Proton-to-electron mass ratio explained

In physics, the proton-to-electron mass ratio (symbol μ or β) is the rest mass of the proton (a baryon found in atoms) divided by that of the electron (a lepton found in atoms), a dimensionless quantity, namely:

μ =

The number in parentheses is the measurement uncertainty on the last two digits, corresponding to a relative standard uncertainty of

Discussion

μ is an important fundamental physical constant because:

• Baryonic matter consists of quarks and particles made from quarks, like protons and neutrons. Free neutrons have a half-life of 613.9 seconds. Electrons and protons appear to be stable, to the best of current knowledge. (Theories of proton decay predict that the proton has a half life on the order of at least 10³² years. To date, there is no experimental evidence of proton decay.);
• Because they are stable, are components of all normal atoms, and determine their chemical properties, the proton is the most prevalent baryon, while the electron is the most prevalent lepton;
• The proton mass m_p is composed primarily of gluons, and of the quarks (the up quark and down quark) making up the proton. Hence m_p, and therefore the ratio μ, are easily measurable consequences of the strong force. In fact, in the chiral limit, m_p is proportional to the QCD energy scale, Λ_QCD. At a given energy scale, the strong coupling constant α_s is related to the QCD scale (and thus μ) as

\alpha _{s =- (2 \pi)/(\beta _{0} ln (E/ Λ _{\rm} ))}

where β₀ = −11 + 2n/3, with n being the number of flavors of quarks.

Variation of μ over time

Astrophysicists have tried to find evidence that μ has changed over the history of the universe. (The same question has also been asked of the fine-structure constant.) One interesting cause of such change would be change over time in the strength of the strong force.

Astronomical searches for time-varying μ have typically examined the Lyman series and Werner transitions of molecular hydrogen which, given a sufficiently large redshift, occur in the optical region and so can be observed with ground-based spectrographs.

If μ were to change, then the change in the wavelength λ_i of each rest frame wavelength can be parameterised as:

λ _{i=λ} _{0} \left[ 1+ K _{i} (\Delta\mu)/(\mu) \right], where Δμ/μ is the proportional change in μ and K_i is a constant which must be calculated within a theoretical (or semi-empirical) framework.

Reinhold et al. (2006) reported a potential 4 standard deviation variation in μ by analysing the molecular hydrogen absorption spectra of quasars Q0405-443 and Q0347-373. They found that . King et al. (2008) reanalysed the spectral data of Reinhold et al. and collected new data on another quasar, Q0528-250. They estimated that, different from the estimates of Reinhold et al. (2006).

Murphy et al. (2008) used the inversion transition of ammonia to conclude that at redshift . Kanekar (2011) used deeper observations of the inversion transitions of ammonia in the same system at towards 0218+357 to obtain .

Bagdonaite et al. (2013) used methanol transitions in the spiral lensing galaxy PKS 1830-211 to find at .^{[1] [2]} Kanekar et al. (2015) used near-simultaneous observations of multiple methanol transitions in the same lens, to find at . Using three methanol lines with similar frequencies to reduce systematic effects, Kanekar et al. (2015) obtained .

Note that any comparison between values of Δμ/μ at substantially different redshifts will need a particular model to govern the evolution of Δμ/μ. That is, results consistent with zero change at lower redshifts do not rule out significant change at higher redshifts.

See also

• Koide formula

References

• Book: Barrow, John D. . John D. Barrow . The Constants of Nature: From Alpha to Omega – the Numbers That Encode the Deepest Secrets of the Universe . London . Vintage . 0-09-928647-5. 2003 .
• Reinhold . E. . Buning . R. . Hollenstein . U. . Ivanchik . A. . Petitjean . P. . Ubachs . W. . 2006 . Indication of a Cosmological Variation of the Proton–Electron Mass Ratio based on Laboratory Measurement and Reanalysis of H2 spectra . Physical Review Letters . 96 . 15. 151101 . 10.1103/physrevlett.96.151101. 2006PhRvL..96o1101R . 16712142.
• King . J. . Webb . J. . Murphy . M. . Carswell . R. . 2008 . Stringent Null Constraint on Cosmological Evolution of the Proton-to-Electron Mass Ratio. Physical Review Letters . 101 . 25. 251304 . 10.1103/physrevlett.101.251304. 19113692 . 0807.4366 . 2008PhRvL.101y1304K . 40976988 .
• Murphy . M. . Flambaum . V. . Muller . S. . Henkel . C. . 2008 . Strong Limit on a Variable Proton-to-Electron Mass Ratio from Molecules in the Distant Universe . Science . 320 . 5883. 1611–3 . 10.1126/science.1156352 . 18566280. 0806.3081 . 2008Sci...320.1611M . 2384708 .
• Kanekar . N. . 2011 . Constraining Changes in the Proton–Electron Mass Ratio with Inversion and Rotational Lines . Astrophysical Journal Letters . 728 . 1 . L12 . 10.1088/2041-8205/728/1/L12 . 1101.4029 . 2011ApJ...728L..12K . 119230502 .
• Kanekar . N. . Ubachs . W. . Menten . K. L. . Bagdonaite . J. . Brunthaler . A. . Henkel . C. . Muller . S. . Bethlem . H. L. . Dapra . M. . 2015 . Constraints on changes in the proton–electron mass ratio using methanol lines. . Monthly Notices of the Royal Astronomical Society Letters . 448 . 1 . L104 . 10.1093/mnrasl/slu206 . free . 1412.7757 . 2015MNRAS.448L.104K .

Notes and References

1. Bagdonaite . Julija . Jansen . Paul . Henkel . Christian . Bethlem . Hendrick L. . Menten . Karl M. . Ubachs . Wim . A Stringent Limit on a Drifting Proton-to-Electron Mass Ratio from Alcohol in the Early Universe . December 13, 2012 . . 10.1126/science.1224898 . 2013Sci...339...46B . 339 . 6115 . 46–48 . 23239626. 716087 . free .
2. Web site: Moskowitz . Clara . Phew! Universe's Constant Has Stayed Constant . December 13, 2012 . . December 14, 2012 .