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Register a new userModel Independent Extraction of the Proton Charge Radius from PRad data
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Authors
Gil Paz
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The proton radius puzzle has motivated several new experiments that aim to extract the proton charge radius and resolve the puzzle. Recently PRad, a new electron-proton scattering experiment at Jefferson Lab, reported a proton charge radius of $0.831pm 0.007_textnormal{statistical}pm 0.012_textnormal{systematic}$. The value was obtained by using a rational function model for the proton electric form factor. We perform a model-independent extraction using $z$-expansion of the proton charge radius from PRad data. We find that the model-independent statistical error is more than 50% larger compared to the statistical error reported by PRad.
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We extract the proton charge radius from the elastic form factor (FF) data using a novel theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike FF at finite $Q^2$ with the derivative at $Q^2 = 0$. The FF calculated in the predictive theory contains the radius as a free parameter. We determine its value by comparing the predictions with a descriptive global fit of the spacelike FF data, taking into account the theoretical and experimental uncertainties. Our method allows us to use the finite-$Q^2$ FF data for constraining the radius (up to $Q^2sim$ 0.5 GeV$^2$ and larger) and avoids the difficulties arising in methods relying on the $Q^2 rightarrow 0$ extrapolation. We obtain a radius of 0.844(7) fm, consistent with the high-precision muonic hydrogen results.
Extracting the proton charge radius from electron scattering data requires determining the slope of the charge form factor at $Q^2$ of zero. But as experimental data never reach that limit, numerous methods for making the extraction have been proposed, though often the functions are determined after seeing the data which can lead to confirmation bias. To find functional forms that will allow for a robust extraction of the input radius for a wide variety of functional forms in order to have confidence in the extraction from upcoming low $Q^2$ experimental data such as the Jefferson Lab PRad experiment, we create a general framework for inputting form-factor functions as well as various fitting functions. The input form factors are used to generate pseudo-data with fluctuations intended to mimic the binning and random uncertainty of a given set of real data. All combinations of input functions and fit functions can then be tested repeatedly against regenerated pseudo-data. Since the input radius is known, this allows us to find fit functions that are robust for radius extractions in an objective fashion. For the range and uncertainty of the PRad data, we find that a two-parameter rational function, a two-parameter continued fraction and the second order polynomial expansion of $z$ can extract the input radius regardless of the input charge form factor function that is used. We have created an easily expandable framework to search for functional forms that allow for a robust extraction of the radius from a given binning and uncertainty of pseudo-data generated from a wide variety of trial functions. This method has enabled a successful search for the best functional forms to extract the radius from the upcoming PRad data and can be used for other experiments.
The PRad experiment has credibly demonstrated the advantages of the calorimetric method in e-p scattering experiments to measure the proton root-mean-square (RMS) charge radius with high accuracy. The PRad result, within its experimental uncertainties, is in agreement with the small radius measured in muonic hydrogen spectroscopy experiments and it was a critical input in the recent revision of the CODATA recommendation for the proton charge radius. Consequently, the PRad result is in direct conflict with all modern electron scattering experiments. Most importantly, it is 5.8% smaller than the value from the most precise electron scattering experiment to date, and this difference is about three standard deviations given the precision of the PRad experiment. As the first experiment of its kind, PRad did not reach the highest precision allowed by the calorimetric technique. Here we propose a new (and) upgraded experiment -- PRad-II, which will reduce the overall experimental uncertainties by a factor of 3.8 compared to PRad and address this as yet unsettled controversy in subatomic physics. In addition, PRad-II will be the first lepton scattering experiment to reach the Q^2 range of 10^{-5} GeV^2 allowing a more accurate and robust extraction of the proton charge radius. The muonic hydrogen result with its unprecedented precision (~0.05%) determines the CODATA value of the proton charge radius, hence, it is critical to evaluate possible systematic uncertainties of those experiments, such as the laser frequency calibration that was raised in recent review articles. The PRad-II experiment with its projected total uncertainty of 0.43% could demonstrate whether there is any systematic difference between $e-p$ scattering and muonic hydrogen results. PRad-II will establish a new precision frontier in electron scattering and open doors for future physics opportunities.
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