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Register a new userWeak charge form factor and radius of 208Pb through parity violation in electron scattering
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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.
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We report the first measurement of the parity-violating asymmetry A_PV in the elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the radius of the neutron distribution (Rn). The result A_PV = 0.656 pm 0.060 (stat) pm 0.014 (syst) ppm corresponds to a difference between the radii of the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.
Parity-odd domains, corresponding to non-trivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along the orbital momentum of the system created in non-central collisions. To study this effect, we investigate a three particle mixed harmonics azimuthal correlator which is a P-even observable, but directly sensitive to the charge separation effect. We report measurements of this observable using the STAR detector in Au+Au and Cu+Cu collisions at $sqrt{s_{NN}}$=200 and 62~GeV. The results are presented as a function of collision centrality, particle separation in rapidity, and particle transverse momentum. A signal consistent with several of the theoretical expectations is detected in all four data sets. We compare our results to the predictions of existing event generators, and discuss in detail possible contributions from other effects that are not related to parity violation.
We report a precision measurement of the parity-violating asymmetry $A_{PV}$ in the elastic scattering of longitudinally polarized electrons from $^{208}$Pb. We measure $A_{PV}=550pm 16 {rm (stat)}pm 8 {rm (syst)}$ parts per billion, leading to an extraction of the neutral weak form factor $F_W(Q^2 = 0.00616 {rm GeV}^2) = 0.368 pm 0.013$. Combined with our previous measurement, the extracted neutron skin thickness is $R_n-R_p=0.283 pm 0.071$~fm. The result also yields the first significant direct measurement of the interior weak density of $^{208}$Pb: $rho^0_W = -0.0796pm0.0036 {rm (exp.)}pm0.0013 {rm (theo.)} {rm fm}^{-3}$ leading to the interior baryon density $rho^0_b = 0.1480pm0.0036 {rm (exp.)}pm0.0013 {rm (theo.)} {rm fm}^{-3}$. The measurement accurately constrains the density dependence of the symmetry energy of nuclear matter near saturation density, with implications for the size and composition of neutron stars.
The effects of parity violation in the interaction of relativistic polarized protons and deuterons are discussed. Within Glaubers approach, estimates are obtained for P-odd asymmetries in the total and elastic scattering cross sections, in the deuteron dissociation cross section, and in the inelastic cross section with meson production in a final state. It is shown that, from the point of view of the magnitude of the P-odd effects, the interaction of polarized deuterons with unpolarized protons has an advantage over the interaction of polarized protons with unpolarized deuterons. A significant P-odd asymmetry was found in the dissociation channel of the polarized deuteron.
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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