EDMs and Lepton Flavor Violation Yasuhiro Okada (KEK/Sokendai) The 4th International Symposium on Lepton Moments July 20, 2010, Centerville, Cape Cod, MA

Now, the LHC has started running… Why do we believe “new things”? LHC =TeV physics =Electroweak symmetry breaking Something beyond the known three gauge interaction is necessary. Other puzzles Origin of the neutrino mass Baryon number of the Universe Dark matter …. Lepton number violation Lepton flavor violation New CP violation Relevant scale is unknown.

An important role of EDMs and Lepton Flavor Violation EDM and LFV searches can provide a hint on the relationship between two scales. If two scales are well separated, EDMs and LFV are suppressed. TeV n, Baryogensis Seesaw neutrino model Leptogenesis

SUSY If two scales are close, large EDMs and LFV are expected. TeV n, Baryogensis TeV Example: Neutrino mass from loop. Electroweak baryogenesis In supersymmetric models, large EDMs and LFV are expected even if two scales are separated. SUSY n, Baryogensis TeV Existence /absence of EDMs and LFV is a clue to fundamental problems such as neutrino mass generation and baryongenesis,

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 and the Dirac neutrino model.

Three muon LFV processes m-e conversion search at 0(10-16) is planned at COMET(KEK) and Mu2e (Fermilab) experiments

Effective interactions 6 additional operators Various llqq operators

Tau LFV processes Various flavor structures and their CP conjugates Current bounds for tau LFV processes: 10-7- 10-8 from Belle and BaBar. O(10-9) at e+e- Super B factories. CMS study: B(t->3m) < 3.8x10 -8 at 30 fb-1 (R. Satinelli and M. Biasini 2002)

Distinguishing various LFV interactions Comparison of three muon LFV processes. (m-> eg, m->eee, m-e conversion) Angular distribution of polarized muon decays in m-> eg, m->eee. Atomic number dependence of the mu-e conversion rate.

(1) Comparison of three branching ratios If the photon penguin process is dominant, there are simple relations among these branching ratios. In many case of SUSY modes, this is true. Other cases: Additional Higgs exchange diagram (SUSY with large tan b) Dominance of tree exchange diagrams (LR symmetric models) Loop-induced but Z-penguin dominance (Little Higgs with T-parity)

(2) Muon Polarization The SUSY seesaw model If the muon is polarized, we can define a P-odd asymmetry for m -> e g and T-odd and P-odd asymmetries for m->3e. These asymmetries are useful　to discriminate different models. The SUSY seesaw model Only LFV coupling for the left-handed slepton mixing =>

m-> 3e P and T-odd asymmetries in minimal SUSY GUT models Two P-odd and one T-odd asymmetries P and T-odd asymmetries in minimal SUSY GUT models

(3) Atomic number dependence of the mu-e conversion rate for various LFV interactions Atomic number dependences for heavier nuclei are different for different types of LFV interactions. “ Finite size effect”, “Relativistic effect” Main sources of theoretical uncertainty are also different. Photonic dipole Vector Scalar gluonic

Maximal in the intermediate nuclei. Atomic number dependence of the mu-e conversion rate for various LFV operators Z-like vector Photon-like vector Photonic dipole Higgs-like scalar Al Ti Pb Maximal in the intermediate nuclei. Different Z dependence for heavy nuclei. Large enhancement in the scalar case (neutron-rich for heavy nuclei). V. Cirigliano, R.Kitano, Y.Okada, and P.Tuson, 2009

Theoretical uncertainty depends on a type of operators Photonic dipole case: Almost no uncertainty The calculation only depends on the charge distribution in a nucleus, which is precisely known by electron scattering. (2) Vector case: The main uncertainty comes from the neutron density. Little uncertainty for light nuclei. Uncertainty is 5% level for heavy nuclei if the proton scattering data is available (ex. Pb). (3) Scalar case: An addition source of uncertainty is scalar quark densities in a nucleon. The new lattice QCD estimation of strange quark scalar density. H. Ohki et.al. (JLQCD) PRD 78, 054502 compared with the previous phenomenological estimate

m e s An example: SUSY seesaw model with a large “tanb” Blue band : Uncertainty from y V. Cirigliano, R.Kitano, Y.Okada, and P.Tuson, 2009

Electric Dipole Moments An intrinsic electric dipole moment breaks T invariance. s H E s•H s•E P + - T If CPT invariance is assumed , EDM implies a new source of CP violation. Effect of the Kobayashi-Maskawa phase is small.

Various EDMs EDMs are measured for neutrons, muons, and various atoms and molecules. Extraction of EDMs for elementary particles are not simple except for muons. We can distinguish models by measuring various EDMs

g-2 EDM LFV Naïve scaling of new physics effects in lepton moments New physics effects can be extracted from the combination of the electron g-2and the muon g-2. EDM LFV The current bound on the muon EDM (O(10-19)) is not competitive to the electron EDM( O(10-27)). No apparent lepton mass dependence. Sensitive to flavor mixing structure. These relations are not exact and there are always exceptions

Muon and electron EDMs in SUSY examples Minimal supergravity model Type-II Seesaw model (Triplet Higgs) EDM from slepton LFV L L T H H d(muon)/d(electron)~200 Hisano-Nagai-Paradisi-Shimizu,09 Can be deviated from the naïve relation (dm/de=mm/me)

New physics examples In order to discriminate theoretical models , comparison of various signals is important. SUSY Seesaw with/without SU(5) GUT model The Littlest Higgs Model with T parity

SUSY GUT and SUSY Seesaw model Quark and neutrino Yukawa couplings are sources of squark and slepton flavor mixings. Flavor univesrality of SUSY breaking terms at the cutoff scale Quark FCNC LFV Quark Yukawa coupling Neutrino Yukawa coupling Yq Yn Neutrino seesaw model mSUGRA GUT L.J.Hall,V.Kostelecky,S.Raby,1986;A.Masiero, F.Borzumati, 1986

m-> eg, t-> eg, t->mg SUSY Seesaw +SU(5) GUT SUSY Seesaw model T.Goto, Y.Okada,T.Shindou,M.Tanaka, 2008

Neutron, electron, and Hg EDMs muon EDM vs. electron EDM T.Goto, Y.Okada,T.Shindou,M.Tanaka, 2008

Little Higgs Model with T parity The Higgs boson is a pseudo Nambu-Goldstone boson of some strong dynamics at ~10 TeV. New gauge bosons and a top partner to stabilize the Higgs potential against large radiative corrections without fine-tuning. T-odd heavy qaurks and leptons are introduced. New flavor mixing matrixes. d qH WH,ZH,AH VHd l lH WH,ZH,AH VHl New quark and lepton flavor mixing-> Quark FCMNC and LFV

Different correlation from SUSY case. m->3e vs. m-eg m-e conv vs m->eg Different correlation from SUSY case. T.Goto, Y.Okada, Y.Yamamoto, 2010

Atomic number dependence for m-e conversion rate T.Goto, Y.Okada, Y.Yamamoto, 2010

Summary EDMs and LFV are important probes to New Physics at the TeV scale. Well-motivated models like SUSY and Little Higgs models with T parity predict interesting range of signals. Correlations between various signals, angular distribution of m-eg and m->3e, atomic number dependence of m-e conversion rate are useful in discriminating different theoretical models.