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We study breakup of the deuteron induced by neutrinos in the neutral $\nud\to \nu np$, $\bar{\nu} d\to \bar{\nu} np$ and the charged $\bar{\nu} d\to e^+n n$, $\nu d\to e^- pp$ processes. Pionless effective field theory withdibaryon fields is used to calculate the total cross sections for neutrinoenergies $E_\nu$ from threshold to 20 MeV. Amplitudes are expanded up tonext-to-leading order, and the partial wave is truncated at $P$-waves. TheCoulomb interaction between two protons is included nonperturbatively in thereaction amplitudes, and an analytic expression of the amplitudes is obtained.The contribution of the next-to-leading order to the total cross section is inthe range of 5.2$-$9.9\% in magnitude, and that of the $P$-wave is 2.4$-$2.8\%at $E_\nu = 20$ MeV. Uncertainty arising from an axial isovector low-energyconstant is estimated to be on the order of 1\%.

Neutrino-Deuteron Reactions at Solar Neutrino Energies in Pionless Effective Field Theory with Dibaryon Fields