Introduction

In Chapters 10–13, we have discussed (anti)neutrino interactions onthe free nucleon target leading to quasielastic (Chapter 10), inelastic(Chapters 11 and 12), and deep inelastic scattering (Chapters 13) dependingupon the energy transferred to the target and the four-momentum transfersquared. The study of such processes is important to understand the variousbasic weak interaction processes induced by (anti)neutrinos from the freenucleons and determine the quasielastic form factors, transition formfactors, and the structure functions of the nucleon at the W NN(ZN N) vertex. In recent times, the study of(anti)neutrino reactions from the nuclear targets has been emphasized asalmost all the present generation (anti)neutrino experiments use moderate toheavy nuclear targets like 12C, 16O, 40Ar,56Fe, 208Pb, where the interactions take placewith the nucleons that are bound inside the nucleus. Various experimentslike MINERvA, NOvA, T2K, etc., are being performed in the few GeV energyregion where the contribution to the scattering cross section comes from allthe possible channels, viz., quasielastic, inelastic, and deep inelasticscattering processes. A good understanding of the nuclear cross sectionswould be very helpful in analyzing these experiments. The precision withwhich the basic neutrino–nucleon cross sections in nuclear targetsare known is still not better than 20–30%.

Neutrino oscillation experiments measure events that are a convolution of

(i) energy-dependent neutrino flux and

(ii) energy-dependent cross section.

Moreover, the nuclear medium effects modulating the cross sections are energydependent. Therefore, it is highly desirable that we understand the energydependence of nuclear medium effects in neutrino scattering processes; thisunderstanding will help in achieving the future goals of physicists involvedin studying CP violation and the mass hierarchy problem in the phenomenologyof neutrino oscillations (Chapter 18).

Broadly, we may divide nuclear processes induced by neutrinos into twocategories. The first one is the exclusive reactions

where Zi (Z f ) isthe charge of initial (final) nucleus. In this case, the final nucleus isleft either in the ground state or in an excited state, which decays intosome final nuclear states through electromagnetic or weak interactions byemitting photons or charged leptons which are observed.

Introduction

Hadrons are strongly interacting particles which also participate in weak andelectromagnetic interactions. They are not elementary particles and arecomposed of quarks, which come in six flavors; and each flavor comes inthree colors (R, B, andG) as shown in Table Hadrons are specified by their quantumnumbers like spin, parity, isospin, strangeness, baryon number, etc., andare classified as mesons and baryons on the basis of their quark content.Mesons are the bound states of a quark and an antiquark pair(qq), while baryons are the bound states of threequarks (qqq). They are bound in such a way that thephysical states of mesons and baryons

are color singlets. The strong forces which bind the quarks together, in thecase of baryons, or quarks and antiquarks together, in the case of mesons,are provided by the exchange of massless vector fields between them calledthe gluons. The dynamics of the strong forces, that is, the binding of thequarks and antiquarks and their interactions is described by the theory ofstrong interactions known as quantum chromodynamics (QCD), in a way similarto QED which describes the interactions among charged particles. In Tables6.2 and 6.3, some of the low lying mesons and baryons, which are consideredin this chapter while discussing their weak interactions, are listed alongwith their quark contents and other quantum numbers.

The theory of the weak interaction of hadrons is not as simple as the weakinteraction of leptons, which has been described in the previous chapter. Wehave seen that the interaction Hamiltonian of the weak interaction, in thecase of leptons, is described by

where

The currents here are of the V − A type. Thesecurrents lμ are constructed from the lepton fieldsψl (x) described by the Diracequation for a point spin particle. In the case of hadrons, the interactionis also of the current × current type with V −A currents at the level of quarks which are considered as pointparticles. However, the hadrons are not point particles.