Axial structure

The weak hadronic current shown in Eq. (2.6) also depends on the axial G_A(Q²) and pseudoscalar G_P(Q²) form factors. The axial one, G_A, has been widely studied in last years [71, 72] in order to determine its functional structure. On the contrary, the pseudoscalar GP ≡ F^P/2MN, is harder to analyze, being its contribution very small in most of the kinematical situations addressed and negligible for the momentum transferred involved in β-decay processes. Moreover, current data are not precise enough to determine the functional form of GA, which is usually parametrized using a dipole form, analogously to the vector form factors,

G_A(Q²) = g_A

1 + _M^Q22 A

2 , (2.84)

where g_A =−1.267 is the axial-vector coupling constant and MA = 1.032(36) GeV is the nucleon axial mass. The gAparameter is determined through β-decay processes with neutrons in the elastic limit Q² → 0 [73], and the axial mass M^Avalue has been extracted from deuterium-filled bubble chamber experiments [17]. More information regarding the functional form of G_Aand the possible quenching of gAcan be found, respectively, in Appendices D and E.

The axial and pseudoscalar form factors can be connected making use of the PCAC (partially conserved axial current) hypothesis (see [74] for details), through the Goldberger-Treiman relation,

G_P(Q²) = 4M_N² Q²+ m²π

G_A(Q²) ; m_π: pion mass . (2.85) In current neutrino-nucleus investigations, one of the main sources of uncertainty comes from the axial form factor, and specifically, its dependence with Q²and M_A. In this sense, recent CCQE neutrino experiments on¹²C, such as MiniBooNE or MINERνA, have estimated higher MAvalues (MA≈ 1.35 GeV) in disagreement with the standard estimations. It must be taken into account that the standard value, M_A= 1.03 GeV, is consistent with deuterium experimental data where nuclear effects are negligible as well as with weak pion production data at low |Q²|. Hence the increase of

2.3. HADRONIC STRUCTURE 37

the axial mass value in these experiments must be interpreted as the lack of some ingredients in the model employed for the data analysis. In particular, the role played by multinucleon effects, such as 2p-2h MEC in CCQE neutrino-nucleus experiments will be explored in Chapter 7 as a possible explanation of the “apparent” increase of M_A.

In Fig. 2.4, we analyze the axial form factors, G_A and G_P, using the world average axial mass value as well as an increase value of 1.35 GeV. Whilst small differences emerge at very low |Q²|, we can observe how G_A increases with M_A for large values of |Q²|. On the contrary, this effect is not visible for G_P due to the factor ¹

1+|Q²|/m²π

where m_π ≪ MA. Moreover, the pseudoscalar form factor falls to zero faster than the axial one which turns into a less relevant contribution of pseudoscalar effects in the region of elastic, QE scattering and beyond.

✵✵ ✵ ✁ ✵✵✁ ✵✁ ✁ ✁✵

Figure 2.4: Axial (G_A) and pseudoscalar (G_P) form factors for two M_A values as a function of

|Q²|.

Finally, it is worth mentioning that the differences between neutrino and antineutrino cross sections, which arise basically from the V-A interference term (2.21), start to disappear as |Q²| increases. Notice that the R_T^{V A}_′ response (see Eq. 2.68) depends on G_A that approaches zero for large |Q²|.

Chapter 3

Charged-current quasielastic neutrino-nucleus scattering

After presenting the formalism of neutrino-nucleon elastic scattering, in this chapter we extend our theoretical description to charged-current neutrino-nucleus interaction in the quasielastic regime and the study of nuclear effects. This is of interest for most recent neutrino experiments that em-ploy different nuclear targets to measure the oscillation parameters at energies where the quasielas-tic regime dominates.

Unlike the elastic scattering where we only consider the inner structure of the nucleon, quasielas-tic reactions require a description of the nuclear structure. In this PhD thesis, the description of the lepton-nucleus interaction and, in particular, the nuclear dynamics, is addressed within the context of the SuperScaling Approach (SuSA), which assumes the existence of universal scaling functions for both electromagnetic and weak interactions. For a proper understanding of this approach, we give a brief description of the relativistic Fermi gas model that will help to introduce the basis of the SuSA model as a semiphenomelogical approach based on the analysis of inclusive (e, e^′) data.

Next, we extend our description to the relativistic mean field (RMF) theory and the relativistic plane wave impulse approximation (RPWIA) models as a more sophisticated procedure to include final-state interaction (FSI) effects as well as the mean field generated by the nuclear constituents in the neutrino-nucleus interaction. The RMF has the merit of treating final-state interactions in a relativistic framework, which is of relevance for the analysis of neutrino experiments. In neutrino-nucleus interactions, after the final-state particles have been created, they propagate out through the nucleus, undergoing strong interactions with the other nucleons inside the nucleus. These “final-state interactions” can significantly alter the momentum and direction of the final-“final-state particles as well as the type and number of particles. Accordingly, pions and nucleons can be absorbed within the nuclear medium or their collisions with other nucleons can generate additional particles. Thus a consistent and relativistic treatment of these interactions is essential to determine the contribution of the different reaction mechanisms to neutrino-nucleus cross section.

The description of the the many-body physics of the interacting nucleons within the RMF and RPWIA models is therefore included in our framework, in the so-called SuSAv2 (SuperScaling Approach version 2) model. This approach has been recently applied to the analysis of QE electron scattering data [38] for several nuclear targets as well as to charged-current quasielastic (CCQE) neutrino-nucleus experiments [39], yielding an accurate description of the experimental data in both cases.

39

40 3. CHARGED-CURRENT QUASIELASTIC NEUTRINO-NUCLEUS SCATTERING

3.1 General formalism of the CCQE process

In this section we show schematically the kinematics involved in studies of lepton scattering from nuclei, focusing on charge-changing neutrino reactions. Most kinematic variables have been pre-viously defined in Chapter 2 for elastic neutrino-nucleon scattering. Here we employ that notation for (ν_l,l⁻) and (ν_l,l⁺) neutrino-nucleus reactions.

We specifically analyze the CCQE neutrino scattering process in which an incident beam of neutrinos with 4-momentum k^µ = (Eν, k_ν) interacts with a nucleus. In the final state, a charged lepton with 4-momentum k^′µ = (E_l^′, k^′_l) emerges as well as an outgoing nucleon. This process is mediated by a weak boson (W) and can be described as,

ν_µ(ν_µ) + A → µ⁻(µ⁺) + p(n) + (A − 1) (3.1) with A the nuclear target and (A − 1) the residual nucleus after the interaction. Compared to the elastic case, the complexity of the nuclear dynamics introduces some uncertainties in the de-scription, related to the inner structure of the nucleus or final-state interactions described above.

Many theoretical approaches evaluate these processes in the Impulse Approximation (IA), which assumes the incident lepton to only interact with a single bound nucleon as shown in Fig. 3.1. The influence of the remaining nucleons over the entire process is taken into account in different ways depending on the nuclear model employed. Hence, the IA describes the nuclear many-body matrix element as a sum of single-nucleon current matrix elements.

Figure 3.1: Schematic view of the charged-current neutrino-nucleus scattering process in the Im-pulse Approximation (IA).

3.1. GENERAL FORMALISM OF THECCQE PROCESS 41