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Overview of Muon g-2 and electron EDM

Overview of Muon g-2 and electron EDM. Jae Ho HEO. Yonsei University. Jeju Workshop Oct. 24&25. Motivation.

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Overview of Muon g-2 and electron EDM

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  1. Overview of Muon g-2 and electron EDM Jae Ho HEO Yonsei University Jeju Workshop Oct. 24&25

  2. Motivation • The anomalous magnetic moment, (g-2), of the muon has shown a sizable deviation (about C.L.) from the standard model prediction. A new physics beyond the standard model is necessary to explain the discrepancy. • The search for the electric dipole will uncover the violation of one of fundamental symmetries, CP violation. The CP violating sources need to be provided.

  3. Contents • Electromagnetic form factors • Electromagnetic moments at • Magnetic dipole moment (MDM) • Experimental measurements, standard model (SM) predictions and discrepancy between those. • Electric dipole moment (EDM) • Experimental bounds and SM prediction • Scenarios for generation of MDM or EDM • Model buildings • Octet-colored scalars • An extra U(1) • Conclusions PLB 661, 259 (2008) [hep-ph/0801.0231] PRD 80, 033001 (2009) [hep-ph/0811.0298]

  4. Electromagnetic form factors Interaction Lagrangian : 10 possible couplings Gordon decomposition 6 possible couplings X X Conservation of EM current 4 possible couplings X X X

  5. Electromagnetic moments Anapole Magnetic dipole Electric dipole Electric charge relativistic nonrelativistic

  6. The transformation properties of the fermion bilinears under C, P and T. MDM : all the discrete symmetries are conservative EDM : P and T violations. Nonzero EDM would be observed by CP violating interaction AM : C and P violations

  7. Otto Stern and Walther Gerlach (1921) : Ag atom has a magnetic moment (Ag molecular-beam passing through inhomogeneous magnetic field split into two beams) Bohr magneton of the electron: me=eћ/2mec within 10% Compton, Uhlenbeck and Goudsmit (1925) : spin: internal property like angular momentum electron spin se=1/2  two eigenstates sz= +1/2,-1/2 Dirac (1928): relativistic effect spin magnetic moment , me=ge(eћ/2mec) se ge=2 due to the spin degree of freedom Magnetic dipole moment (MDM)

  8. Anomalous Magnetic Moment (g-2) Otto Stern and his collaborations(1933) : Magnetic moment of the proton expected gp=2 since sp=1/2, however, measured gp=2.793… Alvarez and Bloch (1940) : Magnetic moment of the neutron expected gn=0 since Qn=0, however, measured gn=-0.913…. Hyperfine structure in hydrogen (1947) : Anomalous magnetic moment of the electron (ge >2 ) Schwinger (1948) : one loop correction (radiative correction) QED effect 1943 Nobel first ‘spin crisis’ An evidence for an internal structure 1965 Nobel PRV 73 416L (1948): 76 790 (1949) No internal structure observed for e so far 1955 Nobel • Kush and Forely confirm the Schwinger prediction through their experiment with 4% precision • Dehmelt : Dedicated experiment 1989 Nobel

  9. g-2 of the muon • Radiative corrections (loop corrections) : • different magnitude of MDMs for charged leptons (electron, muon and tauon) • Current measurements: D. Hanneke, et al, PRL 100, 120801 (2008) G.W. Benett, et al, PRD 73, 072003 (2006) The electron g-2 is 350 times more precisely measured. However, it is much less sensitive to new physics, since the effect of mass is suppressed by the factor Electron g-2 is a test of QED, but not for other aspects of SM

  10. SM predictions of the muon g-2 Schwinger Sommerfield Laporta &Remiddi Kinoshita Milstein et al Main source of present SM prediction uncertainty

  11. The discrepancy from the SM prediction : About 3.0s deviation from the SM prediction Most of people consider that this deviation comes from new physics beyond the standard model

  12. Electric dipole moment (EDM) • No evidences for EDM since 1962 most sensitive one B.C. Regan, et al, PRL 88, 071805 (2002) G.W. Benett, et al, hep-ex/0811.1207 C.A. Baker, et al, PRL 97, 131801 (2006) W.C. Griffith, et al, PRL 102, 101601 (2009) V.F. Dmitriev and R.A. Sen’kov, PRL 91, 212303 (2003) Dependent on quark EDMs and chromo-EDMs (internal structures of nucleons) Besides these, various EDM bounds exist for other (composite) particles

  13. SM predictions of eEDM F. Hoogeveen NPB 341, 322 (1990) CKM matrix Two up-type or down-type quark masses are equal :CP violation vanishes -> gluonic corrections. Khriplovich, Pospelov SJNP 53, 638 (1991)

  14. Model buildings Custodial symmetry • The approximate global symmety Experimentally measured value is near 1: this symmetry is not badly broken. • EW precision measurements of mass of gauge bosons • : provide us the bound of Higgs mass • Any physics responsible for EW symmetry breaking • : should possess custodial symmetry in the Higgs sector • as an approximate symmetry

  15. Flavor changing neutral currents (FCNCs) • Change the flavor of a fermion current • Not altering its electric charge (i.e. not u->d or e->v) Very suppressed 2008 Nobel • CKM (Cabibbo-Kobayashi-Maskawa) matrix in SM • An extension of GIM mechanism, which only includes 2 of 3 currents • Keep track of the weak decays of three generations of quarks gauge eigenstates mass eigenstates There are 4 free parameters, and experimental measurements are well explained so far.

  16. Theories beyond SM • FCNCs are generically predicted. • Their suppression is necessary for an agreement with observations. • A simple example : Yukawa potential with two scalars Higgs doesn’t change flavor, but other scalar is a disaster unless

  17. Anomaly cancellation A big constraint for the extended gauge theories : we can’t add charged fermions arbitrarily. : The sum over the various contributions must vanish at this triangle diagram by Ward identity. + crossing • An easy one like QED or QCD: only vector-like gauge couplings Every particle has antiparticle.

  18. SU(3) U(1) SU(2) U(1) U(1) U(1) U(1) SU(2) SU(3) • Standard Model : a gauged chiral theory • Trivial ones • Non-trivial ones grav. U(1) grav.

  19. SCENARIOS • Octet-colored scalars • An Extra U(1)

  20. Theoretical Description Octet-colored scalars Motivation : various NP models (GUT, SUSY, Top color, Leptoquark models, etc. If it exists, it will be copiously produced at LHC) • Extend the standard 2HDM with two octet-colored scalars • : octet-colored scalars have the same quantum numbers as • standard scalars except color quantum numbers S.L. Glashow, PRD 15 1958 (1977) • Respect MFV (Minimal Flavor Violation) • : Yukawa couplings of octet-colored scalars are proportion to couplings • of the standard scalars in flavor space A.V. Manohar, PRD 74 035009 (2006) They only extend this in the SM context With an octet-colored scalar. No EDM generated • Keep Z2-symmetry conservation • : spontaneous Z2 symmetry breaking is not necessary in this case.

  21. Yukawa potential with two supplemented octet-colored scalars in the standard 2HDM context Ou,Od: octet-colored scalars yu,yd : Yukawa coupling matrix ηu,ηd :complex constants Ta: QCD generator Z2 symmetry : odd, others are even Minimal flavor violation (MFV) respected (y : digonal matrix in flavor space) S.L. Glashow, PRD 15 1958 (1977)

  22. AfLfR coupling Transformation to Higgs Basis Three goldstone boson eaten Mass eigenstate in Z2-symmetry conservation for Higgs potential i.e. there is no mixing between CP- odd and even scalars. AfLfR coupling :

  23. Higgs potential and AOO coupling A lot of CP-violation sources in Higgs potential, but we need AOlOl coupling Z2-symmetry conservative η,η’ :complex constants there are two complex phase, but one phase is absorbed by the global field rotation. So only one phase survives. The unitary diagonalization transformation δ : phase difference between complex couplings ψ : rotation angle between two bases AOO coupling : where desirable CP-phase

  24. Barr-Zee Mechanism Barr,Zee PRL 65 21 (1990) Chang,Keung,Pilaftsis PRL 82 900 (1999) EDM

  25. Electron electric dipole Evaluating the Barr-Zee diagrams, Sum of eight color channels of O Chang,Keung,Pilaftsis, PRL 82 900 (1999) Two-loop function : The asymptotic behavior :

  26. Electron EDM prediction • The neutral pseudoscalar A is not • constrained from LEP data, • so choose light values • The predicted e-EDM is well • below experimental sensitivity. • Expected a sizable e-EDM • by octet-colored scalars B.C. Regan, et al, PRL 88 071805 (2002)

  27. An Extra U(1) Theoretical Frame Work • Extend the SM with an exotic lepton triplet E per family • : • Anomaly cancellations • : additional 6 anomaly cancellations necessary • Gauge invariance with an extra U(1) : renomalizable Lagrangians • Symmetry breakings : 2 steps symmetry breaking Barr, Dorsner, PRD 72 015011 (2005) These constraints provide gauge charges of fermions • An additional singlet necessary. • Assumed the symmetry breaking near the weak scale Usual EW symmetry breaking

  28. Fermion gauge charges

  29. Yukawa potential • Leptons : A Majorana combination Gauge charges of the Higgses by combinations with leptons • Higgs doublet and triplet can have two distinct extra U(1) charges

  30. Higgs gauge charges • Quarks : only couples to a Higgs, respect MFV(minimal flavor violation) • Leptons and quarks interact with two distinctive Higgs doublets • -> different from the standard 2HDM

  31. Neutrino mass generation • Mass matrix of neutral leptons • The coupling y4 must be very small since <f(0)> is of the oder of 100 GeV • Under Z2 symmetry, there is no y4coupling. • y3 and/or <c(-2)> are sized for the neutrino mass • We predict Majorana-type massive neutrinos.

  32. Higgs potential • Higgs potential with the gauge invariance with the extra U(1) • V2HDM : only Higgs doublets involved • functional form is the same as the 2HDM with Z2 symmetry • Two complex trinlinear couplings • :neutrino masses • Two complex quartic couplings • :EDM of fermions

  33. Z’ searches at the Hadron Colliders • The decay into charged leptons : • explore new regions in mass and couplings at Hadron colliders • Partonic cross section For pp collision, proton PDF replaced • K is QCD correction factor (~1.3) : ratio of higher order over leading order M. Carena,et al , PRD 70 093009 (2004) • Branching ratio : depend how many decay channels are open. • Two more channels are possible in this model, • but still within 4~5%, though the channels are open or not

  34. Z’ discovery limit at the Tevatron and LHC MRST, PLB 531 216 (2002)

  35. MDM generation Lagrangian at one loop Not proper interaction terms Introduce new Yukawa coupling in mass eigenstates This coupling is very small from neutrino mass constraint

  36. MDM generation at one loop Heo, PRD 80 033001 (2009) Corresponding one loop function : Asymptotic behaviors : , negligible

  37. Very sensitive to the Yukawa coupling y

  38. MDM and EDM generation at two loop Higgs Two distinctive extra U(1) charges : the exact Z2 symmetry in standard 2HDM -> no mixing between CP-even and -odd Higgses. CP-even Higgs (h, H) : MDM CP-odd Higgs (A) : EDM Yukawa Z2 symmetry conserved Yukawa Interaction terms

  39. Interaction Lagrangian in mass eigenstates MDM : : rotational angle The contribution is suppressed by muon mass and two loop factor • The lower limits of mh and mH atLEP OPAL Col., EPJC 18 425 (2001) This case is considered for the sizable MDM Heo, Keung, PLB 661 259 (2008) EDM : CP-phase CP-violation effect

  40. MDM Lower limit of the doubly charged scalar from the Tevatron and the LEP CDF Col., PRL 95 071801 (2005) L3 Col., PLB 576 18 (2003) • Predictions barely reside • in the allowed band, but still possible parameter space

  41. EDM B.C. Regan, et al, PRL 88 071805 (2002) Experimental bound • The sizable contributions • expected for the moderately • sized CP-phase,

  42. Conclusion • Two models were built in the standard model context. • Two octet-colored scalars under Z2-symmetry, MFV. • An extra U(1) with an exotic lepton triplet per family • in anomaly free gauge • The sizableg-2MDM and EDM could be generated. • Two octet-colored scalars • two-loop contribution of Barr-Zee mechanism • An extra U(1) • g-2 MDM at one and two loops, but the allowed parameter space is very narrow for two loop • eEDM for a moderately sized CP phase

  43. Thanks for attention!!

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