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Register a new userThe proton charge radius extracted from the Initial State Radiation experiment at MAMI
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We report on a comprehensive reinterpretation of the existing cross-section data for elastic electron-proton scattering obtained by the initial-state radiation technique, resulting in a significantly improved accuracy of the extracted proton charge radius. By refining the external energy corrections we have achieved an outstanding description of the radiative tail, essential for a detailed investigation of the proton finite-size effects on the measured cross-sections. This development, together with a novel framework for determining the radius, based on a regression analysis of the cross-sections employing a polynomial model for the form factor, led us to a new value for the charge radius, which is $(0.870 pm 0.014_mathrm{stat.}pm 0.024_mathrm{sys.} pm 0.003_mathrm{mod.}),mathrm{fm}$.
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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.
For experiments of the type A(vec e,evec p) the 3-spectrometer setup of the A1 collaboration at MAMI has been supplemented by a focal plane proton-polarimeter. To this end, a carbon analyzer of variable thickness and two double-planes of horizontal drift chambers have been added to the standard detector system of Spectrometer A. Due to the spin precession in the spectrometer magnets, all three polarization components at the target can be measured simultaneously. The performance of the polarimeter has been studied using elastic p(e,ep) scattering.
[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 discrepancy, 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.
A water Cherenkov luminosity monitor system with associated electronics has been developed for the A4 parity violation experiment at MAMI. The detector system measures the luminosity of the hydrogen target hit by the MAMI electron beam and monitors the stability of the liquid hydrogen target. Both is required for the precise study of the count rate asymmetries in the scattering of longitudinally polarized electrons on unpolarized protons. Any helicity correlated fluctuation of the target density leads to false asymmetries. The performance of the luminosity monitor, investigated in about 2000 hours with electron beam, and the results of its application in the A4 experiment are presented.
We report on a new experimental method based on initial-state radiation (ISR) in e-p scattering, in which the radiative tail of the elastic e-p peak contains information on the proton charge form factor ($G_E^p$) at extremely small $Q^2$. The ISR technique was validated in a dedicated experiment using the spectrometers of the A1-Collaboration at the Mainz Microtron (MAMI). This provided first measurements of $G_E^p$ for $0.001leq Q^2leq 0.004 (GeV/c)^2$.
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