Lepton Moments 2014Centerville, Cape Cod, MA

Fundamental constants and the muon

22 July 2014

Peter Mohr

Outline

IntroductionFundamental ConstantsMuon magnetic moment anomaly aμ

Muonium HFSLamb shift in muonic hydrogenConclusion

Fundamental Constants

R∞ α h e k mμ aμ …CODATA 2010 Least-Squares Adjustment

− Rev. Mod. Phys. 84, 1527 (2012)

− Every four years → 2014

SI values reported

New SI, 2018

Muon anomalous magnetic moment

Least-squares adjustment

Muon to proton moment ratio

↑Muonium hfs

Electron to proton moment ratio

Electron to proton moment ratio

Muonium HFS

Muonium HFS

Muonium HFS

Muonium HFS theory

Muonium HFS output

The charge of the proton is distributed over a radius of about 1 fm.

This affects:

                 Electron scattering by protons

                 Atomic energy levels

The size of the proton, Pohl et al., Nature, July 2010:First report of a measurement of the Lamb shift in muonic hydrogen (negative muon + proton) that implied a radius of the proton that was 5σ disagreement with other determinations.

This result is a puzzle.

Proton radius puzzle

More recently   

CODATA recommended values of the fundamental physical constants: 2010, Reviews of Modern Physics, October 2012:

Reported a new recommended value for the proton radius in 7σ disagreement with the muonic hydrogen result.                

                 

Proton Structure from the Measurement of 2S­2P Transition Frequencies of Muonic Hydrogen, Antognini, et al., Science, January 2013:Reported a measurement of the Lamb shift in a different transition in muonic hydrogen which confirmed their earlier result.

Proton radius puzzle

Proton radius determinations

Spectroscopy of Hydrogen and Deuterium

The CODATA adjustment of the constants includes precise frequency measurements in hydrogen and deuterium as input data.

The theory of the hydrogen frequencies is expressed in terms of various constants, including the Rydberg constant, the radius of the proton, and the radius of the deuteron.

The least-squares adjustment of these constants, along with other constants, determines the values that give the best agreement between theory and experimental values for the frequencies.

In particular, this yields a value for the proton radius that is associated with the spectroscopic data and hydrogen theory.

The 2010 CODATA value for the proton radius is an average of the values from spectroscopic data and electron scattering experiments.

From: Mohr, Taylor, Newell Rev. Mod. Phys. (2012);Tan and Mohr, Springer Tracts (TBP)

Hydrogen 1S-2S frequency

Fine­structure constant

Rydberg constant

Rydberg state theory uncertainties

From Jentschura, Mohr, Tan, Wundt, Phys. Rev. Lett. (2008)

Muonic hydrogen Lamb shift(radius independent)

Muonic hydrogen total transition energy

Pohl, et al. (2010)

Proton polarizability

p p

μ μ

Rosenfelder (1999)

Pachucki (1999)

Martynenko, Faustov (2000)

Proton polarization calculation

Mohr, Griffith, Sapirstein, Phys. Rev. A (2013)

QED calculation of quark-muon electromagnetic interactions

Quarks: Dirac massless fermions bound in a spherical well (MIT Bag-like model)

Muon: In lowest order, bound in a hypothetical point charge field representing the proton charge

Interaction: QED photon exchange between quarks and the muon minus the corresponding point charge interactions

The effects of ordinary perturbation theory with a nucleus with a finite charge distribution correspond to the quarks in the ground state

The proton polarizability correction corresponds to quarks in intermediate excited states

Proton polarization calculations

[24] Martynenko, Phys. At. Nucl. (2006)

[22,23] Pachucki, Phys. Rev. A (1996,1999)

This work: Mohr, Griffith, Sapirstein, Phys. Rev. A (2013)

[21] Carlson, Vanderhaeghen, Phys. Rev. A (2011)

Conclusion

Muonium HFS provides accurate values for the muon to electron mass ratio and the muon­electron moment ratio.

Muonium theory and experiment are consistent to the level of the uncertainties.

In the unlikely case that the discrepancy of the proton radius reflects a problem with quantum electrodynamics (QED), the values of fundamental constants which rely on QED being correct are in question.  These constants include R

∞, r

p, r

d,  , e, m

e, m

.