1. “ OUTLOOK” g-2: Theory vs Experiment (For motivation see D. Stoeckinger’s Talk) William J. Marciano Mainz April 5, 2014

2. Outline I will discuss some Developments & Group Discussion i) g e -2 (5 loops!) & α −1 ( 87 Rb)=137.035999049(90 ) ii) g μ -2 Discrepancy (Hadronic effects or New Physics?) iii) Working group discussion of “Other Topics” “New Physics” Scenarios g μ -2 Discrepancy suggests New Physics ≤ O(2TeV) LHC Territory Supersymmetry (short-distance) favorite “Light” Dark Photon (Dark Matter Force Mediator)? Other …

3. Mount Auburn Cemetery

4. Feynman Diagrams: Anomalous Magnetic Moment Contributions

5. Anomalous Magnetic Moments Today a l =(g l -2)/2 l=e,μ a e (exp)=0.00115965218073(28) unc. 0.28x10 -12 ! (Hanneke, Fogwell, Gabrielse: PRL 2008) g e =2.00231930436146(56) Most precisely known dimensionless quantity! Future: factor ≥ 4 improvement? Good Goal a e (SM)=  /2  -0.328478444002546(  /  ) 2 +1.181234016(  /  ) 3 -1.9097(20)(  /  ) 4 +9.16(58)(  /  ) 5 … +1.68(2)x10 -12 (had) +0.03x10 -12 (EW) Aoyama, Hayakawa, Kinoshita, & Nio 2012 Update! Spectacular Achievement Uncertainty ±7x10 -14 (QED) ±2x10 -14 (Hadronic)

6. Recent alpha determination using R  =1.0973731568527(73)x10 7 m -1 α −1 ( 87 Rb)=137.035999049(90) Bouchendira et al. PRL. (2011) factor 10 improvement! Δa e = a e (exp) − a e (theory) = −1.05 (0.82) × 10 −12 Note Negative Sign Error Budget: ±77x10 -14 (alpha) ±28x10 -14 (exp.) ±7x10 -14 (theory) Ongoing 87 Rb exp. Goal - Another factor of 7 improvement! Δa e Factor 2.6 Sensitivity Improvement! Further Improvement? New Experiment (4 x better a e ) Very good for constraining new long distance physics (eg Dark Photon) Muon (m μ /m e ) 2 ≈ 40,000x more sensitive to short distances NP See: Giudice, Paradisi and Passera JHEP (2012) for exceptions

7. Muon Anomalous Magnetic Moment 1957 Garwin, Lederman & Weinrich study π  ν,  e found parity violation & measured g  =2.00  0.10 Parity Violation Decay  Self Analyzing Polarimeter led to Three Classic CERN Exps. ending in 1977 “The Last g  -2 Experiment” Until Experimental E821 at BNL (2004 Final) a  exp  (g  -2)/2 =116592091(54) stat (33) sys x10 -11 =116592091(63)x10 -11 Factor of 14 improvement over CERN results (statistics) (Goal: Factor 4 further Improvement at FNAL) D. Hertzog, B.L. Roberts… ±16x10 -11

11. Standard Model Prediction a  SM = a  QED +a  EW +a  Hadronic (quark/gluon loops) QED Contributions: a  QED =0.5(  /  )+0.765857425(17)(  /  ) 2 + 24.05050996(32)(  /  ) 3 + 130.8796(63)(  /  ) 4 + 753.29(1.04)(  /  ) 5 +… 2012 Update: Aoyama, Hayakawa, Kinoshita, & Nio  -1(87 Rb ) =137.035999049(90) from h/m RB a  QED =116584718.95(8)x10 -11 Very Precise!

13. Electroweak Loop Effects a  EW (1 loop)=194.8x10 -11 original goal of E821 a  EW (2 loop)=-41.2(1.0)x10 -11 (Higgs Mass = 126GeV)) 3 loop EW leading logs very small O(10 -12 ) a  EW =154(1)x10 -11 Non Controversial Hadronic Contributions (HVP & HLBL) a  Had (V.P.) LO =6923(42)(3)x10 -11 (Hoecker update) a  Had (V.P.) NLO = -98(1)x10 -11 a  Had (LBL) = 105(26)x10 -11 (Consensus?) 3 loop (  /  ) 3 QCD a  SM =116591803(49)x10 -11 (Future Improvement?)  a  =a  exp -a  SM =288(63)(49)x10 -11 (3.6  deviation!)

14. Comparison of Experiment and Theory (Most Recent PDG)  a  =a  exp -a  SM =288(63)(49)x10 -11 (3.6  !) Note, Kunz, Liu, Marquard & Steinhauser find NNLO Hadronic +12.4(1)x10 -11 reduces  a  =276(63)(49)x10 -11 (3.5  !) This is a very large deviation! Remember, the EW contribution is only 154x10 -11 New Physics Nearly 2x Electroweak? Why don’t we see it in other measurements? “New Physics” Scale Implied <mμ/|  a  | ½ ≈ 2TeV

15. Examples of NNLO Hadronic Vacuum Polarization considered by Kunz, Liu, Marquard and Steinhauser

16. NNLO HLBL ~ +3(2)x10 -11 Colangelo, Hoferrichter, Nyffeler, Passera & Stoffer

17. Discussion of Arbuzov and Kopylova Paper Claim if muons are off-shell by~+35eV due to Environment, it will solve exp – theory discrepancy Why should they be off-shell by +35MeV? Does it need to be tested by another exp.? Note: eg μ /2m μ B ≈ 4x10 -7 eV expect very small effect

19. SUSY Loops are like EW, but depend on: 2 spin 1/2  - (charginos) 4 spin 1/2  0 (neutralinos) including dark matter! spin 0 sneutrinos and sleptons with mixing! (light stau may dominate) Enhancement factor tan  =  2  /  1  ~3-40!

20. Interpretations  a  =a  exp -a  SM =288(80)x10 -11 (3.6  !) Generic 1 loop SUSY Conribution: a  SUSY = (sgn  )130x10 -11 (100GeV/m susy ) 2 tan  tan  3-40, m susy  100-500GeV Some LHC-MSSM Tension Other Explanations: Hadronic e + e - Data? HLBL(3loop)? Lattice Gauge Theory Efforts! Multi-Higgs Models (2 loop effects) Extra Dimensions<1-2TeV * Dark Photons  10-200MeV, α’=10 -8 Light Higgs Like Scalar <10MeV? etc.

21. The Dark Boson – A Portal to Dark Matter What if some dark sector particles interact with one another via a new massive but relatively “light” Z d (Dark photon)? U(1) d local gauge symmetry of the Dark Sector Introduced for 1) Sommerfeld Enhancement 2)  d  e + e - (source of positrons,  -rays) 3) Cosmic Stability U(1) d eg Wimp Number (S. Weinberg!) 4) Light Dark Matter (≤8GeV) * 5) Muon Anomalous Magnetic Moment Can we find direct evidence for such a particle (boson)? (or rule out some scenarios)

22. Kinetic U(1) Y x U(1) d Mixing (Holdom) L U(1)YxU(1)d =-¼(B μν B μν -2ε/cosθ W B μν D μν +D μν D μν ) B μν =   B ν -  ν B μ D μν =   Z dν -  ν Z dμ ε= O(few x10 -3 ) or smaller loop effect Remove Mixing by field redefinitions B μ   B μ +ε/cosθ W  dμ or in terms of  & Z A μ   A μ +εZ dμ Z μ   Z μ +εtanθ W Z dμ L int =-eεJ μ em Z d μ

23. Example One Loop gamma-Z d Kinetic Mixing (Through Heavy Charged Leptons) That also carry U(1) d charge Expect ε~eg d /8π 2 ≈O(10 -3 )

24. Effective 3 loop g μ -2 “Dilbert” Diagram a μ Zd =α/2πε 2 F(m Zd /m μ ), F(0)=1 solves g μ -2 discrepancy for ε 2 ≈3-5x10 -6 & m Zd ≈20-50MeV (see figure)

25. Lepton Magnetic Moment Constraints on the Dark Photon Green Band Correspods to a  exp -a  SM =288(63)(49)x10 -11 90% CL Recent g e -2 Constraint (Davoudiasl, Lee, WJM) a e (exp) − a e (theory) = −1.05 (0.82) × 10 −12 wrong sign!

27. Dark Photon Constraints (Some assume BR(Z d  e + e - ~ 1) eg π 0  Z d

28. Near Term Sensitivity Improvements MAMI 2013 ε 2 ≥ 10 -6 for m Zd >40MeV explored NA48 DATA ε 2 ≥ 10 -6 for m Zd >10-20MeV explored Using π 0   Z d Z d  e + e - The g μ -2 scenario may soon be ruled out for Z d  e + e - Very light dark matter allows Z d  dark matter (invisible) New scenario eliminates many constraints but allows K   Z d Z d  “missing energy” constraints

29. K  π + Z d Constraints for BR(  d  dark matter)~1 m Zd =100, 200MeV ruled out?

30. Status of Dark Photon NP Solution (m Zd,ε 2 ) parameter space being squeezed Will be eliminated in the next few years or a revolutionary discovery will be made.

31. Magnet Leaves BNL (Summer 2013)

32. The Ocean Journey Begins: BNL-Fermilab

33. Passing St. Louis

34. The Last Mile

35. Fermilab Celebrates

36. Fermilab + Storage Ring at Night

37. Take Away Messages Old Storage Rings Never Die, they just get taken away Hadronic Uncertainty Must Be Reduced!