Amplitude Analysis of the Decay~$B^0 \to K^+\pi^-\pi^0$

We report an updated amplitude analysis of the charmless hadronic decays of neutral B mesons to $K^+\pi^-\pi^0$. With a sample of 454 million $\Upsilon(4S) \to B^0\overline{B^0}$ decays collected by the {\it B{\footnotesize A}B{\footnotesize AR}} detector at the PEP-II asymmetric-energy B~Factory at SLAC, we measure the magnitudes and phases of the intermediate resonant and nonresonant amplitudes for $B^0$ and $\overline{B^0}$ decays and determine the corresponding branching fractions and charge asymmetries. Combined with measurements of phases from $B$ decays to $K_s\pi^+\pi^-$ we constrain the CKM angle $\gamma$.