Lepton mass effects in weak charged current single pion production

Different approaches to take into account nonzero lepton mass effects in the Rein-Sehgal model are compared. Modification of the axial current due to a pion pole term is included, and it is shown that it leads to large reduction of the antineutrino cross section and a change of the shape of $d\sigma /d{Q}^2$.

Figure 1

In the top row the reduction of the total cross sections for reactions $\nu n\to {\mu }^{-}p{\pi }^0$ (left) and $\overline{\nu }p\to {\mu }^{+}n{\pi }^0$ (right) due to $m\ne 0$ is shown. Three computations are compared: (i) kinematical approximation (dotted line), (ii) exact computation without the pion pole contribution (dashed line), (iii) exact computations with the pion pole contribution included (solid line). In the bottom the ratio $\mathcal{R}$ [full model (iii)] is computed for three SPP channels (lines: solid, dashed, and dotted) and compared with analogical functions for quasielastic scattering (dot-dashed line). The cut on the invariant hadronic mass $W<2\mathrm{GeV}$ in SPP channels is imposed.

Figure 2

The differential cross sections for reactions $\nu n\to {\mu }^{-}p{\pi }^0$ (left) and $\overline{\nu }p\to {\mu }^{+}n{\pi }^0$ (right) at $E=700\mathrm{MeV}$ calculated in three models: (i) kinematical approximation (dotted line), (ii) exact computation without the pion pole contribution (dashed line), (iii) exact computations with the pion pole contribution included (solid line). In the bottom row the cross sections are normalized to the same area below the curve. The cut on the invariant hadronic mass $W<2\mathrm{GeV}$ is imposed.

Figure 3

The relative contributions from structure functions $F_j$ to the differential cross section $d\sigma /d{Q}^2$ for reaction $\nu n\to {\mu }^{-}p{\pi }^0$ at neutrino energies 1 and 5 GeV. The contributions sum to 1.

Figure 4

Reduction of the total cross sections for reactions $\nu n\to {\mu }^{-}p{\pi }^0$ (left) and $\overline{\nu }p\to {\mu }^{+}n{\pi }^0$ (right) due to $m\ne 0$. Two computations are compared: exact computations with the pion pole contribution included (solid line) and the approximation based on the Albright-Jarlskog relations (circles). The cut on the invariant hadronic mass $W<2\mathrm{GeV}$ is imposed.

Figure 5

Differential cross section for reactions $\nu n\to {\mu }^{-}{\pi }^{0}p$ (left) and $\overline{\nu }p\to {\mu }^{+}{\pi }^{0}n$ (right) for $E=700\mathrm{MeV}$. Cross sections are obtained in exact computation (solid lines) and in the approximation with $F_4$ and $F_5$ calculated with Albright-Jarlskog relations (dashed line).

Figure 6

Differential cross sections $d\sigma /d{Q}^2$ for $\nu +p\to {\mu }^{-}+{\pi }^{+}+p$ computed for the ANL [9] and BNL [10, 11] experimental neutrino beams. The ANL and BNL points are denoted as black and white squares correspondingly. Cross sections are obtained in the exact computation with (solid line) and without (dashed line) the pion pole contribution. The results are compared with the differential cross sections obtained with $m_{\mu }=0$ (dotted line). The cut on the invariant hadronic mass is $W<1.4\mathrm{GeV}$. Top and bottom figures were obtained with different axial form factors.