Relativistic recoil corrections to the electron-vacuum-polarization contribution in light muonic atoms

Karshenboim, Savely G.; Иванов, В. П.; Korzinin, Evgeny Yu.

doi:10.1103/physreva.85.032509

Cited by 42 publications

(77 citation statements)

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“…This contribution was first computed in [20] and later corrected in [21,22]. Nevertheless, a different number has been obtained in two recent analyses [23,24]. We confirm this last number, which is the one we quote in table 1.…”

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confidence: 78%

Model-independent determination of the Lamb shift in muonic hydrogen and the proton radius

Peset

Pineda

2015

Eur. Phys. J. A

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Abstract. We obtain a model-independent expression for the Lamb shift in muonic hydrogen. This expres- The latter are controlled by the chiral theory, which allows for their model-independent determination. In this paper we give the missing piece for their complete expression including the pion and Delta particles. Out of this analysis, and the experimental measurement of the Lamb shift in muonic hydrogen, we determine the electromagnetic proton radius: r p = 0.8412 (15) fm. This number is at 6.8σ variance with respect to the CODATA value. The accuracy of our result is limited by uncomputed terms of OThis parametric control of the uncertainties allows us to obtain a model-independent estimate of the error, which is dominated by hadronic effects.The recent measurement [1,2] of the Lamb shift in muonic hydrogen, E(2P 3/2 ) − E(2S 1/2 ),and the associated determination of the root mean square electric radius of the proton: r p = 0.84087(39) fm has led to a lot of controversy. The reason is that this number is 7.1σ away from the CODATA value, r p = 0.8775(51) fm [3]. This last number is an average of determinations coming from hydrogen spectroscopy and electron-proton scattering. It should be mentioned though that the latter have been recently been challenged in refs. [4,5], and its inclusion would certainly diminish this tension. Leaving this aside, in order to asses the significance of the discrepancy, it is of fundamental importance to perform the computation (in particular of the errors) in a model-independent way. In this letter we revisit the theoretical derivation of the Lamb shift in muonic hydrogen with this aim in mind. In this respect, the use of effective field theories is specially useful. They help organizing the computation by providing with power counting rules that asses the importance of the different contributions. This becomes increasingly necessary as higher-order effects are included. Even more important, these power a e-mail: peset@ifae.es b e-mail: pineda@ifae.es counting rules allow to parametrically control the size of the uncalculated terms and, thus, give an educated estimate of the error. This discussion specially applies to the muonic hydrogen, as its dynamics is characterized by several scales:By considering ratios between them, the main expansion parameters are obtained:This approach to the problem has been followed in [6][7][8] (see [9] for a review of these computations) with a combined use of Heavy Baryon Chiral Perturbation Theory (HBChPT) [10] (see also [11]), Non-Relativistic QED (NRQED) [12] and, specially, potential NRQED (pNRQED) [13][14][15]. Particularly relevant for us is ref. [7], which contains detailed information on the application of pNRQED to the muonic hydrogen. We refer to it for details (and to [16] where a more detailed account of the hadronic computation presented here is given).Since pNRQED describes degrees of freedom with E ∼ m r α 2 , any other degree of freedom with larger energy is integrated out. This implies treating the proton

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confidence: 78%

Model-independent determination of the Lamb shift in muonic hydrogen and the proton radius

Peset

Pineda

2015

Eur. Phys. J. A

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“…Indeed, the close proximity of the muon and proton results in huge internal fields that are hardly affected by small external perturbations. On the theoretical side, the QED calculations used to extract r p have been checked and further developed 74,[79][80][81][82][83][84][85][86][87] . A debate arose about the magnitude of the proton polarizability correction in the two-photon-exchange diagram 88 but was settled after several calculations showed satisfactory agreement 78,89,90 .…”

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confidence: 99%

The proton size

2020

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The proton charge radius has been measured since the 1950s using elastic electron-proton scattering and ordinary hydrogen atomic spectroscopy. In 2010, a highly accurate measurement of the proton charge radius using, for the first time, muonic hydrogen spectroscopy unexpectedly led to controversy, as the value disagreed with the previously accepted one. Since then, atomic and nuclear physicists have been trying to understand this discrepancy by checking theories, questioning experimental methods and performing new experiments. Recently, two measurements from electron scattering and ordinary hydrogen spectroscopy were found to agree with results from muonic atom spectroscopy. Is the 'proton-radius puzzle' now resolved? In this Review, we scrutinize the experimental studies of the proton radius to gain insight on this issue. We provide a brief history of the proton before describing the techniques used to measure its radius and the current status of the field. We assess the precision and reliability of available experimental data, with particular focus on the most recent results. Finally, we discuss the forthcoming new generation of refined experiments and theoretical calculations that aim to definitely end the debate on the proton size. Key points• The charge radius of the proton can be determined using two different experimental techniques: measurements of electron-proton elastic scattering cross sections and high-resolution spectroscopy of the hydrogen atom.• A decade ago, the precision of the atomic spectroscopy method was greatly improved using muonic hydrogen atoms, wherein the electron is replaced by a muon. However, the value of the proton radius was in disagreement with previous determinations, giving rise to the 'proton-radius puzzle'.• The latest results from refined scattering and spectroscopy experiments agree with the muonic value. This questions the estimation of systematic uncertainties in previous scattering and ordinary hydrogen experiments.• More measurements are needed to confirm or disprove this trend. Various projects are in progress, aiming to improve some aspects of existing techniques or using new approaches. Website summary:The charge radius of the proton is controversial as measurements by different methods disagree. Recent results indicate that these measurements might be reconciled. In this Review, we discuss the experimental techniques used to measure the proton radius and describe the current status of the field as well as forthcoming experiments.

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“…In view of this discrepancy, a thorough review of the theory is warranted, and a number of such investigations have been carried out, with recent reviews given in Refs. [5][6][7][8][9][10][11][12].…”

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confidence: 99%

Coordinate-space approach to vacuum polarization

2014

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The vacuum-polarization correction for bound electrons or muons is examined. The objective is to formulate a framework for calculating the correction from bound-state quantum electrodynamics entirely in coordinate space, including the Uehling potential which is usually isolated and treated separately. Pauli-Villars regularization is applied to the coordinate-space calculation and the most singular terms are shown to be eliminated, leaving the physical correction after charge renormalization. The conventional derivation of the Uehling potential in momentum space is reviewed and compared to the coordinate-space derivation.PACS numbers: 31.30.J-,03.65.Pm

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Relativistic recoil corrections to the electron-vacuum-polarization contribution in light muonic atoms

Cited by 42 publications

References 44 publications

Model-independent determination of the Lamb shift in muonic hydrogen and the proton radius

Model-independent determination of the Lamb shift in muonic hydrogen and the proton radius

The proton size

Coordinate-space approach to vacuum polarization

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