This paper gives the 2010 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of that adjustment, until 31 December 2010, the closing date of the new adjustment. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2010 set replaces the previously recommended 2006 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

/pdf/codata-recommended-values-of-the-fundamental-physical-4bsdant71c.pdf

CODATA Recommended Values of the Fundamental Physical Constants: 2006

We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a(mu)=(g-2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a(mu)(Expt)=11659208.0(5.4)(3.3)x10(-10), where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a(mu) includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, approximate to 0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e(+)e(-) hadronic cross sections, lie 2.2-2.7 standard deviations below the experimental result.

https://faculty.washington.edu/hertzog/FinalPRDpostedversion.pdf

Final report of the E821 muon anomalous magnetic moment measurement at BNL

Considering that the proton is a basic subatomic component of all ordinary matter — as well as being ubiquitous in its solo role as the hydrogen ion H+ — there are some surprising gaps in our knowledge of its structure and behaviour. A collaborative project to determine the root-mean-square charge radius of the proton to better than the 1% accuracy of the current 'best' value suggests that those knowledge gaps may be greater than was thought. The new determination comes from a technically challenging spectroscopic experiment — the measurement of the Lamb shift (the energy difference between a specific pair of energy states) in 'muonic hydrogen', an exotic atom in which the electron is replaced by its heavier twin, the muon. The result is unexpected: a charge radius about 4% smaller than the previous value. The discrepancy remains unexplained. Possible implications are that the value of the most accurately determined fundamental constant, the Rydberg constant, will need to be revised — or that the validity of quantum electrodynamics theory is called into question. Here, a technically challenging spectroscopic experiment is described: the measurement of the muonic Lamb shift. The results lead to a new determination of the charge radius of the proton. The new value is 5.0 standard deviations smaller than the previous world average, a large discrepancy that remains unexplained. Possible implications of the new finding are that the value of the Rydberg constant will need to be revised, or that the validity of quantum electrodynamics theory is called into question. The proton is the primary building block of the visible Universe, but many of its properties—such as its charge radius and its anomalous magnetic moment—are not well understood. The root-mean-square charge radius, rp, has been determined with an accuracy of 2 per cent (at best) by electron–proton scattering experiments1,2. The present most accurate value of rp (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants3. This value is based mainly on precision spectroscopy of atomic hydrogen4,5,6,7 and calculations of bound-state quantum electrodynamics (QED; refs 8, 9). The accuracy of rp as deduced from electron–proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant3). An attractive means to improve the accuracy in the measurement of rp is provided by muonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, the Lamb shift10 (the energy difference between the 2S1/2 and 2P1/2 states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations11,12,13,14,15 of fine and hyperfine splittings and QED terms, we find rp = 0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value3 of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by −110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.

/pdf/the-size-of-the-proton-1w85tmnp1f.pdf

The size of the proton

http://www-com.physik.hu-berlin.de/~fjeger/gm2review.pdf

The muon g ― 2

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g-2 Experiment for the positive muon magnetic anomaly a_{μ}≡(g_{μ}-2)/2. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω_{a} between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω[over ˜]_{p}^{'} in a spherical water sample at 34.7 °C. The ratio ω_{a}/ω[over ˜]_{p}^{'}, together with known fundamental constants, determines a_{μ}(FNAL)=116 592 040(54)×10^{-11} (0.46 ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both μ^{+} and μ^{-}, the new experimental average of a_{μ}(Exp)=116 592 061(41)×10^{-11} (0.35 ppm) increases the tension between experiment and theory to 4.2 standard deviations.

/pdf/measurement-of-the-negative-muon-anomalous-magnetic-moment-p1xcoi2es9.pdf

Measurement of the negative muon anomalous magnetic moment to 0.7 ppm

High precision measurements of two Zeeman hyperfine transitions in the ground state of muonium in a strong magnetic field have been made at LAMPF using microwave magnetic resonance spectroscopy and a resonance line narrowing technique. These determine the most precise values of the ground state hyperfine structure interval of muonium $\ensuremath{\Delta}\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4463302765(53)\mathrm{Hz}$ $(12\mathrm{ppb})$, and of the ratio of magnetic moments ${\ensuremath{\mu}}_{\ensuremath{\mu}}/{\ensuremath{\mu}}_{p}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.18334513(39)$ $(120\mathrm{ppb})$, representing a factor of 3 improvement. Values of the mass ratio ${m}_{\ensuremath{\mu}}/{m}_{e}$ and the fine structure constant $\ensuremath{\alpha}$ are derived from these results.

/pdf/high-precision-measurements-of-the-ground-state-hyperfine-3hzkl790w5.pdf

P.O. Egan

Papers

High precision measurements of the ground state hyperfine structure interval of muonium and of the muon magnetic moment