Reexamining the proton-radius problem using constrained Gaussian processes

Zhou, Shuang; Giulani, P.; Piekarewicz, J.; Bhattacharya, Anirban; Pati, Debdeep

doi:10.1103/physrevc.99.055202

Title: Reexamining the proton-radius problem using constrained Gaussian processes

Journal Article · Tue May 14 00:00:00 EDT 2019 · Physical Review C

DOI:https://doi.org/10.1103/physrevc.99.055202· OSTI ID:1610205

Zhou, Shuang ^[1]; Giulani, P. ^[2]; Piekarewicz, J. ^[2]; Bhattacharya, Anirban ^[1]; Pati, Debdeep ^[1]

Texas A & M Univ., College Station, TX (United States)
Florida State Univ., Tallahassee, FL (United States)

The “proton radius puzzle” refers to an 8-year-old problem that highlights major inconsistencies in the extraction of the charge radius of the proton from muonic Lamb-shift experiments as compared against experiments using elastic electron scattering. For the latter approach, the determination of the charge radius involves an extrapolation of the experimental form factor to zero momentum transfer. To estimate the proton radius, a novel and powerful nonparametric method based on a constrained Gaussian process is introduced. Furthermore, the constrained Gaussian process models the electric form factor as a function of the momentum transfer. Within a Bayesian paradigm, we develop a model flexible enough to fit the data without any parametric assumptions on the form factor. The Bayesian estimation is guided by imposing only two physical constraints on the form factor: (a) its value at zero momentum transfer (normalization) and (b) its overall shape, assumed to be a monotonically decreasing function of the momentum transfer. Variants of these assumptions are explored to assess their impact.By adopting both constraints and incorporating the whole range of experimental data available we extracted a charge radius of r_p = 0.845 ± 0.001 fm, consistent with the muonic experiment. Nevertheless, we show that within our model the extracted radius depends on both the assumed constraints and the range of experimental data used to fit the Gaussian process. For example, if only low-momentum-transfer data are used, relaxing the normalization constraint provides a value compatible with the larger electronic value. We have presented a novel technique to estimate the proton radius from electron-scattering data based on a constrained Gaussian process. We demonstrated that the impact of imposing sensible physical constraints on the form factor is substantial. Also critical is the range of the experimental data used in the extrapolation. We are hopeful that as the technique gets refined, together with the anticipated new results from the PRad experiment, we will get closer to a resolution of the puzzle.

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Research Organization:: Florida State Univ., Tallahassee, FL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-92ER40750

OSTI ID:: 1610205

Alternate ID(s):: OSTI ID: 1512537

Journal Information:: Physical Review C, Vol. 99, Issue 5; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 24 works

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References (46)

Electron scattering and nuclear structure Frois, B. Progress in Particle and Nuclear Physics, Vol. 13 https://doi.org/10.1016/0146-6410(85)90005-5	journal	January 1985
The size of the proton: From the Lamb-shift in muonic hydrogen Nebel, T.; Antognini, A.; Amaro, F. D. Hyperfine Interactions, Vol. 212, Issue 1-3 https://doi.org/10.1007/s10751-011-0386-5	journal	October 2011
Extraction of the proton radius from electron-proton scattering data Lee, Gabriel; Arrington, John R.; Hill, Richard J. Physical Review D, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevD.92.013013	journal	July 2015
Muonic Hydrogen and the Proton Radius Puzzle Pohl, Randolf; Gilman, Ronald; Miller, Gerald A. Annual Review of Nuclear and Particle Science, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-nucl-102212-170627	journal	October 2013
Bernauer et al. Reply: Bernauer, J. C.; Achenbach, P.; Ayerbe Gayoso, C. Physical Review Letters, Vol. 107, Issue 11 https://doi.org/10.1103/PhysRevLett.107.119102	journal	September 2011
The Rydberg constant and proton size from atomic hydrogen Beyer, Axel; Maisenbacher, Lothar; Matveev, Arthur Science, Vol. 358, Issue 6359 https://doi.org/10.1126/science.aah6677	journal	October 2017
Electric and magnetic form factors of the proton Bernauer, J. C.; Distler, M. O.; Friedrich, J. Physical Review C, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevC.90.015206	journal	July 2014
Nuclear charge-density-distribution parameters from elastic electron scattering De Vries, H.; De Jager, C. W.; De Vries, C. Atomic Data and Nuclear Data Tables, Vol. 36, Issue 3 https://doi.org/10.1016/0092-640X(87)90013-1	journal	May 1987
Accurate nucleon electromagnetic form factors from dispersively improved chiral effective field theory Alarcón, J. M.; Weiss, C. Physics Letters B, Vol. 784 https://doi.org/10.1016/j.physletb.2018.07.060	journal	September 2018
Electron Scattering and Nuclear Structure Hofstadter, Robert Reviews of Modern Physics, Vol. 28, Issue 3 https://doi.org/10.1103/RevModPhys.28.214	journal	July 1956
Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors Alarcón, J. M.; Weiss, C. Physical Review C, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevC.97.055203	journal	May 2018
High-Precision Determination of the Electric and Magnetic Form Factors of the Proton Bernauer, J. C.; Achenbach, P.; Ayerbe Gayoso, C. Physical Review Letters, Vol. 105, Issue 24 https://doi.org/10.1103/PhysRevLett.105.242001	journal	December 2010
Gaussian Process Emulators for Computer Experiments with Inequality Constraints Maatouk, Hassan; Bay, Xavier Mathematical Geosciences, Vol. 49, Issue 5 https://doi.org/10.1007/s11004-017-9673-2	journal	January 2017
Nuclear Ground State Charge Radii from Electromagnetic Interactions Fricke, G.; Bernhardt, C.; Heilig, K. Atomic Data and Nuclear Data Tables, Vol. 60, Issue 2 https://doi.org/10.1006/adnd.1995.1007	journal	July 1995
Proton radius from electron scattering data Higinbotham, Douglas W.; Kabir, Al Amin; Lin, Vincent Physical Review C, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevC.93.055207	journal	May 2016
Zur Theorie der Kernmassen Weizs�cker, C. F. v. Zeitschrift f�r Physik, Vol. 96, Issue 7-8 https://doi.org/10.1007/BF01337700	journal	July 1935
The size of the proton Pohl, Randolf; Antognini, Aldo; Nez, François Nature, Vol. 466, Issue 7303 https://doi.org/10.1038/nature09250	journal	July 2010
The proton radius puzzle Carlson, Carl E. Progress in Particle and Nuclear Physics, Vol. 82 https://doi.org/10.1016/j.ppnp.2015.01.002	journal	May 2015
Final report of the E821 muon anomalous magnetic moment measurement at BNL Bennett, G. W.; Bousquet, B.; Brown, H. N. Physical Review D, Vol. 73, Issue 7 https://doi.org/10.1103/PhysRevD.73.072003	journal	April 2006
Solution to the proton radius puzzle Robson, D. International Journal of Modern Physics E, Vol. 23, Issue 12 https://doi.org/10.1142/S0218301314500906	journal	December 2014
Robust extraction of the proton charge radius from electron-proton scattering data Yan, Xuefei; Higinbotham, Douglas W.; Dutta, Dipangkar Physical Review C, Vol. 98, Issue 2 https://doi.org/10.1103/PhysRevC.98.025204	journal	August 2018
Nuclear Physics A. Stationary States of Nuclei Bethe, H. A.; Bacher, R. F. Reviews of Modern Physics, Vol. 8, Issue 2 https://doi.org/10.1103/RevModPhys.8.82	journal	April 1936
High-precision determination of the electric and magnetic form factors of the proton Bernauer, Jan C.; Hosaka, Atsushi; Khemchandani, Kanchan INTERNATIONAL CONFERENCE ON THE STRUCTURE OF BARYONS (BARYONS' 10), AIP Conference Proceedings https://doi.org/10.1063/1.3647361	conference	January 2011
The proton radius puzzle Blau, Melissa figshare https://doi.org/10.6084/m9.figshare.7272470.v1	text	January 2018
Test of Lepton Universality Using $B^{+} \to K^{+} ℓ^{+} ℓ^{-}$ Decays Aaij, R.; Adeva, B.; Adinolfi, M. Physical Review Letters, Vol. 113, Issue 15 https://doi.org/10.1103/PhysRevLett.113.151601	journal	October 2014
The normal law under linear restrictions: simulation and estimation via minimax tilting Botev, Z. I. Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 79, Issue 1 https://doi.org/10.1111/rssb.12162	journal	February 2016
Bayesian Data Analysis Gelman, Andrew; Carlin, John B.; Stern, Hal S. https://doi.org/10.1201/b16018	book	November 2013
Defining the proton radius: A unified treatment Miller, Gerald A. Physical Review C, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevC.99.035202	journal	March 2019
CODATA recommended values of the fundamental physical constants: 2014 Mohr, Peter J.; Newell, David B.; Taylor, Barry N. Reviews of Modern Physics, Vol. 88, Issue 3 https://doi.org/10.1103/RevModPhys.88.035009	journal	September 2016
Electron scattering and nuclear structure Pandharipande, V. R. Nuclear Physics A, Vol. 497 https://doi.org/10.1016/0375-9474(89)90454-5	journal	June 1989
The proton radius puzzle Blau, Melissa figshare https://doi.org/10.6084/m9.figshare.7272470	text	January 2018
Enhancing the interaction between nuclear experiment and theory through information and statistics Ireland, D. G.; Nazarewicz, W. Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3 https://doi.org/10.1088/0954-3899/42/3/030301	journal	February 2015
Table of experimental nuclear ground state charge radii: An update Angeli, I.; Marinova, K. P. Atomic Data and Nuclear Data Tables, Vol. 99, Issue 1 https://doi.org/10.1016/j.adt.2011.12.006	journal	January 2013
An invariant form for the prior probability in estimation problems Jeffreys, Harold Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 186, Issue 1007, p. 453-461 https://doi.org/10.1098/rspa.1946.0056	journal	September 1946
Model-independent extraction of the proton charge radius from electron scattering Hill, Richard J.; Paz, Gil Physical Review D, Vol. 82, Issue 11 https://doi.org/10.1103/PhysRevD.82.113005	journal	December 2010
The Proton Radius Problem Bernauer, Jan C.; Pohl, Randolf Scientific American, Vol. 310, Issue 2 https://doi.org/10.1038/scientificamerican0214-32	journal	January 2014
The proton radius puzzle Bonesini, Maurizio EPJ Web of Conferences, Vol. 164 https://doi.org/10.1051/epjconf/201716407048	journal	January 2017
Codata Recommended Values Of The Fundamental Physical Constants: 2014 Mohr, Peter J.; Newell, David B.; Taylor, Barry N. Zenodo https://doi.org/10.5281/zenodo.22826	text	January 2015
High-precision determination of the electric and magnetic form factors of the proton Bernauer, J. C.; Achenbach, P.; Gayoso, C. Ayerbe arXiv https://doi.org/10.48550/arxiv.1007.5076	text	January 2010
Model independent extraction of the proton charge radius from electron scattering Hill, Richard J.; Paz, Gil arXiv https://doi.org/10.48550/arxiv.1008.4619	text	January 2010
Muonic hydrogen and the proton radius puzzle Pohl, Randolf; Gilman, Ronald; Miller, Gerald A. arXiv https://doi.org/10.48550/arxiv.1301.0905	text	January 2013
The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting Botev, Z. I. arXiv https://doi.org/10.48550/arxiv.1603.04166	text	January 2016
Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors Alarcón, J. M.; Weiss, C. arXiv https://doi.org/10.48550/arxiv.1710.06430	text	January 2017
Robust extraction of proton charge radius from electron-proton scattering data Yan, Xuefei; Higinbotham, Douglas W.; Dutta, Dipangkar arXiv https://doi.org/10.48550/arxiv.1803.01629	text	January 2018
Accurate nucleon electromagnetic form factors from dispersively improved chiral effective field theory Alarcón, J. M.; Weiss, C. arXiv https://doi.org/10.48550/arxiv.1803.09748	text	January 2018
Defining the Proton Radius: a Unified Treatment Miller, Gerald A. arXiv https://doi.org/10.48550/arxiv.1812.02714	text	January 2018

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