Figure 1

Schematic view of the geometry of a ${\overline{\nu }}_e+p\to e^{+}+n$ event in a water detector.Reuse & Permissions

Figure 2

Left-hand panel: Expected number of events at the detector over a period of 1 yr ($3\times {10}^7\mathrm{s}$) as a function of the Lorentz ion boost $\gamma$, with (solid) and without (dashed) the weak magnetism term. Note that at the highest $\gamma$, the weak magnetism suppresses the total number of events by as much as 17%. Right-hand panel: Angular distribution of the positrons emitted in antineutrino capture by protons as observed in the water detector—Eq. (6)—normalized by the total number of events. The four different curves correspond to two extreme values of the Lorentz boost, with (solid is for $\gamma =14$; dash-dotted is for $\gamma =7$) and without (dashed is for $\gamma =14$; dotted is for $\gamma =7$) the weak magnetism term.Reuse & Permissions

Figure 3

Ratio of the first ($A_1$) and second ($A_2$) order Legendre polynomials to the zeroth order one ($A_0$, the number of events) with (solid is for $A_1/A_0$; dash-dotted is for $A_2/A_0$) and without (dashed is for $A_1/A_0$; dotted is for $A_2/A_0$) the weak magnetism term, as a function of the Lorentz boost. The overall effect of the weak magnetism term on the angular distribution is considerably larger than on the total number of events. Note that, when the weak magnetism is considered, its value is set to the one of Eq. (4).Reuse & Permissions

Figure 4

$\Delta {\chi }^2$ obtained from the total number of events (dashed) and from the angular distribution of events (solid) in the cases when the total error is purely statistical (left-hand panel) and when a 2% systematic error is added to the total error (right-hand panel). For a purely statistical error, the $1\sigma$ ($\Delta {\chi }^2=1$) relative uncertainty in ${\mu }_p-{\mu }_n$ is close to 5% from both the number of events and the angular distribution analysis. Even though the angular distribution is more sensitive to the weak magnetism term, its smaller statistical error makes the analysis through the number of events more advantageous in the absence of systematic errors. As soon as a 2% systematic error is added to the total error in both the number of events and in the angular distribution, the latter becomes a better method to measure the weak magnetism. These results were obtained considering $\gamma =12$.Reuse & Permissions

Figure 5

$\Delta {\chi }^2$ obtained from the angular distribution of events in the cases when the total error is purely statistical (solid), and when one includes 2% (dashed), 5% (dash-dotted), and 10% (dotted) systematic errors. The $1\sigma$ ($\Delta {\chi }^2=1$) relative uncertainty in ${\mu }_p-{\mu }_n$ is 4.7%, 5.6%, 9.0%, and more than 20%, respectively. These results were obtained considering $\gamma =12$.Reuse & Permissions