The g-factor of a bound electron - indico.fnal.gov fileThe puzzle of the muon magnetic moment The...
Transcript of The g-factor of a bound electron - indico.fnal.gov fileThe puzzle of the muon magnetic moment The...
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The g-factor of a bound electron
LoopFest BuffaloAugust 17, 2016
Andrzej Czarnecki University of Albertawith M. Dowling, J. Piclum, R. Szafron
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Outline
Three Loop-related themes in bound states:
Spectrum: Lamb shift, Rydberg, proton radius
Interactions with external fields: g-2 of a bound electron
Decay of a bound particle: muon decay in orbit and the muon --> electron conversion
Robert Szafron's talk
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The puzzle of the muon magnetic moment
The 3.6 sigma discrepancy,
PRD 86, 095009 (2012)
PRD 86, 095009 (2012)
is large compared with other bounds on New Physics.
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How to check gµ-2?
Electron g-2 is likely sensitive to the same New Physics; but at present it is used to determine the fine-structure constant.
A new source of alpha is needed.
Note: Centenary!First introduced by Sommerfeld 1916
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How to check gµ-2?
The second best determination of alpha: from atomic spectroscopy
Nature 2014Sturm et al
for Rb(better for He)
improvementneeded byfactor ~10
(but is itfor sure?)
Nature 442, 516 (2006)PRA 89, 052118 (2014)
gives h/m
PRL 106, 080801 (2011)
Needed precision:
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Magnetic moment (bound electron)
Why useful?- determination of the electron mass- future determination of alpha
Why interesting?- quantum effects in external field- simple system, model for more complex ones- numerical estimates exist for large Z- should be analytically feasible for small Z (many have
tried)
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Determination of electron's mass
Larmor frequency
Cyclotron frequency
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Electron anchored in an ion
Larmor frequency
Cyclotron frequency
Interesting complication:this g-factor is modified by the binding
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Bound-electron g-2: the leading effect
Breit 1928: energy correction due to magnetic field in the hydrogen ground state.
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Bound-electron g-2: the leading effect
Breit 1928: energy correction due to magnetic field in the hydrogen ground state.
Important: dependenceon alpha; may be exploitedto determine its value.(Use ions with various Z)
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Bound-electron g-2: the leading effect
Breit 1928: energy correction due to magnetic field in the hydrogen ground state.
Valid to all orders in Zα
Harder to achieve when loops present.
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Bound-electron g-2: binding and loops
Pachucki,ACJentschura,Yerokhin(2005)
two-loop corrections
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Bound-electron g-2: binding and loops
Together with experiments in Mainz, this improved the accuracy of me by about a factor 3,
theory error
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Recent experimental improvement
This improved the accuracy of me by about a factor 3,
Nature 2014Sturm et al
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Recent experimental improvement
This improved the accuracy of me by about a factor 3,
Nature 2014Sturm et al
Next theory challenge:(Zα)5 effects.
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To find Δg, consider the energy in a magnetic field
The result is gauge-invariant; but not yet complete.
What if the magnetic field couples to an external line?
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Next goal: α2(Zα)5 corrections to g
Examples:
More than 300 contributions.
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A set of 32 master integrals
Typical expression
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Reevaluation of the α2(Zα)5 Lamb shift
Dowling, Mondejar, Piclum, AC, PRA 81, 022509
Previous results
-7.61(16) Pachucki 1994-7.724(1) Eides and Shelyuto, 1995
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New source of alpha: medium-charged ions
e-
Hydrogen-like ion Lithium-like ion
Combine H-like and Li-like ions to remove nuclear dependence;then combine with a different nucleus, to remove free-g dependence! Much interesting theoretical work remains to be done!
Yerokhin, Berseneva, Harman, Tupitsyn, Keitel: PRL (2016)
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Summary
* Binding modifies the electron g-factor
* Theory of a bound electron is more fun than for free particles
* Synergy with beautiful experiments: mass of the electron and, in future, the fine structure constant.
* α(Zα)5 effects almost finished; α2(Zα)5 hopefully soon.
* Opportunities for more theoretical improvement...
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Can we use the electron to check muon g-2?
Measured with relative error 25 · 10-11
Provides the fine structure constant withthe same precision,
Phys. Rev. Lett. 100, 120801 (2008)
Phys. Rev. Lett. 109, 111807 (2012)
Experimental error dominates (for now) Numerical errors from
4- and 5-loop diagrams