TY - JOUR

T1 - Reexamining the proton-radius problem using constrained Gaussian processes

AU - Zhou, Shuang

AU - Giulani, P.

AU - Piekarewicz, J.

AU - Bhattacharya, Anirban

AU - Pati, Debdeep

N1 - Funding Information:
We are enormously grateful to Prof. Douglas Higinbotham for his unconditional help, guidance, and lightning fast email responses. This material is based upon work supported by the U.S. Department of Energy Office of Science, Office of Nuclear Physics, Award No. DE-FG02-92ER40750. Dr. Bhattacharya acknowledges NSF CAREER (Grant No. DMS 1653404), NSF Grant No. DMS 1613193, and the National Cancer Institute's Grant No. R01 CA 158113, and Dr. Pati acknowledges NSF Grant No. DMS 1613156 for supporting this research.
Funding Information:
We are enormously grateful to Prof. Douglas Higinbotham for his unconditional help, guidance, and lightning fast email responses. This material is based upon work supported by the U.S. Department of Energy Office of Science, Office of Nuclear Physics, Award No. DE-FG02-92ER40750. Dr. Bhattacharya acknowledges NSF CAREER (Grant No. DMS 1653404), NSF Grant No. DMS 1613193, and the National Cancer Institute's Grant No. R01 CA 158113, and Dr. Pati acknowledges NSF Grant No. DMS 1613156 for supporting this research.
Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/5/14

Y1 - 2019/5/14

N2 - Background: 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. Purpose: To estimate the proton radius, a novel and powerful nonparametric method based on a constrained Gaussian process is introduced. The constrained Gaussian process models the electric form factor as a function of the momentum transfer. Methods: 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. Results: By adopting both constraints and incorporating the whole range of experimental data available we extracted a charge radius of rp=0.845±0.001fm, 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. Conclusions: 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.

AB - Background: 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. Purpose: To estimate the proton radius, a novel and powerful nonparametric method based on a constrained Gaussian process is introduced. The constrained Gaussian process models the electric form factor as a function of the momentum transfer. Methods: 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. Results: By adopting both constraints and incorporating the whole range of experimental data available we extracted a charge radius of rp=0.845±0.001fm, 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. Conclusions: 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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U2 - 10.1103/PhysRevC.99.055202

DO - 10.1103/PhysRevC.99.055202

M3 - Article

AN - SCOPUS:85065851465

VL - 99

JO - Physical Review C

JF - Physical Review C

SN - 2469-9985

IS - 5

M1 - 055202

ER -