Weak charged and neutral current induced one pion production off the nucleon

We present a study of neutrino/antineutrino induced charged and neutral current single pion production off the nucleon. For this, we have considered $P_{33}(1232)$ resonance, non-resonant background terms, other higher resonances like $P_{11}(1440)$, $S_{11}(1535)$, $D_{13}(1520)$, $S_{11}(1650)$ and $P_{13}(1720)$. For the non-resonant background terms a microscopic approach based on SU(2) non-linear sigma model has been used. The vector form factors for the resonances are obtained by using the relationship between the electromagnetic resonance form factors and helicity amplitudes provided by MAID. Axial coupling $C_5^{A}(0)$ in the case of $P_{33}(1232)$ resonance is obtained by fitting the ANL and BNL $ν$-deuteron reanalyzed scattering data. The results are presented with and without deuteron effect for the total scattering cross sections for all possible channels viz. $ν_l(\barν_l)~+~N\rightarrow l^-(l^+)~+~N^\prime~+~π^i$; $ν_l(\barν_l)~+~N\rightarrow ν_l(\barν_l)~+~N^\prime~+~π^i$, where $N, N^\prime=p,n$, $π^i=~π^\pm$ or $π^0$ and $l=e, μ$.

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