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Register a new userWeak radius of the proton
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Authors
C. J. Horowitz
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The weak charge of the proton determines its coupling to the $Z^0$ boson. The distribution of weak charge is found to be dramatically different from the distribution of electric charge. The protons weak radius $R_W= 1.545pm 0.017$ fm is 80% larger than its charge radius $R_{ch}approx 0.84$ fm because of a very large pion cloud contribution. This large weak radius can be measured with parity violating electron scattering and may provide insight into the structure of the proton, various radiative corrections, and possible strange quark contributions.
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We present a feasibility study of a simultaneous sub-percent extraction of the weak charge and the weak radius of the ${}^{12}$C nucleus using parity-violating electron scattering, based on a largely model-independent assessment of the uncertainties. The corresponding measurement is considered to be carried out at the future MESA facility in Mainz with $E_{rm beam} = 155$ MeV. We find that a combination of a $0.3%$ precise measurement of the parity-violating asymmetry at forward angles with a $10%$ measurement at backward angles will allow to determine the weak charge and the weak radius of ${}^{12}$C with $0.4%$ and $0.5%$ precision, respectively. These values could be improved to $0.3%$ and $0.2%$ for a $3%$ backward measurement. This experimental program will have impact on precision low-energy tests in the electroweak sector and nuclear structure.
In a series of recent publications, different authors produce a wide range of electron radii when reanalyzing electron proton scattering data. In the light of the proton radius puzzle, this is a most unfortunate situation. However, we find flaws in most analyses that result in radii around 0.84 fm. In this paper, we explain our reasoning and try to illustrate the most common pitfalls.
It is suggested that proton elastic scattering on atomic electrons allows a precise measurement of the proton charge radius. Very small values of transferred momenta (up to four order of magnitude smaller than the ones presently available) can be reached with high probability.
The precise determination of the proton radius from recent elastic scattering electron-proton data is discussed. The necessary precision on the elastic cross section to discriminate among the values coming from atomic spectroscopy is scrutinized in terms of the relevant quantity, i.e., the derivative of the form factor. It is shown that such precision is two orders of magnitude higher than the precision on the cross section, that is the measured observable. Different fits on the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associated to the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions and the range of the data sample. This error is shown to be even orders of magnitude larger than commonly assumed.
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.
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