Nuclear radiative recoil corrections to the hyperfine structure of S-states in muonic hydrogen

Фаустов, Р. Н.; Martynenko, A. P.; Martynenko, F. A.; Sorokin, V. V.

doi:10.1134/s106377961705015x

Cited by 7 publications

(6 citation statements)

References 9 publications

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“…4, where we also account for the radiative corrections of Refs. [62][63][64]. Our result is in a reasonable agreement with estimates of Refs.…”

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confidence: 93%

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Hyperfine splitting in ordinary and muonic hydrogen

Tomalak

2018

Eur. Phys. J. A

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Abstract.We provide an accurate evaluation of the two-photon exchange correction to the hyperfine splitting of S energy levels in muonic hydrogen exploiting the corresponding measurements in electronic hydrogen. The proton structure uncertainty in the calculation of α 5 contribution is sizably reduced.The theoretical knowledge of the two-photon exchange (TPE) correction to the hyperfine splitting (HFS) of the S energy levels in muonic hydrogen exceeds by two orders of magnitude the expected ppm level of the experimental accuracy in the forthcoming measurements of 1S HFS by CREMA [1] and FAMU [2,3] Collaborations as well as at J-PARC [4]. In the ordinary hydrogen, the uncertainty of TPE is even six orders of magnitude above the experimental precision [5,6], the measurements were performed in the 1970s [7][8][9][10][11][12][13][14][15] and discussed in refs. [16,17].The graph with two exchanged photons, see fig. 1 for the notation of particles momenta, also contributes the largest theoretical uncertainty in the proton size extractions from the Lamb shift in muonic hydrogen (μH) [18,19]. It was a subject of extensive theoretical studies [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] since the formulation of the proton radius puzzle in 2010, when the accurate extraction of the proton charge radius (R E ) from the muonic hydrogen Lamb shift by the CREMA Collaboration at PSI [18,19] gave a significantly smaller result than the electron data based extractions [35][36][37], see refs. [19,38] for recent reviews.Besides the Lamb shift, the CREMA Collaboration has extracted the HFS of the 2S energy level in μH [39], where the leading theoretical uncertainty is also coming from TPE. The corresponding correction to HFS of S energy levels is expressed in terms of the proton elastic form factors and spin structure functions [5,[40][41][42][43][44][45][46][47][48][49][50][51][52]. The first full dispersive calculation of this contribution was performed in refs. [5,49], where it was evaluated with 213 ppm uncertainty. The subsequent studies expressing the region with small photons virtualities in terms of proton radii and moments of the spin structure functions led to the uncertainty 105 ppm [53]. The model-independent evaluation within the frameworks of Non-Relativistic Quantum a e-mail: tomalak@uni-mainz.de Electrodynamics and Chiral Perturbation Theory exploiting the electronic hydrogen (eH) HFS measurement was recently performed in ref.[51], for results in Chiral Effective Field Theory see ref. [50].In this work, we aim to reduce the proton structure uncertainty in the dispersive evaluation of the TPE correction to HFS of the S energy levels in μH exploiting precise measurements of the HFS in eH [16].The TPE contribution to the nS-level HFS δE HFS nS is expressed in terms of the relative correction Δ HFS and the leading-order HFS E HFS,0 nSwhere M and m are the proton and the lepton masses in the energy units, m r (m) = Mm/(M + m) is the reduced mass, μ P is the proton magnetic moment, α is the electromagnetic ...

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“…4, where we also account for the radiative corrections of Refs. [62][63][64]. Our result is in a reasonable agreement with estimates of Refs.…”

supporting

confidence: 93%

“…[48,66] to 1S energy level with account of recent evaluations in Refs. [51,[62][63][64]. We also calculate the hadronic vacuum polarization contirbutions exploiting up-to-date fits of the electron-proton annihilation cross section to hadrons [67,68].…”

mentioning

confidence: 99%

Hyperfine splitting in ordinary and muonic hydrogen

Tomalak

2018

Eur. Phys. J. A

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“…III, we provide the hyperfine-splitting TPE contributions as well as extractions from the experimental data exploiting radiative corrections of Refs. [25,37,[82][83][84][85][86][87][88][89]. The experimental value of the hyperfine splitting in muonic hydrogen is taken from Ref.…”

Section: Indeed E µHmentioning

confidence: 99%

Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels

Tomalak

2019

Eur. Phys. J. A

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We evaluate the two-photon exchange corrections to the Lamb shift and hyperfine splitting of S states in electronic hydrogen relying on modern experimental data and present the two-photon exchange on a neutron inside the electronic and muonic atoms. These results are relevant for the precise extraction of the isotope shift as well as in the analysis of the ground state hyperfine splitting in usual and muonic hydrogen.The discrepancy between the proton charge radius extractions from the Lamb shift in muonic hydrogen [1,2] and electron-proton scattering [3-5] triggered a lot of theoretical and experimental efforts both in scattering and spectroscopy, see Refs. [6,7] for recent reviews. Twophoton exchange (TPE) hadronic correction, see Fig. 1, is a limiting factor extracting radii from the muonic hydrogen spectroscopy [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Moreover, an accurate evaluation of two-photon corrections to hyperfine splitting (HFS) of ground state in electronic hydrogen in combination with an excellent experimental knowledge [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] (known with mHz accuracy) could help to analyse future precise measurements of 1S HFS in muonic hydrogen [41][42][43][44], which aim to decrease an uncertainty of 1S-level HFS from the level of 40 µeV [2] up to the level of 0.2 µeV. Though the two-photon correction is smaller than the modern accuracy of Lamb shift measurements in usual hydrogen, it can affect the precisely measurable 1S-2S transition [45,46] (with the experimental uncertainty 10-11 Hz), as well as the isotope shift [47,48] (with the experimental uncertainty 15 Hz), above the accuracy level of the difference between proton and deuteron charge radii [25,49]. In the latter references, the elastic Friar term [50] was accounted for and the inelastic correction was estimated in the leading logarithmic approximation [51][52][53]. Besides two-photon corrections, the more involved three-photon exchange contribution to the Lamb shift was recently evaluated in the nonrecoil limit neglecting magnetic dipole and electric quadrupole moments of the nucleus in Ref. [49]. FIG. 1: Two-photon exchange graph.In this paper, we provide a first complete dispersive calculation of α 5 two-photon exchange contribution to the Lamb shift in electronic hydrogen, summarize the current status of this correction to the hyperfine splitting of S states and provide an update of Ref.[40] for S-level HFS in µH. Additionally, we present contributions to the Lamb shift arising from the two-photon exchange on the neutron inside a nucleus.We evaluate the correction to the Lamb shift of S energy levels E LS following Refs. [8,13]. It can be expressed as a sum of three terms:the Born contribution E Born , the subtraction term E subt and the inelastic correction E inel . To evaluate the dimensionless forward unpolarized amplitude, we always normalize the TPE contributions to the energy E 0 :where M is the proton mass, m is the lepton mass, |ψ nS (0)| 2 = α 3 m 3 r /(πn...

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“…The radiative corrections to the muon line found in Ref. (151,152) for the 2γ finite-nuclearsize contribution are slightly larger in magnitude. As these corrections will become more relevant in the future, an independent cross-check would be desirable.…”

Section: E Radiative Corrections To Spin-dependent Two-photon Exchangementioning

confidence: 66%

The proton structure in and out of muonic hydrogen

Antognini¹,

Hagelstein²,

Pascalutsa³

2022

Preprint

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Advances in laser spectroscopy of light muonic atoms led to an order-ofmagnitude improvement in the determination of the proton, deuteron, and helium-4 charge radii. This resulted in a number of tensions with previous measurements, based on electron scattering and spectroscopy of ordinary atoms; most notably, the "proton radius puzzle". We start with an introduction to nuclear effects in hydrogen-like atoms, including a discussion of radiative corrections. We briefly review the current status of the nucleon structure quantities (form factors, polarized and unpolarized structure functions, polarizabilities) and of their effect in the Lamb shift and hyperfine splitting (hfs) of muonic hydrogen (µH) through forward two-photon exchange. Updated theory predictions for the Lamb shift and hfs in µH are presented. Focusing on the groundstate hfs in µH, we review the challenges of the ongoing effort to produce a first-ever measurement of this fundamental quantity, and of its potential impact on our understanding of the nucleon spin structure. We show that, leveraging radiative corrections, a novel theory prediction based on the empirical hfs in hydrogen allows to narrow down the search for the transition considerably. We summarize the very recent developments in the field of spectroscopy of simple atomic and molecular systems, with emphasis on how they, together with the scattering studies, allow for precise determinations of fundamental constants, bound-state QED tests, and New Phyics searches. We conclude with prospects for theoretical developments and an outlook on the ongoing and planned experiments at both the scattering and atomic facilities.

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Nuclear radiative recoil corrections to the hyperfine structure of S-states in muonic hydrogen

Cited by 7 publications

References 9 publications

Hyperfine splitting in ordinary and muonic hydrogen

Hyperfine splitting in ordinary and muonic hydrogen

Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels

The proton structure in and out of muonic hydrogen

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