The Temperature Dependence of the Diamagnetic Shielding Correction for Proton NMR in Water

Petley, B. W.; Donaldson, Ralph W.

doi:10.1088/0026-1394/20/3/002

Cited by 36 publications

(9 citation statements)

References 9 publications

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“…The ratio of the electron to proton g factors in hydrogen is known to 9 ppb [34], and the bound-state corrections relating the g factor of a free proton to one in hydrogen were calculated in [35,36]. We also corrected for the measured temperature dependence of the shielding constant, dσ(H 2 O, T )/dT = 10.36(30) × 10 −9 /K [37].…”

Section: Absolute Calibration Probementioning

confidence: 99%

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

Bennett¹,

Bousquet²,

Brown³

et al. 2006

Phys. Rev. D

2,632

1,910

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We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a µ = (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 µ (Expt) = 11 659 208.0(5.4)(3.3) × 10 −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 µ includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ≈ 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.

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Section: Absolute Calibration Probementioning

confidence: 99%

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

Bennett¹,

Bousquet²,

Brown³

et al. 2006

Phys. Rev. D

2,632

1,910

View full text Add to dashboard Cite

show abstract

“…where δ T corrects for the temperature dependence of the diamagnetic shielding of H 2 O between the temperature T of the measurement and the chosen reference temperature T r = 34.7 °C [38,51,52]; δ b is a correction dependent on water magnetic susceptibility and sample shape; and δ t is the sum of corrections for the probe materials and other effects related to the probe. The probe temperature T , typically close to 26 °C, was measured to 0.5 °C 2 In principle, the corrections would be multiplicative but we use the approximation with a PT-1000 sensor installed in the probe near the sample.…”

Section: A Systematic Effectsmentioning

confidence: 99%

Magnetic Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab

Albahri,

Anastasi,

Badgley

et al. 2021

Preprint

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The Fermi National Accelerator Laboratory (FNAL) Muon g −2 Experiment has measured the anomalous precession frequency a µ ≡ (g µ −2)/2 of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7 °C. The measured field is weighted by the muon distribution resulting in ω p , the denominator in the ratio ω a /ω p that together with known fundamental constants yields a µ . The reported uncertainty on ω p for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb.

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“…The bound-state correction relating the g-factor of the proton bound in hydrogen to the free proton are calculated in References [68,69]. The temperature dependence of σ is corrected for using dσ(H 2 O, T )/dT = 10.36(30) × 10 −9 / • C [70]. The free proton frequency is determined to an accuracy of 0.05 ppm.…”

Section: Calibration Of the Trolley Probesmentioning

confidence: 99%

Muon (g − 2): experiment and theory

2007

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A review of the experimental and theoretical determinations of the anomalous magnetic moment of the muon is given. The anomaly is defined by a = (g −2)/2, where the Landé g-factor is the proportionality constant that relates the spin to the magnetic moment. For the muon, as well as for the electron and tauon, the anomaly a differs slightly from zero (of order 10 −3 ) because of radiative corrections. In the Standard Model, contributions to the anomaly come from virtual 'loops' containing photons and the known massive particles. The relative contribution from heavy particles scales as the square of the lepton mass over the heavy mass, leading to small differences in the anomaly for e, µ, and τ . If there are heavy new particles outside the Standard Model which couple to photons and/or leptons, the relative effect on the muon anomaly will be ∼ (m µ /m e ) 2 ≈ 43 × 10 3 larger compared with the electron anomaly. Because both the theoretical and experimental values of the muon anomaly are determined to high precision, it is an excellent place to search for the effects of new physics, or to constrain speculative extensions to the Standard Model. Details of the current theoretical evaluation, and of the series of experiments that culminates with E821 at the Brookhaven National Laboratory are given. At present the theoretical and the experimental values are known with a similar relative precision of 0.5 ppm. There is, however, a 3.4 standard deviation difference between the two, strongly suggesting the need for continued experimental and theoretical study.

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The Temperature Dependence of the Diamagnetic Shielding Correction for Proton NMR in Water

Cited by 36 publications

References 9 publications

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

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

Magnetic Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab

Muon (g − 2): experiment and theory

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