o)

ρ

| deE | [

e cm

]

( Φ1 , Φ2 ) = (0o, 90o)

χ±

χ0

H0

ρ

| dn / d

EXP | ( Φ1 , Φ2 ) = (0o, 90o)

dE u,d

dC u,d

dG

ρ| d

dC | [ cm

] ( Φ1 , Φ2 ) = (0o, 90o)

χ±

χ0

g~

H0

10-1

1

10

10 2

10 3

1 1010

-1

1

10

10 2

10 3

1 1010

-1

1

10

10 2

10 3

1 10

10-28

10-27

10-26

10-25

10-24

1 1010

-1

1

10

10 2

10 3

1 1010

-28

10-27

10-26

10-25

10-24

10-23

1 10

♠ EDMs (3/4)

• Analytic determination of the cancellation regions: EDM-free directions andOptimal direction J. Ellis, JSL and A. Pilaftsis, JHEP10(2010)049

Subspace of EDM-free directions

EDM vector An Observable vector

An Optimal direction

Φ = E × (O × E)

CP-phase space

♠ EDMs (4/4)

• Optimal direction : the higher-dimensional generalization with N CP phases and

n EDM constraints

Φα = ǫαβ1···βnγ1···γN−n−1

E(1)

β1· · ·E(n)

βnBγ1···γN−n−1

where (N -n-1)-dimensional B form is

Bγ1···γN−n−1= ǫ

γ1···γN−n−1σβ1···βnOσE

(1)

β1· · ·E(n)

βn


II-D Dark Matter


Colliders

LEP Holes

LHC Signatures

B-meson Obsrvables

8><>:


B → τν , B → Xsγ ,

· · ·


Dark Matter


♠ Dark Matter (1/1)

• LEP Holes ⇒ Very light 7.5 GeV Higgs signals through the inclusive processχχ → H → γ , p JSL and S. Scopel, Phys. Rev. D 75 (2007) 075001 [arXiv:hep-ph/0701221]

♠ MAOS momenta of the missing neutrinos (1/2)

• MAOS = MT2-Assisted On-shell Scheme:

H → W (p + k)W (q + l) → l(p) ν(k) l′(q) ν ′(l)

(M 2H)MAOS = (p + kMAOS + q + lMAOS)2

kMAOST = −qT and lMAOS

T = −pT

kMAOSL =

|kMAOST ||pT | pL, lMAOS

L =|lMAOS

T ||qT | qL

♠ MAOS momenta of the missing neutrinos (2/2)

• Is the modified MAOS scheme working well?:

[GeV]T, L k∆-300 -200 -100 0 100 200 300

Nu

mb

er

of e

ven

ts

0

2000

4000

6000

8000

10000

12000

14000

16000T k∆ (modified)L k∆ (original)L k∆

[GeV]T, L k∆-300 -200 -100 0 100 200 300

Nu

mb

er

of e

ven

ts

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

T k∆ (modified)L k∆ (original)L k∆

MH = 140 GeV MH = 180 GeV

♠ MT2: 1/2

• Transverse Mass MT :

X

χ(k)

V (p)pµ = (

√mV

2 + |pT |2 + p2L ,pT , pL)

kµ = (√

mχ2 + |kT |2 + k2

L ,kT , kL)

kT = pT/ (fully determined)

MX2 = mV

2 + mχ2 + 2

(√mV

2 + |pT |2 + p2L

√mχ

2 + |kT |2 + k2L − pT · kT − pLkL

)

MT2 = mV

2 + mχ2 + 2

(√mV

2 + |pT |2√

mχ2 + |kT |2 − pT · kT

)

MT ≤ MX

♠ MT2: 2/2

• ... then MT2 ?: Generalization of MT when there are 2 missing particles

X(1)

X(2)

χ(k)

V (p)

χ(l)

V (q)

kT + lT = pT/

Only determined are ...

the 2 among the 4 unknown degrees of freedom !

... but we know:

maxM (1)T , M

(2)T (ktrue

T , ltrueT ) ≤ MX

♠ MT2: 2′/2

• ... then MT2 ?: Generalization of MT when there are 2 missing particles

kT + lT = pT/

Only determined are ...

the 2 among the 4 unknown degrees of freedom !

... but we know:

maxM (1)T , M

(2)T (ktrue

T , ltrueT ) ≤ MX

maxM (1)T ,M

(2)T (kmin

T , lminT ) ≤ maxM (1)

T , M(2)T (ktrue

T , ltrueT ) ≤ MX

MT2 ≡ minkT+lT=pT/

[max

M

(1)T ,M

(2)T

]≤ MX

♠ AFB at the Tevatron: 1/2

• qq → tt and AFB at the Tevatron Shabamina(Blois2010)

AFB ≡ Nt(cos θ ≥ 0) − Nt(cos θ ≥ 0)

Nt(cos θ ≥ 0) + Nt(cos θ ≥ 0)= (0.15 ± 0.05 ± 0.024)

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]

L6 =g2

s

Λ2CAB

8q (qAT aγµqA)(tBT aγµtB)

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

C2

(1

TeV

/Λ)2

C1 (1 TeV/Λ)2

σ = 7.02 pbσ = 7.98 pb

A FB =

0.2

1A FB =

0.0

9

I

II

III

IV

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

DF

B

D

g L8q g L

8t (Λ 2 / m

V2

)= 2

g L8q g L

8t (Λ 2 / m

V2

)= 1

g L8q g L

8t (Λ 2 / m

V2

)=-1

g L8q g L

8t (Λ 2 / m

V2

)=-2

C1 ≡ CRR8q + CLL

8q , C2 ≡ CLR8q + CRL

8q , D , DFB ∝ (CRR8q − CLL

8q ) ± (CLR8q − CRL

8q )

♠ Backup

• Large tanβ and MpoleH± ∼ 150 GeV ⇒ Trimixing scenario J. Ellis, JSL and A. Pilaftsis,

PRD70(2004)075010, PRD71(2005)075007, PRD72(2005)095006, and NPB718(2005)247

tanβ = 50, MpoleH± = 155 GeV,

MQ3= MU3

= MD3= ML3

= ME3= 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 MZ: Three gauge couplings α1(MZ), α2(MZ), and α3(MZ)

– At mpolet : Quark and Lepton masses mq,l(m

polet ) and VCKM(mpole

t )

– At MSUSY: tanβ(MSUSY)

– At MMFV = MGUT: 19 MCPMFV Parameters

|M1,2,3| ei Φ1,2,3 , |Au,d,e| ei ΦAu,d,e , M2Q,U,D,L,E , M2

Hu,d

Specifically, we have taken the parameter set:

|M1,2,3| = 250 GeV

M2Hu

=M2Hd

=M2Q=M2

U=M2D=M2

L=M2E = (100 GeV)2

|Au| = |Ad| = |Ae| = 100 GeV

This parameter set is equivalent to SPS1a when ΦAu,d,e= 180 and Φ1,2,3 = 0 if MSUSY = m

polet and

tan β = 10

♠ Backup

• The B-meson observables strike against CPX!: B(Bs → µ+µ−) (95 %), B(B →Xsγ) (2 σ), RBτν (1 σ), Υ(1S) → H1γ CPX scenario with ΦA = Φ3 = 90 and MSUSY = 0.5

TeV JSL, M. Carena, J. Ellis, A. Pilaftsis, C.E.M. Wagner, arXiv:0712.2360; JSL and S. Scopel, PRD75(2007)075001

Υ → H1 γ

B(b → sγ)

RBτν

B(Bs → µµ)

ρ = 1

MH1 [ GeV ]

tan

β

5

10

15

20

25

30

35

40

45

50

0 20 40 60 80 100 120

ρ = 10

MH1 [ GeV ]

tan

β

5

10

15

20

25

30

35

40

45

50

0 20 40 60 80 100 120

The CPX scenario excluded ? ... flavour-mixing terms

higgs, supersymmetry, and cp violation jae sik lee · higgs, supersymmetry, and cp violation jae...

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