What do we actually know about the proton radius?

Two-photon exchange contributions to elastic electron-scattering are reviewed. The apparent discrepancy in the extraction of elastic nucleon form factors between unpolarized Rosenbluth and polarization transfer experiments is discussed, as well as the understanding of this puzzle in terms of two-photon exchange corrections. Calculations of such corrections both within partonic and hadronic frameworks are reviewed. In view of recent spin-dependent electron scattering data, the relation of the two-photon exchange process to the hyperfine splitting in hydrogen is critically examined. The imaginary part of the two-photon exchange amplitude as can be accessed from the beam normal spin asymmetry in elastic electron-nucleon scattering is reviewed. Further extensions and open issues in this field are outlined.

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“…Hydrogen hyperfine splitting (hfs) in the ground state is known to 13 significant figures in frequency units [61], …”

Section: Remarks On Related Topicsmentioning

confidence: 99%

Two-Photon Physics in Hadronic Processes

Carlson

Vanderhaeghen

2007

Annu. Rev. Nucl. Part. Sci.

162

173

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“…An important part of the error in ∆E(1S) theory is due to uncalculated higher order corrections. For the 1S Lamb shift the uncertainty [29] was estimated to be about 40 kHz. This number is the linear sum of a 8 kHz uncertainty in the self energy correction, the 16 kHz uncertainty caused by the unknown α 2 (Zα) 6 terms and the 16 kHz uncertainty due to unknown α 3 (Zα) 4 terms.…”

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confidence: 99%

Three-Loop Slope of the Dirac Form Factor and the1SLamb Shift in Hydrogen

2000

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The last unknown contribution to hydrogen energy levels at order mα 7 , due to the slope of the Dirac form factor at three loops, is evaluated in a closed analytical form. The resulting shift of the hydrogen nS energy level is found to be 3.016/n 3 kHz. Using the QED calculations of the 1S Lamb shift, we extract a precise value of the proton charge radius rp = 0.883 ± 0.014 fm.Precision experiments with hydrogen and, more generally, with hydrogen-like atoms serve as an excellent laboratory to test theoretical approaches to bound state QED (for a recent review see, e.g. [1]). These experiments address a number of features of the simplest atoms, such as the energy levels of the ground and excited states, and the corresponding lifetimes.In recent years we have seen remarkable progress in the experimental study of the hydrogen atom. In particular the accuracy of the 1S Lamb shift measurements has increased dramatically over the years [2][3][4][5][6][7]. All measurements are consistent with each other and the most accurate value so far was determined in Ref. [7]:This result was obtained by analysing the most precise measurements for the transition frequencies in hydrogen (see [7] for details). Theoretically, since the ratio of the electron mass m to the proton mass M is very small, it is convenient to write hydrogen energy levels as a double expansion in α and m/M . The corrections which survive in the limit M → ∞ are known as non-recoil corrections, the other corrections are called recoil ones. It is further convenient to organize non-recoil corrections in powers of α n (Zα) l , assigning an auxiliary notation Z for the proton charge. In this case the correction α n (Zα) l describes a contribution of all diagrams with l − 3 Coulomb photons exchanged between the electron and the proton and with * e-mail: melnikov@slac.stanford.edu † e-mail: timo@particle.physik.uni-karlsruhe.de n photons emitted and absorbed by the electron. The general expression for the nS-level shift can be written as:where we have also added a contribution of muons and hadrons to photon vacuum polarization and a contribution due to the proton structure (see a discussion below). We begin with non-recoil corrections. These corrections can be parameterized as (see e.g. [8][9][10]):where m r = mM/(m + M ) is the reduced mass of the electron and L = log m/(m r (Zα) 2 ) and the function A(Zα) contains all higher order terms in the expansion in Zα. We have also indicated that the higher order corrections contain a logarithm of the fine structure constant in the third power [11]. All the terms in the above equation, with the exception for C 40 , are currently known. It is the purpose of this paper to report on the calculation of the last missing ingredient in C 40 , the slope of the Dirac form factor at zero momentum transfer.The hydrogen atom is formed because of a Coulomb interaction of the proton with the electron. The interaction of the virtual photon with the electron on its mass shell can be parameterized by the so-called Dirac and Pauli form facto...

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“…Experimentally, the hfs of the hydrogen ground state is known to 13 significant figures in frequency units [178],…”

Section: Proton Zemach Radiusmentioning

confidence: 99%

High Precision Measurement of the Proton Elastic Form Factor Ratio at Low Q<sup>2</sup>

Zhan

2010

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Experiment E08-007 measured the proton elastic form factor ratio µ p G E /G M in the range of Q 2 = 0.3−0.7(GeV/c) 2 by recoil polarimetry. Data were taken in 2008 at the Thomas Jefferson National Accelerator Facility in Virginia, USA. A 1.2 GeV polarized electron beam was scattered off a cryogenic hydrogen target. The recoil proton was detected in the left HRS in coincidence with the elasticly scattered electrons tagged by the BigBite spectrometer. The proton polarization was measured by the focal plane polarimeter (FPP).In this low Q 2 region, previous measurement from Jefferson Lab Hall A (LEDEX) along with various fits and calculations indicate substantial deviations of the ratio from unity. For this new measurement, the proposed statistical uncertainty (< 1%) was achieved. These new results are a few percent lower than expected from previous world data and fits, which indicate a smaller G Ep at this region. Beyond the intrinsic interest in nucleon structure, the new results also have implications in determining the proton Zemach radius and the strangeness form factors from parity violation experiments.

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What do we actually know about the proton radius?

Cited by 62 publications

References 65 publications

Two-Photon Physics in Hadronic Processes

Two-Photon Physics in Hadronic Processes

Three-Loop Slope of the Dirac Form Factor and the1SLamb Shift in Hydrogen

High Precision Measurement of the Proton Elastic Form Factor Ratio at Low Q<sup>2</sup>

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