Diffractive neutrino-production of pions on nuclei: Adler relation within the color-dipole description

Effects of coherence in neutrino-production of pions off nuclei are studied employing the color dipole representation and path integral technique. If the nucleus remains intact, the process is controlled by the interplay of two length scales. One is related to the pion mass and is quite long (at low Q^2), while the other, associated with heavy axial-vector states, is much shorter. The Adler relation is found to be broken at all energies, but especially strongly at \nu > 10 GeV, where the cross section is suppressed by a factor ~A^{-1/3}. On the contrary, in a process where the recoil nucleus breaks up into fragments, the Adler relation turns out to be strongly broken at low energies, where the cross section is enhanced by a factor ~A^{1/3}, but has a reasonable accuracy at higher energies, where all the coherence length scales become long.