素粒子理論から 岡田安弘（KEK/総合研究大学院大学） 2009年3月26日 Ｊ−ＰＡＲＣハドロン実験ホールへの最初のビームを記念するワークショップ 　@ 東海

LHC era New era will start from the LHC experiment. TeV scale physics = Electroweak symmetry breaking. Many proposals for physics beyond the Standard Model. SUSY, composite Higgs model (little Higgs models), Extra-dimension models, etc.

Hints for physics beyond the SM Origin of neutrino masses. Dark matter. Baryon number of the Universe The TeV scale physics may provide answers, or clues, or may not be relevant.

Indirect search for new physics B CPV and rare decays D CPV and rare decays tau CPV and rare decays Bs CPV and rare decays K CP(T)V and rare decays muon rare decays muon g-2 EDM Super B facotory LHCb J-PARC hadron hall experiments

EDM ~0 SUSY CP Lepton flavor Quark flavor Neutrino mixing B,D,K LFV~0 SM has a characteristic feature among various flavor and CP signals. EDM ~0 SUSY CP Lepton flavor Neutrino mixing LFV~0 Quark flavor B,D,K slepton mixing GUT Relationship may be quite different for new physics contributions.

[1] 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)

K-> pnn in the SM Both KL->pnn and K+->pnn are theoretically under control. Top contribution Charm contribution Sub-leading contribution From Ulich Haisch hep-ph/060517 A few % theoretical errors for both processes.

Supersymmetry quark squark lepton slepton gluon gluino W,Z,g, Supersymmetry is a new type of symmetry connecting bosons and fermions. Gauge coupling unification is realized with SUSY particles. The LHC experiment can find squarks and gluon up to 2-3 TeV. Coupling unification In SUSY GUT W,Z,g, H gluon lepton quark neutralino, chargino gluino slepton squark SM particles Super partners Spin 1/2 Spin 0 Spin 1

Squark mass matrixes carry information on the SUSY breaking mechanism and interactions at the GUT scale. Origin of SUSY breaking (mSUGRA, AMSB, GMSB, Flavor symmetry, etc.) SUSY breaking terms at the Mw scale (squark, slepton, chargino, neutralino, gluino masses) Renormalization (SUSY GUT, neutrino Yukawa couplings etc.) Diagonal : LHC/LC Off-diagonal: Flavor exp.

Prediction of B(K->pnn) in SUSY models B(K0->p0nn)/B(K0->p0nn)SM Generic MSSM Stop mass 2 1 0.5 1.5 Minimal Flavor Violation (MFV)scenario in minimal SUSY SM (MSSM) >15% >12.5% >10% Stop mass Chargino mass MFV: squark mixing ~ quark mixing G.Isidori, et al. 2006

Little 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”. ~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. N.Arkani-Hamed,A.G.Cohen, E.Katz,and A.E.Nelson,2002 C.H.Cheng and I.Low,2003 Mirror quarks and new flavor mixing d u W VCKM d qH WH,ZH,AH VHd

Little Higgs Model with T parity (talk by M.Blanke at CERN meeting)

Models with extra dim. Models with extra dimensions were proposed as an alternative scenario for a solution to the hierarchy problem. Various types of models: Flat extra dim vs. Curved extra dim. Various particles are allowed to propagate in the bulk. Geometrical construction of the fermion mass hierarchy => non-universality of KK graviton/gauge boson couplings Fermion mass hierarchy in the warped extra dim.

K->pnn in a warped extra dimension model Flavor changing Z coupling The flavor mixing is CKM-type exists at the the tree level.. M.Blanke, A.J.Buras, B.Duling, K.Gemmler and S.Gori, 2008

[2] 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.

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 constraint from B(B->tn) at B factory experiments Present KEK-E246 limit.

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 T violation processes will become important if LHC find a charged Higgs boson but not SUSY.

[3] Lepton Flavor Violation No lepton flavor violation (LFV) in the Standard Model. LFV in charged lepton processes is negligibly small for a simple seesaw　neutrino model.

Three muon LFV processes Back to back emission of a positron and a photon with an energy of a half of the muon mass. Nucleus A monochromatic energy electron emission for the coherent mu-e transition. Muon in 1s state

Experimental bounds Process Current Near future (Ti) Current bounds on tau LFV processes (t->mg,t->3m,t->mh, etc.) are 0(10-8)-0(10-7) .

Comparison of three processes If the photon penguin process is dominated, there are simple relations among these branching ratios. In many case of SUSY modes, this is true, but there is an important case In which these relations do not hold.

Slepton flavor mixing g-2: the diagonal term EDM: complex phases In SUSY models, LFV processes are induced by the off-diagonal terms in the slepton mass matrixes g-2: the diagonal term EDM: complex phases LFV: the off-diagonal term Off-diagonal terms depend on how SUSY breaking is generated and what kinds of LFV interactions exist at the GUT scale.

m -> e g branching ratio (typical example) SUSY Seesaw model B(m->.eg) ~10-14  B(mN->eN) ~10-16 slepton mass =170 GeV MR=4X1014 GeV 10-14 Slepton mass =3TeV MR=1014GeV T.Goto, Y.Okada,T.Shindou,M.Tanaka, 2007 J.Hisano and D.Nomura,2000

SUSY seesaw with a large tan b R.Kitano,M.Koike,S.Komine, and Y.Okada, 2003 SUSY loop diagrams can generate a LFV Higgs-boson coupling for large tan b cases. (K.Babu, C.Kolda,2002) s m e The heavy Higgs-boson exchange provides a new contribution of a scalar type. Higgs-exchange contribution Photon-exchange contribution

mu-e conversion rate normalized at Al. R.Kitano, M.Koike and Y.Okada. 2002 As Sb Ti Al Pb Z dependence of the mu-e conversion rate is different for dipole, scalar and vector LFV interactions.

Ratio of the branching ratios and Z-dependence of mu-e conversion rates mu-e conversion is enhanced. Z-dependence indicates the scalar exchange contribution.

Little Higgs Model with T-parity a talk by M.Blanke at CERN meeting

Neutrino mass generation at TeV scale and LFV Although the simple seesaw or Dirac neutrino model predicts too small branching ratios for the charged lepton LFV, other models of neutrino mass generation can induce observable effects if there is a new source of lepton flavor mixing at TeV scale, Examples SUSY seesaw model (F.Borzumati and A.Masiero 1986) Neutrino mass from the warped extra dimension (R.Kitano,2000) Triplet Higgs model (E.J.Chun, K.Y.Lee,S.C.Park; N.Kakizaki,Y.Ogura, F.Shima, 2003) Left-right symmetric model (V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004) m->3e m-e conv m ->eg H++

m->eg and m->3e asymmetries Triplet Higgs model N.Kakizaki,Y.Ogura, F.Shima LR symmetric model m->eg and m->3e asymmetries A(m->eee) V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, A.Akeroyd, M.Aoki and Y.Okada,2006

Comparison of three muon processes in various new physics models SUSY GUT/Seesaw B( m->e g ) >> B(m->3e) ~B(mN-eN) Various asymmetries in polarized m decays SUSY with large tan b B( m->e g ) > B(mN-eN) > B(m->3e) Z-dependence in m-e conv. branching ratio Triplet Higgs for neutrino B(m->3e) >> B(m->eg) ~B(mN-eN ) or B(m->3e) ~ B(m->eg) ~B(mN-eN) RL model B(m->3e) >> B(m->eg) ~B(mN-eN) in generic cases. Asymmetry in m->3e Little Higgs model with T parity 0.01< B(mN->eN)/B(m->eg) <100 B(m->3e) ~ B(m->eg)

Summary LHC will open a new era of particle physics. There are many possibilities concerning how new physics effects appear in various indirect processes. Tree vs. Loops New sources of flavor mixings and CPV vs. MFV Kaon CP and T violation/ rare decays and muon LFV processes provide good opportunities to explore different cases of new physics candidates.