JUZGADO COLEGIADO

Although the various processes available to neutrinos interacting with nuclei are broadly known, the precision of that understanding and our ability to make predictions is limited by the current state of experimental data, which is often sparse, scattered or both.

Such data is required to constrain inputs to theoretical models, such as the form-factors discussed in Section 3.5.1. It is also required to better understand the processes involved in the “shallow inelastic” transition region between resonance and DIS dominance. And it is necessary to resolve the convoluted effects from the initial nuclear state, hadronisation and final-state interactions. The least ambiguous measurement which can be made is the total CC cross- section for ν_μ or ν_μ, since its definitions from theory and experiment are both equivalent and clear. However even here the existing experimental data

provides only weak constraints on predictions. The data for the total ν_μ CC cross-section was shown previously in Figure 3.4, however it spans a wide range in both cross-section and energy. Placing the energy on a log-scale and dividing the cross-section by energy, as in Figure 3.14, shows more clearly the freedom afforded both in absolute normalisation and in shape, particularly when E_ν < 10 GeV. This situation is worse for ν_μ, also shown in Figure 3.14, where the data is more sparse in general and particularly so at low energies.

While the total interaction cross-section is unambiguous, it is less useful in constraining theoretical predictions and parameters because, particularly at low energy, it represents the combination of multiple interaction channels. To constrain predictions more effectively, more specific cross-sections are required. The first plot in Figure 3.15 shows cross-sections measured for ν_μ CC QE in experiments either at high energies, or at low energies on light targets such as deuterium. The situation is similar to that for the total cross-section: at high energies the data is scattered and with large uncertainties, at low energies it is very sparse. However this data does still provide some constraint, one well known example being the fitting of M_A = 1.014 ± 0.014 GeV [20] for the axial form-factor (Equation 3.27).

The second plot in Figure 3.15 shows more recent data on ν_μ CC QE on 12C from the NOMAD experiment, and the lower energy MiniBooNE experiment. The data is clearly incompatible with the CC QE cross-section. Early attempts to explain the MiniBooNE discrepancy included fitting a higher value of M_A = 1.35 ± 0.17 GeV [26]. However, while improving the theoretical agreement with the MiniBooNE data, such a high value of M_A was clearly in conflict with all other experimental data.

Since then two significant observations have been made regarding the MiniBooNE data. First, the analysis was conducted on a sample of interactions producing a muon and no charged pion, in contrast with the muon plus proton topology for NOMAD and most other data. Second, MiniBooNE were the first to attempt a measurement of the CC QE cross-section both at low-E_ν and on a heavy target. Given the discussion in Section 3.6, both of these observations highlight differences which are greatly influenced by nuclear effects which are larger at lower E_ν, and can substantially affect the particles produced by both CC QE interactions and its backgrounds. Attempts to include additional

Figure 3.14: Data on total ν_μ (top) and ν_μ (bottom) CC cross-sections divided by energy, compared with the GENIE prediction. It is clear that the data affords a lot of freedom.

nuclear effects have had some success in explaining the MiniBooNE data while keeping M_A ≈ 1 GeV [27].

Data on other neutrino interaction cross-sections starts to become sparse. Figure 3.16 shows data on ν_μ CC cross-sections for the production of various

Figure 3.15: Data on the ν_μ CC QE cross-section, compared with the GENIE prediction for deuterium. (left) Data either at high energy or on deuterium matches well the model in GENIE. (right) The ν_μ CC QE cross-section cannot be

simultaneously compatible with both the low-E_νMiniBooNE data and NOMAD data (all on12_C).

Figure 3.16: Data on cross-sections for ν_μ CC interactions with various pion- producing final-states: (top left) μ-_{p π}+_{, (top right) μ}-_{p π}0_{, (bottom left) μ}-_{p π}-_,

(bottom right) μ-_{p π}+_π+_{. All data are on hydrogen/deuterium, with the exceptions}

of the Gargamelle and SKAT Freon detectors.

topologies which include pions. No cross-section calculations are shown in these plots, since they clearly relate to particle topologies and not a single interaction channel. It is data such as this which must be used to validate and constrain theoretical models of inelastic scattering, and the importance of nuclear effects is highlighted again in the top two plots of Figure 3.16 where the data on heavy targets (Gargamelle and SKAT) is clearly separate from the data on hydrogen and deuterium.

Data on NC processes is even rarer than for CC ones, with many processes having just one measurement available, if any at all. There is however a reasonable amount of experimental data on coherent pion production, though this is left until Chapter 4 where it is discussed in detail.

The plots in this section show data from the processes for which the most data is available. Given the degree of scatter and uncertainty in even the best of these, it is clear that a great deal of uncertainty will also exist in the theoretical models and parameters which they constrain. These models are in turn used in the simulations with which experiments define their analyses and interpret their data. It is for this reason that neutrino interactions contribute some of the largest uncertainties to neutrino oscillation measurements, and why improved understanding is essential to the field's progress.