Measurement of the CP-Violating Asymmetries in $B^0 \to K^0_S \pi^0$ and of the Branching Fraction of $B^0 \to K^0 \pi^0$

8 pages, 2 postscript figure, submitted to PRD-RCWe present a measurement of the time-dependent CP-violating asymmetries in $B^0 \to K^0_{\scriptscriptstyle S}\pi^0$ decays based on 383 million $\Upsilon(4S)\to B\kern 0.18em\bar{\kern -0.18em B}$ events collected by the \mbox{\slshape B\kern-0.1em{\smaller A}\kern-0.1em B\kern-0.1em{\smaller A\kern-0.2em R}} experiment at the PEP-II asymmetric-energy $B$ Factory at SLAC. We measure the direct CP-violating asymmetry $C_{K^0_{\scriptscriptstyle S}\pi^0} = 0.24 \pm 0.15 \pm 0.03$ and the CP-violating asymmetry in the interference between mixing and decay $S_{K^0_{\scriptscriptstyle S}\pi^0} = 0.40 \pm 0.23 \pm 0.03$, where the first errors are statistical and the second are systematic. On the same sample, we measure the decay branching fraction, obtaining ${\cal B}(B^0 \to K^0\pi^0)= (10.3 \pm 0.7 \pm 0.6)\times 10^{-6}$