This paper presents the first combined measurement of the double-differential
muon neutrino and antineutrino charged-current cross sections with no pions in
the final state on hydrocarbon at the off-axis near detector of the T2K
experiment. The data analyzed in this work comprise 5.8$ imes$10$^{20}$ and
6.3$ imes$10$^{20}$ protons on target in neutrino and antineutrino mode
respectively, at a beam energy peak of 0.6 GeV. Using the two measured cross
sections, the sum, difference and asymmetry were calculated with the aim of
better understanding the nuclear effects involved in such interactions. The
extracted measurements have been compared with the prediction from different
Monte Carlo generators and theoretical models showing that the difference
between the two cross sections have interesting sensitivity to nuclear effects.
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