content_image/405611.jpg
<img src='content_image/405611.jpg'>

In addition, it has to be kept in mind that at | q | ∼ p$_{F}$ long-range correlations, involving more than one nucleon, also play a significant role [6]. 

Despite the fact that, being based on the nonrelativis- tic approximation, the approach of Ref. [6] should not be used in the calculation of the MiniBooNE event dis- tribution, it helps to clarify why the Q 2 rec distribution of events measured by this experiment can be described by the RFG model [2] and the SF approach only for Q 2 rec ≥ 0 . 25 GeV $^{2}$. 

To improve the description at lower Q $^{2}$, the Mini- BooNE Collaboration introduced the ad hoc additional parameter κ in the RFG model. While the authors of Ref. [2] argue that this procedure allows for a better treatment of Pauli blocking, we think that the inclusion of κ cannot be justified on physics ground. Therefore, we refer to the modified RFG model of Ref. [2] as the κ -fit. 2 

Figure 6 shows that in the region of lower values of Q rec the contribution of | q | ’s below 2 p$_{F}$ is dominant. Hence, to explain the neutrino-nucleus cross section dσ/dQ 2 rec at quantitative level in the whole range of Q 2 rec one needs a consistent description of both short- and long-range cor- relations. Unfortunately, due to the difficulties involved in the treatment of relativistic particles in the final state, such a description has not been fully developed yet. 

## IV. EXPERIMENTAL ISSUES 

The average axial mass extracted by past experiments turns out to be significantly lower than the values re- cently reported by K2K and MiniBooNE [9]. Although the early experiments were carried out using a variety of targets, about 60% of the total number of recorded events were collected on deuteron. The results of deuteron mea- surement with highest statistics [10–12] are very consis- tent with one another and have small error bars. Com- 

pared to deuteron experiments, those carried out with heavier targets have much poorer statistics, the typical number of events being lower by one order of magnitude. Moreover, using a deuteron target allows one to mini- mize the systematic error associated with the treatment of nuclear effects. 

A lower value of the axial mass is also supported by the result recently obtained by the NOMAD Collabora- tion [13] using a carbon target. 

On the other hand, MiniBooNE collected more events than all other experiments combined, and carried out an analysis based on the shape of the reconstructed Q 2 distribution. MiniBooNE reported 193709 events sur- viving the cuts, of which about 180000 correspond to 0 ≤ Q 2 rec < 1 GeV $^{2}$. In the analysis not involving the additional parameter κ , two cuts were applied: one at low Q 2 $_{rec}$, to exclude the region where the RFG model is expected to break down, and one at high Q 2 $_{rec}$, to ex- clude the region of low statistics. After rejection of the events excluded by the cuts, the data sample employed to extract the axial mass reduced to ∼ 112000 events, i.e. ∼ 62% of the total. Note, however, that this figure is still ∼ 60 times larger than the number of events typically col- lected in deuteron experiments. 

The first problem to be addressed in the comparison between theoretical calculations and experimental results is background simulation, which is, to a significant ex- tent, detector dependent. 

The extraction of the axial mass requires an accurate selection of the CCQE events and a quantitative descrip- tion of the irreducible backgrounds which may change the topology of the observed event. For example, a Δ-production process followed by pion absorption may be undistinguishable from a CCQE interaction, whereas a primary CCQE process may yield pions due to final state interactions. Therefore, a more complete theoreti- cal analysis should account for intranuclear cascade in a consistent way. 

Although cascade calculations including nucleon- nucleon correlations have not been developed yet, we can gauge the relevance of these effects using the results of a comparison of the MC generators employed in the anal- ysis of neutrino experiments, reported in Ref. [14]. The predicted ratio between true and observed CCQE events turns out to be in the range 82%–89% for a 1-GeV ν$_{µ}$ beam and oxygen target. On the other hand, the frac- tion of events misidentified as inelastic due to pion pro- duced in final state interactions is typically 0.5%–3%. The uncertainty in the modeling of pion production and absorption may be partly responsible for the disagree- ment between the values of the axial mass reported by K2K and MiniBooNE and those resulting from different experiments. 

Scattering off a correlated pair of nucleons may also 

## A. Identification of CCQE events 

