1. 岡田安弘（ＫＥＫ/総研大） 2007年10月26日 ＫＥＫ 第三回 J-PARC遅い取り出しユーザー加速器連絡会
K 中間子稀崩壊実験の意義
岡田安弘（ＫＥＫ/総研大）
2007年10月26日　ＫＥＫ
第三回　J-PARC遅い取り出しユーザー加速器連絡会　

2. Role of flavor physics in the past
Flavor physics has provided basic inputs to formulate the particle physics model.
Absence of Lepton Flavor Violation in charged lepton decays
=> Two neutrino theory (Generation structure)
Suppression of Flavor Changing Neutral Current Processes
=> GIM mechanism (Charm quark)
CP violation in K decays
=> Kobayashi-Maskawa theory (Three generation structure)
“Basis of the Standard Model”

3. Critical time for particle physics
LHC experiment will start next year to explore the TeV physics.
TeV is the scale of the electroweak symmetry breaking, and most probably related to the “New Physics” scale.
After 8 years of successful B factory experiments, focus of flavor physics is also shifting to new physics searches.

4. Status of quark flavor physics
The Cabibbo-Kobayashi-Maskawa matrix works perfectly.

5. Is this enough?
Not, to study New Physics effects.
In order to disentangle new physics
effects, we should first determine CKM
parameters by “tree-level” processes.
Fit from tree level processes
|Vub|, f3/g
Bd mixing and CP asymmetries
eK and B(K->pnn)
Bs mixing and CP asymmetries +
Then, we know (or constrain) which sector is affected by new physics.
“New physics contributions of several 10 % are still allowed. “

6. K vs. B in the SM Flavor signals and CP violation are quite different.
Kaon
B meson
(predictions from the present CKM
parameter fit)
This is in accordance with the pattern predicted in the Standard Model.

7. Rare Kaon decays Rare dacays KL-> pnn K+-> pnn KL->pll
“Null” test
T violation in K->pmn
LFV
K->me, pme
Lepton universality test
B(K->mn)/B(K->en)

8. KL->pnn, K+->pnn
Theoretically clean processes
The relevant form factor is obtained by K->p en.
Completely short distance dominated.
Top loop dominated (+ charm loop for K+ decay)
A few % theoretical uncertainty.
(a)
(b)
(g)
B(K0->p0nn)
B(K+ -> p+nn)

9. Grossman-Nir bound (1997)
Since the two processes are determined by the imaginary part and the absolute value of the same coupling, a simple model-independent bound is obtained.
Present experimental bounds
BNL E949
KEK E391a
The GN bound can be violated if lepton flavor violation exists.

10. New physics examples Supersymmetry
SUSY models introduce SUSY partners.
Squark/sleption mass matrixes are new sources of flavor mixing and CP violation.
Squarks up to ~3 TeV will be searched for at LHC.
Flavor signals depends on how the off-diagonal terms are generated.

11. B(K0->p0nn)/B(K0->p0nn)SM
In SUSY models, SUSY particle and charged Higgs loops contribute to B(K->pnn)
The size of the SUSY contributions depends on a SUSY breaking scenario.
Generic MSSM
mSUGRA-type model
B(K0->p0nn)/B(K0->p0nn)SM
Stop mass
T.Goto.Y.O.Y.Shimizu, 1997
G.Isidori, et al. 2006
Need to update => a few%?

12. Little Higgs model with T parity
~10 TeV,
new strong dynamics
~ 1TeV
WH, ZH, fij,
uH,dH AH
T+,T-
~200 GeV
A Higgs boson and SM particles
Particle content of the littlest
Higgs model with T parity.
Little Higgs model : a model with a composite
Higgs boson.
New particles (heavy gauge bosons, a heavy top
partner) are introduced to cancel the quadratic
divergence of the Higgs mass at one loop level.
The mass of these particles are around
1 TeV if the model is extended with “T parity”.
N.Arkani-Hamed,A.G.Cohen, E.Katz,and A.E.Nelson,2002
C.H.Cheng and I.Low,2003

13. T-odd SU(2) doublet mirror fermions => A new flavor mixing matrix
M.Blanke et.al, 2007
B(K0->p0nn) d u W
VCKM d qH
WH,ZH,AH
VHd
B(K+ -> p+nn)
Large effects on K->pnn are possible.

14. T violation in K decays T-odd triple vector product
A window to new physics.
Small contribution from the KM phase
Small and calculable effects of QED final state interaction

15. Effective four fermion interaction
The transverse polarization needs interference between the SM four fermion
term and new contributions and a relative phase between them.

16. New physics examples
The multi-Higgs model is a simplest model with a possible transverse muon polarization by the charged Higgs boson exchange.
If the tree-level neutral Higgs boson FCNC is forbidden by a discrete symmetry, more than three Higgs doublets are necessary to induce the transverse polarization.
If we do not require natural flavor conservation, two Higgs doublet may work.
SUSY with a large squark flavor mixing or SUSY without R-parity could induce the transverse polarization of O(10-3).

17. Three Higgs doublet model
Yukawa couplings
Charged Higgs boson mixing
Charged Higgs boson coupling s u m n W

18. Keeping only the lighter charged Higgs contribution,
Present bound of the right hand side.
From B(B->tn) at B factory experiments in the type II two Higgs
doublet model (except for two folded ambiguity),
This is translated to
and compared to the KEK-E246 result.

19. Future improvement on the bound of the RHS.
LHC charged Higgs boson search
Borrowing from the MSSM
heavy Higgs boson search study
Super B Factory (~50/ab) with B-> tn and B-> Dtn measurements
can reach a similar sensitivity for tanb/mH.
Transverse tau polarization can be also determined at Super B Factory.
Rough estimate is

20. B(K->en)/B(K->mn)
This ratio can be different from the SM if there is a slepton flavor mixing in the SUSY model. Flavor changing charged Higgs coupling .
From G.Isidori, KAON 2007 summary,
Present combined result
A.Masiero, P.Paradisi and R.Petronzio, 2006

21. LFV K decays Current bounds LFV LNV
From A.Belyaev, et al, hep-ph/

22. LFV K decays in the MSSM with a slepton mixing, m->eg
10-11
K->me
10-16
m-e conversion
10-13
Muon LFV are more promising.
If R-parity is broken, LFV K decays
can be the limiting processes.
A.Belyaev, et al, hep-ph/

23. Concluding remarks
In the next 7-10 years, we anticipate further progress in B physics ( B factory and LHCb). New physics sensitivity will improve roughly from several 10 % (now ) to several % level.
At the same time, results of LHC will become clear. Future high energy programs will be planned according to the outcome of LHC.
It is likely that desired sensitivity to “New physics effects” is a few % level (or less) in order that flavor physics can play a significant role at that time. This requires both theoretical clean ways and precise experimental measurements.
It is important to find a path to ultimate kaon experiments by the time when we will make the planning.