Possible effects of collective neutrino oscillations in the three flavor multi-angle simulations on supernova $ u p$ process

We study the effects of collective neutrino oscillations on $ u p$ process nucleosynthesis in proton-rich neutrino-driven winds by including both the multi-angle $3times3$ flavor mixing and the nucleosynthesis network calculation. The number flux of energetic electron antineutrinos is raised by collective neutrino oscillations in a $1$D supernova model for $40 M_{odot}$ progenitor. When the gas temperature decreases down to $sim2-3times10^{9}$ K, the increased flux of electron antineutrinos promotes $ u p$ process more actively, resulting in the enhancement of $p$-nuclei. In the early phase of neutrino-driven wind, blowing at $0.6$ s after core bounce, oscillation effects are prominent in inverted mass hierarchy and $p$-nuclei are synthesized up to $^{106}mathrm{Cd}$ and $^{108}mathrm{Cd}$. On the other hand, in the later wind trajectory at $1.1$ s after core bounce, abundances of $p$-nuclei are increased remarkably by $sim10-10^{4}$ times in normal mass hierarchy and even reaching heavier $p$-nuclei such as $^{124}mathrm{Xe}$, $^{126}mathrm{Xe}$ and $^{130}mathrm{Ba}$. The averaged overproduction factor of $p$-nuclei is dominated by the later wind trajectories. Our results demonstrate that collective neutrino oscillations can strongly influence $ u p$ process, which indicates that they should be included in the network calculations in order to obtain precise abundances of $p$-nuclei. The conclusions of this paper depend on the difference of initial neutrino parameters between electron and non-electron antineutrino flavors which is large in our case. Further systematic studies on input neutrino physics and wind trajectories are necessary to draw a robust conclusion. However, this finding would help understand the origin of solar-system isotopic abundances of $p$-nuclei such as $^{92,94}mathrm{Mo}$ and $^{96,98}mathrm{Ru}$.