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be misinterpreted as pion production, as it produces two hadron tracks in the final state. However, even neglect- ing nucleon absorption this background does not exceed 3% of the CCQE events in the MiniBooNE kinematical range, and is therefore not likely to be significant. Be- cause of the weaker Q 2 dependence, resulting from the higher nucleon removal energy, a proper interpretation of these events may only marginally increase the value of axial mass extracted from the analysis. 

The effect of FSI, negligible in light nuclei and not taken into account in this paper, is expected to make the Q 2 rec distribution flatter, quenching its maximum and re- distributing strength towards higher values of the four- momentum transfer [15]. This behavior is due to the fact that FSI couple one-hole states to one-particle–two- hole states, thus leading to an increase of the average removal energy. As a result, the neutrino-nucleon inter- action takes place at higher Q $^{2}$. Hence, part of the dis- crepancy between the results of K2K and MiniBooNE, on the one hand, and deuteron-based experiments, on the other hand, may be ascribable to FSI effects. 

It is also very important to realize that the influence of reaction mechanisms beyond the IA cannot be mini- mized increasing the beam energy [16]. It turns out that low momentum transfers ( | q | ≲ p$_{F}$ ) provide almost the same contributions to the CCQE cross section for neu- trino energy 0.4 GeV and 100 GeV. In the absence of a fully consistent theoretical description of all the relevant mechanisms, the most reasonable option for the experi- mental analysis appears to be a cutoff, to reject events with | q | ≲ 2 p$_{F}$ . 

It should be kept in mind that in the region where the IA is not valid the cross section may not scale with the number of nucleons. As a consequence, the axial mass (or any other parametrization of the axial form factor) extracted from neutrino-nucleus data at low Q 2 rec may turn out to be target dependent. 

## B. Proposal of new kinematical variables 

The axial mass is currently extracted from experimen- tal data using the shape of the Q 2 rec distribution of CCQE events. However, as pointed out in Section II, Q 2 rec can- not be directly measured; its definition [see Eq. (2)] in- volves the nucleon separation energy and depends on the applied approximations, e.g. the assumption that the struck nucleon be at rest. 2 

It may be convenient replacing Q rec with the new, model independent, variable 

whose definition only involves measured quantities. From 

it follows that the β distribution exhibits the same be- havior as the Q 2 rec distribution, and can be comparably 

<img src='content_image/426101.jpg'>

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<img src='content_image/426096.jpg'>

useful in the extraction of the axial mass or in the anal- ysis of nuclear effects. Figure 7 shows the distributions obtained for the MiniBooNE flux as a function of β . 

An even better choice appears to be provided by the variable 

Figure 8, showing the φ distributions of the Mini- BooNE data obtained using different approaches, clearly illustrates that the main advantage of using φ lies in the fact that the deviations of the κ fit from the RFG model, reflecting the breakdown of the IA, show up in the high φ tail of the distribution. As a consequence, a single cut at φ = 3 GeV − 1 allows one to reject both the region of low statistics and the region where effects beyond the IA are expected to be important. Hence, the extraction of the axial mass from the φ distribution would be based on a larger data sample. Moreover, the dependence of the φ distribution on the axial mass turns out to be only visible at φ > 1.6 GeV − $^{1}$, corresponding to the region of highest statistics. Note that in the case of the Q 2 rec distribution the situation is reversed. 

In this paper, we have analyzed possible sources of the observed disagreement between the Q 2 rec distributions of CCQE events reported by several recent experiments and the prediction of Monte Carlo simulations. 

As far as the treatment of nuclear effects is concerned, our work suggests that, in addition to the known limita- tions of the RFG model, discussed in, e.g., Refs. [15, 17], the most critical feature of present analyses is the as- sumption that the IA scheme be applicable over the whole range of Q $^{2}$. Electron scattering studies have provided ample evidence that the IA breaks down in the region of low momentum transfer, which turns out to provide a 

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## V. CONCLUSIONS 

