New Precision Measurement for Proton Zemach Radius with Laser Spectroscopy

Ma, Yue; Ishida, K.; Iwasaki, M.; Matsuzaki, Yuichiro; Oishi, Yuji; Okada, S.; Sato, Masaharu; Midorikawa, Katsumi; Saito, Norihito; Wada, Satoshi; Aikawa, S.; Kanda, S.; Matsuda, Y.; Tanaka, Kotaro; Takamine, A.

doi:10.1142/s2010194516600466

Cited by 20 publications

(30 citation statements)

References 6 publications

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“…In view of the forthcoming high-precision measurements of the 1S hyperfine splitting in muonic hydrogen with ppm precision level [24,26,27], we provide the corresponding best estimates of the TPE correction in Table 5. The uncertainty of our result is 100 times larger than the expected experimental accuracy.…”

Section: Discussionmentioning

confidence: 99%

“…The new highly precise insights on the proton electromagnetic structure will be obtained by the forthcoming measurements of 1S hyperfine splitting (HFS) in muonic hydrogen with an unprecedented ppm precision by the CREMA [24] and FAMU [25,26] Collaborations as well as at J-PARC [27]. In these experiments, the expected accuracy level is two orders of magnitude smaller than the theoretical knowledge of the TPE correction with 213 ppm uncertainty in the dispersive estimate [28] and 109 ppm in the effective field theory approach [29].…”

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confidence: 99%

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Two-photon exchange correction to the hyperfine splitting in muonic hydrogen

Tomalak¹

2017

Eur. Phys. J. C

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We reevaluate the Zemach, recoil and polarizability corrections to the hyperfine splitting in muonic hydrogen expressing them through the low-energy proton structure constants and obtain the precise values of the Zemach radius and two-photon exchange (TPE) contribution. The uncertainty of TPE correction to S energy levels in muonic hydrogen of 105 ppm exceeds the ppm accuracy level of the forthcoming 1S hyperfine splitting measurements at PSI, J-PARC and RIKEN-RAL.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Two-photon exchange correction to the hyperfine splitting in muonic hydrogen

Tomalak¹

2017

Eur. Phys. J. C

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“…We presented the current knowledge of the TPE correction to S energy levels. The Lamb shift results can be useful in future extractions of the isotope shift, while the contributions to the hyperfine splitting can help to tune and analyze forthcoming 1S HFS measurements in µH [41][42][43][44].…”

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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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“…Only in the case of simple two particle bound states the theoretical methods are well developed to calculate the energy levels including nuclear effects from first principles. In general, it can be noted that the program for studying muon systems is gaining momentum: a precision study of the ground state hyperfine structure of muonic hydrogen, the energy interval (1S − 2S), and the processes of production of dimuonium are planned [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Hyperfine structure of P states in muonic ions of lithium, beryllium, and boron

Dorokhov¹,

Martynenko²,

Martynenko³

et al. 2019

Phys. Rev. A

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We calculate hyperfine structure intervals ∆E hf s (2P 1/2 ) and ∆E hf s (2P 3/2 ) for P-states in muonic ions of lithium, beryllium and boron. To construct the particle interaction operator in momentum space we use the tensor method of projection operators on states with definite quantum numbers of total atomic momentum F and total muon momentum j. We take into account vacuum polarization, relativistic, quadruple and structure corrections of orders α 4 , α 5 and α 6 . The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data of the CREMA collaboration.

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New Precision Measurement for Proton Zemach Radius with Laser Spectroscopy

Cited by 20 publications

References 6 publications

Two-photon exchange correction to the hyperfine splitting in muonic hydrogen

Two-photon exchange correction to the hyperfine splitting in muonic hydrogen

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

Hyperfine structure of P states in muonic ions of lithium, beryllium, and boron

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