Advanced extraction of the deuteron charge radius from electron-deuteron scattering data

Zhou, Jingyi; Khachatryan, V.; H, Gao; Higinbotham, D. W.; Parker, Asia; Bai, X.; Dutta, D.; Gasparian, A.; Gnanvo, K.; Khandaker, M.; Liyanage, N.; Pasyuk, E.; Peng, C.; Xiong, Weizhi

doi:10.1103/physrevc.103.024002

Cited by 14 publications

(14 citation statements)

References 46 publications

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“…Furthermore, one can note that the / πEFT expression for the deuteron charge FF at N3LO, as given in Ref. [21,Sec. IV], can serve as an analytic one-parameter fit to the electron-deuteron scattering data in the low-Q 2 range that is to be covered in the planned DRad experiment [31].…”

Section: Smentioning

confidence: 99%

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

Lensky,

Hagelstein,

Pascalutsa

2022

Preprint

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We present a study of the two-photon-exchange (2γ-exchange) corrections to the S-levels in muonic (µD) and ordinary (D) deuterium within the pionless effective field theory (/ πEFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the / πEFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon-nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen-deuterium isotope shift. We find the elastic 2γ-exchange contribution in µD larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of 2γ-exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order 2γ-exchange contributions in µD, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the / πEFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the µD Lamb shift, the 2S − 1S transition in D, and the 2S − 1S hydrogen-deuterium isotope shift, with the respective 2γ-exchange effects evaluated in a unified / πEFT approach, are in perfect agreement. CONTENTSI. Introduction II. Theoretical Framework A. 2γ Exchange in (Muonic) Deuterium B. Unpolarized Deuteron VVCS in Pionless EFT III. 2γ Exchange in Muonic Deuterium A. Elastic Contribution B. Inelastic Contribution C. Single-Nucleon Effects Beyond N3LO D. Summary of Results IV. Hydrogen-Deuterium Isotope Shift A. 2γ Exchange in Deuterium B. 2γ Exchange in Isotope Shift and Determination of Low-Energy Constant l C0 S 1

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Section: Smentioning

confidence: 99%

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

Lensky,

Hagelstein,

Pascalutsa

2022

Preprint

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“…4 by employing an adequate selection of other fit models. It is perhaps plausible to construct such models with constraints, such as the Rational (1,3) or a bounded high-order polynomial, using the so-called data-driven method from [37], or using some theoretical frameworks and approaches, like DIχEFT. With such constrained functions, one could try to refitting the entire Q 2 range of available data (such as the data from A1) with an analytically well-behaved function [47].…”

Section: Discussionmentioning

confidence: 99%

Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$

Zhou¹,

Khachatryan²,

H³

et al. 2021

Preprint

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Systematic differences exist between values of the proton's electric form factors in the low-Q 2 region extracted by different experimental and theoretical groups, though they are all making use of basically the same electron-proton scattering data. To try understand the source of these differences, we make use of the analytically well-behaved rational (N=1, M=1) function, a predictive function that can be reasonably used for extrapolations at Q 2 → 0. First, we test how well this deceptively simple two-parameter function describes the extremely complex and state-of-the-art dispersively improved chiral effective field theory calculations. Second, we carry out a complete re-analysis of the 34 sets of eletron-proton elastic scattering cross-section data of the Mainz A1 Collaboration with its unconstrained 31 normalization parameters up to Q 2 = 0.5 (GeV/c) 2 . We find that subtle shifts in the normalization parameters can result in relatively large changes in the extracted physical qualities. As a final check of the results of this extraction, we compare it to the PRad data that was not included in the regression and find that with the well-behaved analytic function the extracted results, both charge form factor and charge radius, of the two sets of data become consistent.

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“…At low values of Q 2 most relevant for the charge radius determination, in the range 10 −2 to 10 −4 (GeV/c) 2 , and small scattering angles, the unpolarized e − d elastic scattering cross section is dominated by the deuteron charge form factor. One can therefore extract G Cd with negligible systematic uncertainties using data driven parameterizations for G M d , and G Qd (Zhou et al, 2021) from measured scattering cross section. The deuteron rms charge radius radius, r d can then be determined by fitting the experimental G Cd data as a function of Q 2 , and calculating the slope of this function at Q 2 = 0, according to…”

Section: The Deuteron Charge Radiusmentioning

confidence: 99%

“…in analogy to how r Ep is obtained. Zhou et al (Zhou et al, 2021) demonstrated how one can extract r d reliably using robust fitters. Like the proton charge radius, the deuteron r d can also be determined from atomic spectroscopic measurements using ordinary deuterium or muonic deuterium atoms.…”

Section: The Deuteron Charge Radiusmentioning

confidence: 99%

The proton charge radius

Gao,

Vanderhaeghen

2021

Preprint

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Nucleons (protons and neutrons) are the building blocks of atomic nuclei, and are responsible for more than 99% of the visible matter in the universe. Despite decades of efforts in studying its internal structure, there are still a number of puzzles surrounding the proton such as its spin, and charge radius. Accurate knowledge about the proton charge radius is not only essential for understanding how quantum chromodynamics (QCD) works in the non-perturbative region, but also important for bound state quantum electrodynamics (QED) calculations of atomic energy levels. It also has an impact on the Rydberg constant, one of the most precisely measured fundamental constants in nature. This article reviews the latest situation concerning the proton charge radius in light of the new experimental results from both atomic hydrogen spectroscopy and electron scattering measurements, with particular focus on the latter. We also present the related theoretical developments and backgrounds concerning the determination of the proton charge radius using different experimental techniques. We discuss upcoming experiments, and briefly mention the deuteron charge radius puzzle at the end. CONTENTS I. Introduction 1 II. The Proton Charge Radius Puzzle 3 A. Before the millennium 3 B. After the millennium 3 III. Elastic Electron-Proton Scattering 3 A. Introduction to Electron-Proton Scattering and Proton Electromagnetic Form Factors 3 B. Three-dimensional parton distributions 5 C. The nucleon transverse charge densities 7 D. GPDs and quark densities in longitudinal momentum and transverse position in a proton 10 E. Radii of quark distributions in a proton 12 F. Unpolarized electron-proton elastic scattering 16 G. Double-Polarization Elastic Electron-Proton Scattering 17 1. Spin-Dependent Asymmetry from p( e, e )p 17 2. Recoil Proton Polarization from p( e, e p) 18 H. Two-Photon-Exchange Contribution to Electron-Proton Scattering 18 I. Radiative Corrections in Electron Scattering 20 J. The Extraction of the Proton Charge Radius from Proton Electric Form Factor 21 IV. Atomic Hydrogen Spectroscopy 21 V. Modern lepton scattering experiments 24 A. Mainz 2010 24 B. JLab recoil polarization experiment 24 C. Mainz ISR measurements 24 D. The PRad experiment at JLab 25 E. Proton charge radius from modern analyses of proton electric form factor data 29 VI. Modern spectroscopic measurements 31 A. Muonic hydrogen spectroscopic experiments 31 B. Ordinary Hydrogen spectroscopic experiments 33 VII. Ongoing and upcoming experiments 35 A. The MUSE experiment at PSI 35 B. The COMPASS++/AMBER Experiment at CERN 35 C. The PRad-II experiment at Jefferson Lab 36 D. Future electron scattering experiments at Mainz 38 E. The ULQ 2 experiment at Tohoku University 39 VIII. The deuteron charge radius 39 IX. Conclusions 42 X. Acknowledgments 42 References 43

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Advanced extraction of the deuteron charge radius from electron-deuteron scattering data

Cited by 14 publications

References 46 publications

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$

The proton charge radius

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