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Upsetting the Fine Structure Constant without 12672 Diagrams

Upsetting the Fine Structure Constant without 12672 Diagrams. Mihailo Backovic , John Ralston, Rainer Schiel. Outline. Fine Structure Constant and the Anomalous Magnetic Moment of the Electron. Recent Calculations and Measurements of a e Hadronic Contributions New Hadronic Bound State

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Upsetting the Fine Structure Constant without 12672 Diagrams

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  1. Upsetting the Fine Structure Constant without 12672 Diagrams MihailoBackovic, John Ralston, Rainer Schiel

  2. Outline • Fine Structure Constant and the Anomalous Magnetic Moment of the Electron. • Recent Calculations and Measurements of ae • Hadronic Contributions • New Hadronic Bound State • Contributions of New Hadrons to ae ,α

  3. Fine Structure Constant • The most recent measurement (Hanneke, Fogwell, Gabrielse, 2008): • Fine structure constant related to the electron’s magnetic moment anomaly • Most accurate measurement of α from electron’s anomalous magnetic moment.

  4. Measurments / Calculations of ae • Recent measurement of ae (Hanneke, Fogwell, Gabrielse, 2008): • Recent calculation of ae (eight order) (Aoyama, Hayakawa, Kinoshita, Nio, 2008 ):

  5. Measurments / Calculations of ae • Recent measurement of ae (Hanneke, Fogwell, Gabrielse, 2008): • Recent calculation of ae (eight order) (Aoyama, Hayakawa, Kinoshita, Nio, 2008 ):

  6. Recent Measurments / Calculations Hanneke, Fogwell, Gabrielese, 2008

  7. ae • Magnetic moment anomaly usually calculated as: • Most attention is directed towards the QED corrections (Currently eight order accuracy, work towards tenth order with 12672 diagrams).

  8. ae • Magnetic moment anomaly usually calculated as: • Most attention is directed towards the QED corrections (Currently eight order accuracy, work towards tenth order with 12672 diagrams). Ralston, Schiel, Backovic

  9. Hadronic Contributions • Dispersion Integral:

  10. Hadronic Contributions • Dispersion Integral:

  11. Hadronic Contributions • Dispersion Integral: Will come back to this.

  12. Hadronic Contributions Davier et al, 2002

  13. Hadronic Contributions Davier et al, 2002

  14. Hadronic Contributions Davier et al, 2002 No data for low energies!!!!!

  15. Hadronic Contributions • What about bound states of pions? J(PC) = 1(--)

  16. Hadronic Contributions • What about bound states of pions? Pi-rhonium (Ralston, Schiel, 2007) J(PC) = 1(--) Explains the 3σ discrepancy in muon’s anomalous magnetic moment.

  17. Hadronic Contributions • What about bound states of pions? Pi-rhonium (Ralston, Schiel, 2007) J(PC) = 1(--) Pionic atoms (π+π-) have already been observed (DIRAC experiment) Explains the 3σ discrepancy in muon’s anomalous magnetic moment.

  18. Pi-rhonium Contribution Use the Breit-Wigner formula to obtain:

  19. Pi-rhonium Contribution Use the Breit-Wigner formula to obtain: 28eV if the state amounts for the full discrepancy of the muon’s anomalous magnetic moment. (Ralston, Schiel, 2007) Mixes with ρ To about 1% Unknown. No data

  20. Pi-rhonium Contribution • So… if then… Significant at next order! Add this contribution to the fine structure constant calculation to get: (Calculate the error bars from the muon)

  21. Conclusions • Excited state of a pionic atom could contribute to the next order of accuracy of the fine structure constant. • Need data in the low energy part of R(s). • Work in progress – need to explore options from non-perturbative bound state hadronic physics. • Next order calculation / experiment should consider this contribution!

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