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تسجيل مستخدم جديدTowards a resolution of the proton form factor problem: new electron and positron scattering data
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There is a significant discrepancy between the values of the proton electric form factor, $G_E^p$, extracted using unpolarized and polarized electron scattering. Calculations predict that small two-photon exchange (TPE) contributions can significantly affect the extraction of $G_E^p$ from the unpolarized electron-proton cross sections. We determined the TPE contribution by measuring the ratio of positron-proton to electron-proton elastic scattering cross sections using a simultaneous, tertiary electron-positron beam incident on a liquid hydrogen target and detecting the scattered particles in the Jefferson Lab CLAS detector. This novel technique allowed us to cover a wide range in virtual photon polarization ($varepsilon$) and momentum transfer ($Q^2$) simultaneously, as well as to cancel luminosity-related systematic errors. The cross section ratio increases with decreasing $varepsilon$ at $Q^2 = 1.45 text{ GeV}^2$. This measurement is consistent with the size of the form factor discrepancy at $Q^2approx 1.75$ GeV$^2$ and with hadronic calculations including nucleon and $Delta$ intermediate states, which have been shown to resolve the discrepancy up to $2-3$ GeV$^2$.
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[Background] The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. [Purpose] In an attempt to understand the di
screpancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. [Method] We make use of stepwise regression techniques using the $F$-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. [Results] Starting with the precision, low four-momentum transfer ($Q^2$) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the $F$-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on $G_E$ from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-$Q^2$ data on $G_E$ to select functions which extrapolate to high $Q^2$, we find that a Pade ($N=M=1$) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, $G_E(Q^2) = ( 1 + Q^2/0.66,mathrm{GeV}^2)^{-2}$. [Conclusions] From this statistical analysis, we conclude that the electron scattering result and the muonic hydrogen result are consistent. It is the atomic hydrogen results that are the outliers.
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 propose
d, 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.
We use distorted wave electron scattering calculations to extract the weak charge form factor F_W(q), the weak charge radius R_W, and the point neutron radius R_n, of 208Pb from the PREX parity violating asymmetry measurement. The form factor is the
Fourier transform of the weak charge density at the average momentum transfer q=0.475 fm$^{-1}$. We find F_W(q) =0.204 pm 0.028 (exp) pm 0.001 (model). We use the Helm model to infer the weak radius from F_W(q). We find R_W= 5.826 pm 0.181 (exp) pm 0.027 (model) fm. Here the exp error includes PREX statistical and systematic errors, while the model error describes the uncertainty in R_W from uncertainties in the surface thickness sigma of the weak charge density. The weak radius is larger than the charge radius, implying a weak charge skin where the surface region is relatively enriched in weak charges compared to (electromagnetic) charges. We extract the point neutron radius R_n=5.751 pm 0.175 (exp) pm 0.026 (model) pm 0.005 (strange) fm$, from R_W. Here there is only a very small error (strange) from possible strange quark contributions. We find R_n to be slightly smaller than R_W because of the nucleons size. Finally, we find a neutron skin thickness of R_n-R_p=0.302pm 0.175 (exp) pm 0.026 (model) pm 0.005 (strange) fm, where R_p is the point proton radius.
In 1963, a proton radius of $0.805(11)~mathrm{fm}$ was extracted from electron scattering data and this classic value has been used in the standard dipole parameterization of the form factor. In trying to reproduce this classic result, we discovered
that there was a sign error in the original analysis and that the authors should have found a value of $0.851(19)~mathrm{fm}$. We additionally made use of modern computing power to find a robust function for extracting the radius using this 1963 datas spacing and uncertainty. This optimal function, the Pad{e} $(0,1)$ approximant, also gives a result which is consistent with the modern high precision proton radius extractions.
We report new precision measurements of the elastic electron-proton scattering cross section for momentum transfer squared (Q$^2$) up to 15.75~gevsq. These data allow for improved extraction of the proton magnetic form factor at high Q$^2$ and nearly
double the Q$^2$ range of direct longitudinal/transverse separated cross sections. A comparison of our results to polarization measurements establishes the presence of hard two-photon exchange in the $e$-$p$ elastic scattering cross section at greater than 95% confidence level for Q$^2$ up to 8 (GeV/c)$^2$.
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