Precision $e^{-}$ beam polarimetry at an $e^{+}{e}^{-}$ $B$ factory using tau-pair events

We present a new technique, “tau polarimetry,” for measuring the longitudinal beam polarization present in an $e^{+}{e}^{-}$ collider through the analysis of $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ events. By exploiting the sensitivity of $\tau$ decay kinematics to the longitudinal polarization of the beams, we demonstrate that the longitudinal polarization can be measured with a 3 per mil systematic uncertainty at the interaction point using a technique that is independent of spin and beam transport modeling. Using $424.2\pm 1.8{\mathrm{fb}}^{-1}$ of BABAR data at $\sqrt{s}=10.58\mathrm{GeV}$, the average longitudinal polarization of the PEP-II $e^{+}{e}^{-}$ collider has been measured to be $⟨P⟩=0.0035\pm 0.0024_{\mathrm{stat}}\pm 0.0029_{\mathrm{sys}}$. The systematic uncertainty studies are described in detail, which can serve as a guide for future applications of tau polarimetry. A proposed $e^{-}$ beam longitudinal polarization upgrade to the SuperKEKB $e^{+}{e}^{-}$ collider would benefit from this technique.

Figure 1

Diagrams illustrating $\theta$ (left) where $f$ represents a final-state particle, ${\theta }^{\star }$ (center), and $\psi$ (right).

Figure 2

Distribution of $\cos \theta$ for simulated events after detector response reconstruction for (a) positively and (b) negatively charged $\tau$ decays to ${\rho }^{\pm }\to {\pi }^{\pm }{\pi }^0$. $\mathrm{\Gamma }$ represents the total number of entries and $\mathrm{d}\cos \theta$ represents the bin width of 0.04.

Figure 3

Distribution of $\cos {\theta }^{*}$ for simulated events after detector response reconstruction for ${\tau }^{+}$ decays for (a) $\cos \theta <0$ and (b) $\cos \theta >0$, and for ${\tau }^{-}$ decays for (c) $\cos \theta <0$ and (d) $\cos \theta >0$. $\mathrm{\Gamma }$ represents the total number of entries and $\mathrm{d}\cos {\theta }^{*}$ represents the bin width of 0.04.

Figure 4

Distribution of $\cos \psi$ for simulated events after detector response reconstruction for ${\tau }^{+}$ decays for (a) $\cos \theta <0$ and (b) $\cos \theta >0$, and for ${\tau }^{-}$ decays for (c) $\cos \theta <0$ and (d) $\cos \theta >0$. $\mathrm{\Gamma }$, which represents the total number of entries and $\mathrm{d}\cos \psi$ represents the bin width of 0.04.

Figure 5

Fit validation MC study: beam polarization outputs of fits as a function of input polarization, produced by mixing polarized ${\tau }^{+}{\tau }^{-}$ MC samples as described in the text. The red points correspond to the measurements for positively charged signal candidates while the blue points correspond to the negatively charged candidates. Diagonal line plotted to show optimal correlation.

Figure 6

Schematic of a signal type event in the c.m. frame with a signal ${\tau }^{-}\to {\rho }^{-}{\nu }_{\tau }\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ decay tagged with a ${\tau }^{-}\to e^{-}{\overline{\nu }}_e{\nu }_{\tau }$ decay.

Figure 7

Projection of the three-dimensional event distributions onto the $\cos {\theta }^{*}$ vs $\cos \psi$ plane for positively charged signal events. (a) Data, $\cos \theta <0$, (b) data, $\cos \theta >0$, (c) fit result, $\cos \theta <0$, (d) fit result, $\cos \theta >0$, (e) left-polarized MC sample, $\cos \theta <0$, (f) left-polarized MC sample, $\cos \theta >0$, (g) right-polarized MC sample, $\cos \theta <0$, (h) right-polarized MC sample, $\cos \theta >0$.

Figure 8

Projection of the three-dimensional event distributions onto the $\cos {\theta }^{*}$ vs $\cos \psi$ plane for negatively charged signal events. (a) Data, $\cos \theta <0$, (b) data, $\cos \theta >0$, (c) fit result, $\cos \theta <0$, (d) fit result, $\cos \theta >0$, (e) left-polarized MC samples, $\cos \theta <0$, (f) left-polarized MC samples, $\cos \theta >0$, (g) right-polarized MC samples, $\cos \theta <0$, (h) right-polarized MC samples, $\cos \theta >0$.

Figure 9

One-dimensional projection of $\cos \theta$ from ${\rho }^{+}$ fits for runs 1–6, (a) through (f), respectively.

Figure 10

One-dimensional projection of $\cos \theta$ from ${\rho }^{-}$ fits for runs 1–6, (a) through (f), respectively.

Figure 11

One-dimensional projection of $\cos {\theta }^{*}$ from ${\rho }^{+}$ fits for runs 1–6, (a) through (f), respectively.

Figure 12

One-dimensional projection of $\cos {\theta }^{*}$ from ${\rho }^{-}$ fits for runs 1–6, (a) through (f), respectively.

Figure 13

One-dimensional projection of $\cos \psi$ from ${\rho }^{+}$ fits for runs 1–6, (a) through (f), respectively.

Figure 14

One-dimensional projection of $\cos \psi$ from ${\rho }^{-}$ fits for runs 1–6, (a) through (f), respectively.