超対称性とフレーバー混合
山口 昌弘(東北大）
2005年3月8日
科研費特定領域第3回研究会「質量起源と超対称性物理の研究」

Introduction• 質量起源：– W/Z bosonの質量– quark/leptonの質量– hadronの質量は議論しない• Electroweak Symmetry Breakdown (EWSB)
would-be Nambu-Goldstone bosons
Æ eaten by W/Z bosons
Æ W/Z massive
2005/3/8

質量起源と超対称性の物理

2

Standard Model (SM)• Two Roles of Higgs Fields:• Higgs: elementary scalar with SU(2)L doublet– Generates masses to W/Z bosons• 4 degrees of freedom• 3 are eaten by W/Z bosons to give their masses• 1 remains as physical Higgs

Æ target of search at collider experiments– Geneates masses to quarks/leptons• Yukawa interaction• very economical approach
2005/3/8

質量起源と超対称性の物理3Naturalness Problem in SM• Scalar Mass:– unstable against radiative corrections– Quadratic divergence• Fine-tuning needed to keep EW scale small• Probably this is a real problem.
(cf. Cosmological Constant Problem)

2005/3/8

質量起源と超対称性の物理

4

Theories/Models/Scenarios of EWSB– Supersymmetry– Extra-Dimensions– Higgs as Pseudo NG boson– Technicolor– Composite Higgs– Higgsless…..

2005/3/8

質量起源と超対称性の物理5• Dynamical EWSB– very attractive: Many people hate elementary scalar– symmetry breakdown ÆNG bosons ÆW/Z bosonmasses– Difficulty to generate q/l masses• FCNC/large top mass
• Elementary Higgs: easy to generate q/l masses
Yukawa couplings• SUSY: Minimal version (MSSM) is compatible withgauge coupling unification.
– This is not the case for LED.

• SUSY: still the prime candidate for Beyond-SM(since ’90)
2005/3/8

質量起源と超対称性の物理

6Supersymmetry• A solution to naturalness problem– “how” problem: how is EW scale protected from hugeradiative corrections?
– “why” problem: why is EW scale so small?

• SUSY gives an answer to the “how” problem.
– cancellation of quadratic divergence between bosons
and fermions “technically natural”• Approach to the “why” problem– dynamical SUSY breaking?
– Still a big mystery (fine tuning in string landscape !?)2005/3/8

質量起源と超対称性の物理

7

SUSY phenomenology••••••

superparticles not far from EW scale
light Higgs <~130 GeV
gauge coupling unification
dark matter candidate (neutralino LSP)
possible effects in FCNC processes (B/D/K and leptons)
possible effects in CP violation: EDMs

• solid framework– experimental study for more than 10 yrs– properties well-known by simulation, though not discovered yet– advantage to discuss FCNC as well
2005/3/8

質量起源と超対称性の物理

8Talk Plan
• Introduction• Where is SUSY?
– naturalness– dark matter argument– split SUSY

• SUSY around the corner !?
– Higgs– g-2 of muon
– B-physics
2005/3/8

質量起源と超対称性の物理

9Where is SUSY?

2005/3/8

質量起源と超対称性の物理

10Where are Superpartners?
• Lower bounds– charginos/sleptons >100 GeV (LEP)– gluinos/squarks >300 GeV (Tevatron)– Higgs >114GeV
Æ stop typically heavier than 500 GeV (MSSM)• Upper bounds on superpartners?
– difficult to answer– Let’s discuss a bit more (though no clear answer).
2005/3/8

質量起源と超対称性の物理

11naturalness• naturalness/fine-tuning– difficult to address quantitatively– Usual statement: they are not far away from
EW scale– typically(!?) within reach of LEP/ Tevatron/LHC…. time dependent statement• Fine-tuning may not be a criterion at all.
(e.g. split SUSY) see below
2005/3/8

質量起源と超対称性の物理

12Dark Matter Argument• SUSY provides an excellent candidate for cold
dark matter: neutralino dark matter• Assumptions:– Neutralino LSP:
• A neutralino (a combination of neutral gauginos and neutralhiggsinos) is lightest superparticle (LSP).

– R-parity conservation Æ LSP is stable– Thermal Relic under Standard Thermal History• The Universe gradually cools down from very hot universe(T>100GeV) as the Universe expands. Nothing special(such as huge entropy production) happens.
2005/3/8

質量起源と超対称性の物理

13

Thermal Relic Abundance
From
Text Book byKolb & Turner
At high T, the neutralinos are in thermalequilibrium. As Universe cools down, theneutralinos get non-relativistic and theirabundance is Boltzmann suppressed.
Eventually one neutralino LSP cannot findanother neutralino to annihilate each other.
ÆFreeze-out !

High Temp.
2005/3/8

Low Temp.

Final Abundance is proportional to theinverse of the annihilation cross section.
A crude estimate:Ωh2 ~ 1 x (<σannv >/ 10-10 GeV-2) -1
motivation for WIMPs

質量起源と超対称性の物理

14

Discovery Reach at Tevatron/ LHC/ ILC
Baer, Belyaev, Krupovnickas & Tata ‘03

Even LHC may not be able to cover the whole region.
2005/3/8

質量起源と超対称性の物理

15• No practical upper bound on supreparticle
masses from the dark matter argument– co-annihilation with stau: very effective toreduce the relic abundance– (Annihilation into W is also effective in
higgsino LSP.)• Remember that the argument relies on thethree assumptions.
2005/3/8

質量起源と超対称性の物理

16

Split SupersymmetryArkani-Hamed,
Dimopoulos 04• New scenario motivated by string landscape– landscape:
この世はfine tuningでできた 終末思想?
• scalar massのfine tuning は気にしない！
開き直り!?

2005/3/8

質量起源と超対称性の物理

17

Split Supersymmetry (cont.)• scalar masses >> gaugino masses, higgisino masses
× naturalness○ Higgs mass ~150-160 GeV○ No SUSY FCNC
○ No SUSY CP○ dark matter○ gauge coupling unification•phenomenology– long-lived (practically stable) gluinos•

will be (dis)proved in future collider experiments

2005/3/8

質量起源と超対称性の物理

18

SUSY around the corner !?

2005/3/8

質量起源と超対称性の物理

19

Some Hints on New Physics• Higgs Mass
• (g-2) of muon
• B-physics: CP asymmetry in BÆphi K,eta’ K

2005/3/8

質量起源と超対称性の物理

20

Higgs Mass(although Higgs is a part of SM)
Current limit from direct searchmh (MSM)>114 GeV(Smoking Gun Events at LEP II !?)Global fit prefers light Higgs (inminimal SM)
mh(MSM)=114+69-45 GeV

2005/3/8

質量起源と超対称性の物理

21

Higgs in MSSM
mh<mZ=91 GeV at tree-levelÅ quartic coupling given by gauge couplingTop-stop loopÆraises mh significantly
Large radiation correction needed to raise mh above 114 GeV(especially for low mt): Heavy SUSY mass spectrum preferred“little hierarchy problem in SUSY”
Higgs is waiting to be descovered in MSSM.
We expect Tevatron to tell us crucial information on Higgs.
Note: Higgs mass is very sensitive to top mass– mt=174 GeVÆ178 GeV pushes up mh by 2 GeV or so.

2005/3/8

質量起源と超対称性の物理22

(g - 2)μ: Current Status
Values of aμ=(g-2)μ/2
Experiment : 0.0011659203(7) (μ- included) PDG2004
SM prediction: 0.00116591763(74)e.g. Hagiwara et al 2004 based on e e → π π+ −+−δ a µ ∼ 2 6 (1 0 ) × 1 0 − 1 0

still more than 2-sigma deviation
cf. situation in year 2001:
Exp. 0.0011659202(14)(6)
δ a µ ∼ 43(16) × 10 − 102005/3/8

質量起源と超対称性の物理

23

B physics• CP asymmetry in bÆc transition:– measurement of sin 2 beta (phi_1)– good agreement with SM.

The Kobayashi-Maskawa
framework has been established.
• bÆs penguin is now a hot subject.

2005/3/8

質量起源と超対称性の物理

24BÆS penguin is interesting• b Æ c tree level in SM• b Æ s loop level in SM– Increasing chance to see New Physics Effects– Not fully explored yet• Prejudice: Mixing between 2-3 generation
may be large, as suggested byatmospheric neutrino.
2005/3/8

質量起源と超対称性の物理

25

Time dependent CP asymmetry of BÆφK & BÆη'K
mixing-induced CP asymmetry

BfCP
B

B-factoriesの実験の現状(summer 2004)

Belle
BaBar

Belle
BaBar
2005/3/8

質量起源と超対称性の物理

26

History of “sin2φ1” with φK0“sin2φ1”

Hazumi, fpcp2004_sin2φ1 from ccs

BABAR
Belle×106

2005/3/8

質量起源と超対称性の物理

27

• Clearly we need more data of year 2005, 2006,
2007,... to say something definite.
• Stay tuned!
• A new feature:– Apparent anomalies are seen in more than one mode!
(B Æ φK and B Æ η'K)

2005/3/8

質量起源と超対称性の物理

28

-- Ken-Ichi Hikasa
talk in the same meeting
last year

Take the second approach! In fact we wrote apaper and are preparing another one.
Let us consider SUSY interpretation.
2005/3/8

質量起源と超対称性の物理

29

FCNC and CP in SUSY SM
New sources of flavor mixing (with CP violation):
soft SUSY breaking terms– eg. squark masses, slepton masses (3x3 matrices, nondiagonal)
SM: FCNC is suppressed by GIM mechanism
SUSY contribution: No GIM suppression for arbitrary choice of soft masses
Æ Too large FCNC for weak scale SUSY“SUSY FCNC problem”
Sensible Choice of soft masses required:
Various proposals:– Universal sfermion masses: mSUGRA, gauge mediation,…
– Aligned sfermion masses: flavor symmetry,…..

2005/3/8

質量起源と超対称性の物理30

SUSY contribution to B → φ K ,η ' Kfourquark

chromodipole

four-quark

dipole2005/3/8

質量起源と超対称性の物理

31

Left-Handed (LH) VS Right-Handed (RH)
• SM: W-loop, V-A current (LH structure)• NP: Both chiralities can arise.
– Pattern of NP contribution depends on
chirality structure of flavor violation in NP• SUSY: Flavor mixing in squark masses– LH (SU(2) doublet) squarks– RH (SU(2) singlet) squarks
2005/3/8

質量起源と超対称性の物理32

RH vs LH in “SDOWN” sector• RH:– Large 2-3 RH sdown mixing in SUSY GUT see-saw models(Moroi 01)• Atmospheric neutrino implies large 2-3 mixing in neutrino Yukawa• SUSY GUTsÆ large 2-3 mixing in RH sdown sector• Large contribution to BÆphi K– Cf. solar neutrino Æ Kaon physics

YNYN

• LH:
– Renormalization Group Flow: does not give significant flavor
mixing with new CP phase– May be imprinted at Ultra-High Energy Scale– Flavor symmetry!?
– Large 2-3 neutrino mixing may also give large 2-3 mixing in LH
squark sector.
2005/3/8

質量起源と超対称性の物理33

A SUSY Interpretation of Current DataEndo, Mishima & MY hep-ph/0409245
Parityodd
evenoddeven
odd

2005/3/8

質量起源と超対称性の物理

Key Points:
1. Anomalies in morethan one mode
(φ K ,η ' K )2. The final states
have opposite
parity.

34

Sign of Contributions by Final-state Parity
Effective Hamiltonian

Decay Amplitude
Kagan; Khalil&Kou

2005/3/8

LH

質量起源と超対称性の物理

35

Numerical Estimation of Sb-s in MSSM
Endo, Mishima & MY 04
favored by current datafrom B-factories (1σ)

The current data
prefers LH dominant
case!

GF:
2005/3/8

質量起源と超対称性の物理36

RH completely excluded?
Larson,Murayama& Perez 04

LH interpretation:

RH interpretation:

OK for genericchoice of CP phase

may marginally workfor
special choice of CP
phase and r~1

Å detailed study(Endo,Mishima &MY, inpreparation)(danger of bÆs gamma etc)
2005/3/8

質量起源と超対称性の物理

37

Lesson from this analysis
Future confirmation of the s-penguin
anomalies will tell us– not only the existence of NP– but also the pattern of chiral structure (andhopefully more structure) of the NP.

Determination of Wilson coefficients
Usage of more than one mode is crucial!
2005/3/8

質量起源と超対称性の物理

38

Prospects
More Data on s-penguin: wait and watch!
Correlation with other B decay processes
e.g. BS − BS mixing: ∆mS ≥ 20 − 100 ps −1
Br ( B → µ + µ − ) can be 10-7>>10-9 (SM)

Correlation with Lepton Flavor Violation
τ → µγ ,τ → µη etcµ → eγ etc
2005/3/8

質量起源と超対称性の物理

39

Conclusions• SUSY: 腐ってもSUSY– the prime candidate for Beyond-SM• Sparticles/Higgs Searches Æ Lower bounds• No Clear Upper bounds on Sparticle Masses• EW precision data prefers light Higgs– top発見の直前の状況に似ている– Expect Evidence (?) from Tevatron RUN II• Some anomalies:– g-2 of muon
– CP in bÆs penguin

More data from B-factories to conclude• We also expect– discovery of superparticles– dark matter detection– new events such as LFV BS − BS2005/3/8

B → µ+µ−

質量起源と超対称性の物理40