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　

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”

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.

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

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. “

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.

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)

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)

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.

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.

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%?

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

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.

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

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

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).

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

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.

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

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

LFV K decays Current bounds LFV LNV From A.Belyaev, et al, hep-ph/0008276

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/0008276

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.