Impact of nuclear effects on the determination of the nucleon axial mass

Omar Benhar and Davide Meloni

Phys. Rev. D 80, 073003 – Published 12 October 2009

Abstract

We analyze the influence of nuclear effects on the determination of the nucleon axial mass from nuclear cross sections. Our work is based on a formalism widely applied to describe electron-nucleus scattering data in the impulse approximation regime. The results of numerical calculations show that correlation effects, not taken into account by the relativistic Fermi gas model, sizably affect the $Q^{2}$ dependence of the cross section. However, their inclusion does not appear to explain the large values of the axial mass recently reported by the K2K and MiniBooNE Collaborations.

Received 13 March 2009

DOI:https://doi.org/10.1103/PhysRevD.80.073003

Authors & Affiliations

Omar Benhar¹ and Davide Meloni²

¹INFN and Department of Physics, “Sapienza” Università di Roma, I-00185 Roma, Italy
²Department of Physics and INFN, Università “Roma Tre,” I-00146 Roma, Italy

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Vol. 80, Iss. 7 — 1 October 2009

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Images

Figure 1
$Q^{2}$ dependence of the cross section of the process $ν_{μ} + {}^{16}O \to μ + p + X$ , for neutrino energy $E_{ν} = 1.2 GeV$ . The dashed line refers to the RFG model, with Fermi momentum $p_{F} = 225 MeV$ , removal energy $ϵ = 27 MeV$ and $M_{A} = M_{A}^{K 2 K}$ , whereas the solid line has been obtained using the approach of Refs. 5, 15 with $M_{A} = M_{A}^{WA}$ . The shaded area corresponds to the $1 σ$ error associated with the axial mass quoted in Ref. 2.Reuse & Permissions
Figure 2
Normalized $Q^{2}$ dependence of the cross section of the process $ν_{μ} + {}^{16}O \to μ + p + X$ , for neutrino energy $E_{ν} = 1.2 GeV$ . The solid and dashed lines, as well as the shaded area, are defined as in Fig. 1.Reuse & Permissions
Figure 3
Normalized $Q^{2}$ dependence of the number of events (divided in $Q^{2}$ bins of size $Δ Q^{2} = 0.2 {GeV}^{2}$ ) for the process $ν_{μ} + {}^{16}O \to μ + p + X$ in K2K. The histogram is the event estimate obtained from the SF model with $M_{A} = M_{A}^{WA}$ , while the points with error bars correspond to the RFG model and $M_{A} = M_{A}^{K 2 K}$ , with its $1 σ$ error.Reuse & Permissions
Figure 4
$Q^{2}$ dependence of the cross section of the process $ν_{μ} + {}^{12}C \to μ + p + X$ , for neutrino energy $E_{ν} = 0.7 GeV$ . The dashed line refers to the RFG model, with Fermi momentum $p_{F} = 225 MeV$ , removal energy $ϵ = 27 MeV$ and $M_{A} = M_{A^{MB}}$ , whereas the solid line has been obtained using the approach of Refs. 5, 15 with $M_{A} = M_{A}^{WA}$ . The shaded area corresponds to $1 σ$ on the axial mass error quoted in 3. The left and right panels corresponds to non-normalized and normalized distributions, respectively.Reuse & Permissions
Figure 5
Upper panel: Neutrino energy distribution at $E_{μ} = 600 MeV$ and $θ_{μ} = 60 °$ , reconstructed from Eq. (8) using $2 \times 10^{4}$ pairs of $(| p_{n} |, E)$ values sampled from the probability distributions associated with the oxygen spectral function of Ref. 18 (SF) and the Fermi gas (FG) model, with Fermi momentum $p_{F} = 225 MeV$ and removal energy $ϵ = 27 MeV$ . The arrow points to the value of $E_{ν}$ obtained from Eq. (9). Lower panel: The same as the upper panel, but for $E_{μ} = 1 GeV$ and $θ_{μ} = 35 °$ .Reuse & Permissions
Figure 6
Upper panel: Differential cross section of the process $ν_{μ} + A \to μ + p + (A - 1)$ , at $E_{μ} = 600 MeV$ and $θ_{μ} = 60 °$ , as a function of the incoming neutrino energy. The solid line shows the results of the full calculation, carried out within the approach of Refs. 5, 15, whereas the dashed line has been obtained neglecting the effects of FSI. The dotted-dashed line corresponds to the RFG model with Fermi momentum $p_{F} = 225 MeV$ and removal energy $ϵ = 27 MeV$ . The arrow points to the value of $E_{ν}$ obtained from Eq. (9). Lower panel: The same as the upper panel, but for $E_{μ} = 1 GeV$ and $θ_{μ} = 35 °$ .Reuse & Permissions

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