Neural network parameterizations of electromagnetic nucleon form-factors

Graczyk, Krzysztof M.; Płoński, P.; Sulej, R.

doi:10.1007/jhep09(2010)053

Cited by 17 publications

(37 citation statements)

References 84 publications

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“…The resulting radii, for three different values of q max , are plotted in Figure 11 as a function of the evidence. The density, calculated from the coefficients given in [106] (q max ∼ 10 fm −1 ), is well behaved and out to 2.7 fm very close to the MD and SOG densities (to be shown in Figure 12), which include a physics constraint at large r. From these values, the authors extract the charge-rms radius, which for the three values of q max of Figure 11 [97]. The points in black are corrected for the effects of two-photon exchange.…”

Section: R From Bayesian Inferencementioning

confidence: 99%

Proton Charge Radius from Electron Scattering

Sick

2017

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Abstract:The rms-radius R of the proton charge distribution is a fundamental quantity needed for precision physics. This radius, traditionally determined from elastic electron-proton scattering via the slope of the Sachs form factor G e (q 2 ) extrapolated to momentum transfer q 2 = 0, shows a large scatter. We discuss the approaches used to analyze the e-p data, partly redo these analyses in order to identify the sources of the discrepancies and explore alternative parameterizations. The problem lies in the model dependence of the parameterized G(q) needed for the extrapolation. This shape of G(q < q min ) is closely related to the shape of the charge density ρ(r) at large radii r, a quantity that is ignored in most analyses. When using our physics knowledge about this large-r density together with the information contained in the high-q data, the model dependence of the extrapolation is reduced, and different parameterizations of the pre-2010 data yield a consistent value for R = 0.887 ± 0.012 fm. This value disagrees with the more precise value 0.8409 ± 0.0004 fm determined from the Lamb shift in muonic hydrogen.

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Section: R From Bayesian Inferencementioning

confidence: 99%

Proton Charge Radius from Electron Scattering

Sick

2017

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“…This approach has already been adapted to approximate the electromagnetic nucleon FFs [27] and, here, it is developed to study the TPE effect. The BF was designed to:…”

Section: Bayesian Frameworkmentioning

confidence: 99%

“…This property only seems to be approximate, but we use it to reduce the number of regularization parameters to three. Eventually, we noticed that in our previous paper, it was shown that it was enough to consider one regularization parameter to fit the FF data [27]. Hence, to simplify the numerical calculations and also to accelerate the training process (more than 45 000 training processes have been performed), we consider the simplest regularization scenario with one α parameter.…”

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confidence: 99%

Two-photon exchange effect studied with neural networks

Graczyk

2011

Phys. Rev. C

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An approach to the extraction of the two-photon exchange (TPE) correction from elastic ep scattering data is presented. The cross section, polarization transfer (PT), and charge asymmetry data are considered. It is assumed that the TPE correction to the PT data is negligible. The form factors and TPE correcting term are given by one multidimensional function approximated by the feed forward neural network (NN). To find a model-independent approximation the Bayesian framework for the NNs is adapted. A large number of different parametrizations is considered. The most optimal model is indicated by the Bayesian algorithm. The obtained fit of the TPE correction behaves linearly in ǫ but it has a nontrivial Q 2 dependence. A strong dependence of the TPE fit on the choice of parametrization is observed.

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“…[24] to extract the proton radius from scattering data is described in more detail in Refs. [27][28][29]. In this approach the electric and magnetic form factors are simultaneously parametrized by one feed-forward neural network (with one hidden layer of units) with two outputs:1 A^/(G2;[m,■}) = (««.…”

Section: Bayesian Analysis and Numerical Resultsmentioning

confidence: 99%

Zemach moments of the proton from Bayesian inference

Graczyk

Juszczak

2015

Phys. Rev. C

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The first and the third Zemach moments are obtained, (/-)<2> = 1.1108 ± 0.0021 fm and (r3)(2) = 2.889 ± 0.008 f m \ from the Bayesian analysis of the elastic ep scattering data. The quantitative discussion of the dependence of the results on the parametrization choice is presented and the corresponding systematic uncertainties are estimated-about 0.6% and 1.6% for the first and the third Zemach moments, respectively.

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Neural network parameterizations of electromagnetic nucleon form-factors

Cited by 17 publications

References 84 publications

Proton Charge Radius from Electron Scattering

Proton Charge Radius from Electron Scattering

Two-photon exchange effect studied with neural networks

Zemach moments of the proton from Bayesian inference

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