Muon g g- -2 and 2 and Muon a peculiar extra U(1) a peculiar - PowerPoint PPT Presentation

Muon g g- -2 and 2 and Muon a peculiar extra U(1) a peculiar extra U(1) PRD 80, 033001 (2009) [hep-ph/0811.0298] Jae Ho Heo Theoretical High Energy Group jheo1@uic.edu University of IL at Chicago PHENO 2010 PHENO 2010

g- -2 2 of the of the muon muon g • Radiative corrections (loop corrections) : different magnitude of MDMs for charged leptons (electron, muon and tauon) Assuming QED is correct,  a provides the most accurate value . e • Current measurements: D. Hanneke, et al , PRL 100, 120801 (2008)   10 - a (exp) 11 596521 . 8073 ( 0 . 0028 ) 10 Havard e   - 10 (exp) 11 659208 . 0 ( 6 . 33 ) 10 BNL E821 a  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,  2 since the effect of mass is suppressed by the factor ( m  / m ) 4300 0 e Electron g-2 is a test of QED, but not for other aspects of SM Jae Ho Heo 2

SM predictions of the muon muon g g- -2 2 SM predictions of the   - 10 (QED) 11 658471 . 8113 ( 162 ) 10 a  2 3 4 5                               a (QED) 0 . 765857388 ( 44 ) 24 . 050509 ( 2 ) 126 . 04 930 ( 170 )               2 Schwinger Sommerfield Laporta &Remiddi Kinoshita Milstein et al   - 10 a (EW) 1 5 . 4 ( 0 . 2 ) 10    - 10 a (hadrons) 693 . 07 ( 6 . 89 ) 10  • The discrepancy from the SM prediction :      - 10 a a (exp) a (SM) 27 . 7 ( 9 . 3 ) 10    About 3.0  deviation from the SM prediction We consider that this deviation comes from new physics beyond the standard model Jae Ho Heo 3

Theoretical Frame Work Theoretical Frame Work • Extend the SM with an exotic lepton triplet E per family : Barr, Dorsner, PRD 72 015011 (2005) These constraints provide gauge charges of fermions • Anomaly cancellations : additional 6 anomaly cancellations necessary • Gauge invariance with an extra U(1) : renomalizable Lagrangians • Symmetry breakings : 2 steps symmetry breaking            ( 2 ) ( 1 ) ( 1 ) ( 2 ) ( 1 ) ( 1 ) SU U U SU U U       L Y X L Y em Usual EW symmetry breaking  An additional singlet necessary.  Assumed the symmetry breaking near the weak scale Jae Ho Heo 4

5 Jae Ho Heo X ) 1 ( U  gravity Fermion gauge charges and X ) 1 ( U  2 ) 2 ( SU

Yukawa potential potential Yukawa ,  : bidoublet representa tion E • 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  0  Z symmetry : E is odd and all other particles are even E is a dark matter candidate 2 Jae Ho Heo 6

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 Jae Ho Heo 7

Neutrino mass generation Neutrino mass generation • Mass matrix of neutral leptons The coupling y 4 must be very small since <  (0)  > is of the order of 100 GeV  Under Z 2 symmetry, there is no y 4 coupling. y 3 and/or  (-2)  are sized for the neutrino mass  This VEV has to very small to avoid large radiative correction s to the parameter  We predict Majorana-type massive neutrinos. Jae Ho Heo 8

Higgs potential Higgs potential • Higgs potential with the gauge invariance with the extra U(1) • V 2HDM : only Higgs doublets involved functional form is the same as the 2HDM with Z 2 symmetry • Two complex trilinear couplings :neutrino masses and Baryogensis via Leptogenesis Ma, Sarkar, PRL 80 5716 (1998) • Two complex quartic couplings : often mentioned for EDM of fermions Heo,Keung, PLB 661 259 (2008) Jae Ho Heo 9

searches at the Hadron Hadron Colliders Colliders Z’ ’ searches at the Z       • The decay into charged leptons : p p ( p ) Z ' explore new regions in mass and couplings at Hadron colliders  Partonic cross section For pp collision, proton PDF replaced      Hadronic cross section in the channel  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 Jae Ho Heo 10

discovery limit at the Tevatron Tevatron and LHC and LHC Z’ ’ discovery limit at the Z The prediction s : MRST LO PDFs are used MRST, PLB 531 216 (2002) Intersecti ons of the curves : lower mass limits of M Z'  The lower limits of the extra U(1) symmetry breaking : 200 ~ 800 GeV The horizontal lines :   - 1 Tevatron ( s 1 . 96 TeV and L 1.3 fb )   - 1 LHC( s 14 TeV and L 100 fb ) Jae Ho Heo 11

g- -2 MDM generation 2 MDM generation Lagrangian Lagrangian at one loop at one loop g Not proper interaction terms Introduce new Yukawa coupling in mass eigenstates This coupling is very small from neutrino mass constraint Jae Ho Heo 12

MDM generation at one loop MDM generation at one loop  Negligible contributi on,   since the particles ( , ) on the line E E whic h are hooked up by the photon have opposite charges.     2 2 m M 3     y      a f       2 2 M M 8     E E Corresponding one loop function : Asymptotic behaviors : 2 2 m g       10 z ' a 10 , negligible   2 2 12 M z ' Jae Ho Heo 13

    2 2 m M 3 y         ( one ) a f       2 2 • Very sensitive to the Yukawa coupling y M M 8     E E  Prediction s in the allowed band  around y 0 . 05   for 0.1TeV M , M 1 TeV.  E   y 0 . 06 region is possible  for , 1 TeV. M M  E  a as a function of M E at the one loop for variou s values of M   Jae Ho Heo 14

MDM generation at two loop MDM generation at two loop Higgs Two distinctive extra U(1) charges : the exact Z 2 symmetry in standard 2HDM -> no mixing between CP-even and -odd Higgses. CP-even Higgs (h, H) : MDM CP-odd Higgs (A) : EDM Yukawa Z 2 symmetry conserved Yukawa Interaction terms Jae Ho Heo 15

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) 2   Q 5 due to singly and doubly  charged scalars in the inner loop   The Yukawa coupling :  the same size as the SM Higgs quartic couling for the SM Higgs of 120 GeV • Predictions barely reside in the allowed band, but still possible parameter space   a as a function of m at the two loop for variou s values of tan  h Jae Ho Heo 16

Conclusion Conclusion A model (Lagrangian) with a peculiar extra U(1) was built.  An extra U(1) with an exotic lepton triplet per family in anomaly free gauge The sizable g-2 MDM could be generated.  g-2 MDM at one and two loops, but the allowed parameter space is very narrow for two loop Jae Ho Heo 17