We attempt a general phenomenological analysis of the neutral weak current in the inclusive neutrino reactions using the parton model as a tool. From the recently reported data on these processes we determine the strengthH of the neutral-current interaction as well as the amount of theVA interference. We find (H/G)²=0·54±0·06 whereG is the Fermi coupling constant and theVA interference contribution turns out to be 33±23%. We also discuss the comparison of the data with various models for the neutral hadronic current.

On the basis of some general assumptions on the deep inelastic structure functions, such as scaling and chiral symmetry we determine the values of {(H_V³)²+(H_A³)²}+η{(H_V⁰)²+(H_A⁰)²} andH_V³H_A³+ηH_V⁰H_A⁰ whereH_V^3,0 andH_A^3,0 are the four coupling constants characterizing the hadronic neutral current andη is the ratio of the isoscalar to isovector structure functions. General expressions are given for the kinematical averages 〈v〉 and 〈Q²〉 for the neutral-current reactions in terms of the coupling constants. This analysis does not depend on the validity of the quark-parton model.

The contribution of neutral spin-1 gluons to the deep inelastic neutral-current processesv(v)+N→v(v)+ hadrons is worked out in the parton model. Such a contribution violates Bjorken scaling strongly.

In order to reconcile the life time of the new particle observed in the cosmic ray neutrino experiment with its production rate, it is proposed that the particle has a new quantum number (κ) which may be assigned to leptons and hadrons. In the production of the new particle, assumed to be a heavy charged lepton,κ is conserved by creating an associated lepton-hadron pair. Suppression of theκ-violating interaction is invoked to interpret the long life time of this particle.

Deep inelastic weak and electromagnetic processes are considered within the parton framework taking the partons to be integrally charged quarks and coloured gluons. Despite the participation of the spin-one gluons in these processes, scaling is shown to be maintained by treating the problem in a unified gauge model based on the groupSU (3)_colour⊗SU_L (2)⊗U(1). This is a consequence of the vector-dominance type of couplings between the gluons and the weak or electromagnetic vector bosons which are induced by the spontaneous breakdown of gauge symmetry. As a further consequence it is found that in the asymptotic region far above the gluon masses the colour octet parts of the weak and electromagnetic currents of the quarks are damped so that, in particular, the integrally charged quarks behave as fractionally charged quarks in this region.

It is pointed out that the coupling characterizing theψ-γ vertex must change substantially between the limits,ψ on mass-shell which occurs inψ→e⁺e⁻ and photon on mass-shell which is relevant in radiative decays likeψ→ππγ, ψ→ηγ and photoproduction ofψ. This has the consequence that the value ofψN total cross section must be larger than what is inferred from the use of naive vector dominance in photoproduction.

We show that experimental data on inclusive neutrino reactions can be used to obtain general bounds on the coupling constants of the isovector part of the hadronic weak neutral current provided this isovector current is related to the charged current by isospin rotation. These bounds are free from the assumption of a specific model for the neutral current as well as any dynamical assumption on the hadronic structure functions. We derive upper bounds on the coupling constants which involve only the cross sections for isospin-averaged nucleon target as well as lower bounds which require a knowledge of the cross sections for proton and neutron separately.

By using Kikkawa’s method the equivalence of the nonrenormalizable pair interaction$$\bar \psi \psi \phi ^2 $$ to a renormalizable theory is proved. Equivalence relationships between a few other nonrenormalizable and renormalizable interactions are also indicated.

We study a model of quark confinement defined by the vanishing of colour currents. The model is shown to be equivalent to quantum chromodynamics and this equivalence is interpreted as due to the compositeness of the colour gluons. The Green’s functions of the theory are found to contain nontrivial structure only for colour singlet composites which can be identified with hadrons.

Defining the ratiosr_p =σ(vp →vx)/σ(vp →μ⁻x) and$$\bar r_p = \sigma (\bar \nu p \to \bar \nu x)/\sigma (\bar \nu p \to \mu ^ + x)$$ we obtain the bounds 0.28 ⩽r_p ⩽ 0.61 and$$0 \cdot 15 \leqslant \bar r_p \leqslant 0 \cdot 37$$ using only the parton model and the data of CDHS group with iron target. We also give the complete set of parton-model relations which would allow the determination of all the neutral-current coupling constants from inclusive cross sections alone.

We find the classical solutions of a model of quark confinement defined by the vanishing of colour currents. Both plane-wave type of solutions extending all over space as well as string-type of solutions confined to restricted regions of space are found.

We analyse all the neutral-current phenomena following from the general class of gauge models based on the group SU(2)_L ⊗ SU(2)_R ⊗ U(1). It is found that the neutral-current couplings in these models bear a remarkable similarity to those in the standard Weinberg-Salam gauge model. The parameter which plays the role of sin²ϑ_w is found to lie between 0 and 1/2. Comparison with experimental data shows that even a model with the ratio of the masses of the twoZ bosons as small as 1.9 is not ruled out.

Ifμ-e universality is assumed, there are 17 neutral-current parameters of current experimental interest, including the parity-violating nuclear force sector. We deduce the general relations among these parameters implied by gauge models. In single-Z boson models, there are 10 relations, while two-boson models lead to 4 relations. Ifμ-e universality is abandoned, the number of parameters increases to 31, while the number of relations becomes 21 in single-boson models and 12 in two-boson models. We derive all these relations.

We study in detail the factors that influence the unification relations among the coupling parameters of strong and electroweak interactions. We find that the factor that decides the unification relations in a theory is the fermion content of the theory. The specific ‘observed’ group of strong and electroweak interactions used and the specific unification group in which these interactions are embedded are largely irrelevant. In particular, we find that the unification value of the electroweak mixing angle is the same for almost all models of interest. We also explicitly illustrate that the canonical value 3/8 of the mixing angle is a characteristic result of the currently popular sequential doublets scheme of fermions. Addition of extra fermion singlets reduces the mixing angle to 1/4. We propose this sequential triplets scheme of fermions as an interesting alternative to the current scheme.

A general analysis of the renormalisation corrections to the unification results for the coupling constants of strong and electroweak interactions is attempted. In particular, the effects of introducing an energy scale intermediate between the unification energy and the low-energy regions are studied and found to be important. This analysis is applied to unification schemes of both kinds, namely, unification at superhigh energies, and unification at accessible energies.

We give current algebra arguments to show that toO(α) the colour octet vertices do not renormalize the effective weak vertex between colour singlet hadrons in models with broken colour symmetry. The result does not depend on the details of the mixing between colour gluons and electro-weak bosons.

The two-gluonic decay modes ofW andZ in the broken colour model with integrally charged quarks are considered. The gluonic branching ratios are found to be 3% and 2·7% forW andZ respectively. The angular distributions of the decays ofW andZ to two jets of hadrons are also worked out.

We consider spinor, scalar and vector fields with colour degrees of freedom and find the classical solutions when the constraint of vanishing colour currents is imposed. We find that there are no non-trivialc-number solutions for spinor fields transforming as a triplet under SU(3), although solutions exist for scalar and vector fields. We also show that the colour current of spinor fields coupled to an instanton is zero.

We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV^±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q²|≪M², in addition to the usual condition |q²|≪W²,W being theV⁺V⁻ invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q²||q′²|W⁴ ≪ 16M⁸, in addition to |q²| ≪M², |q′²| ≪M² and |q²| ≪W², |q′²| ≪W². Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q²| ≪W² and |q′²| ≪W².

We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q²||q′²|W⁴ ≪ 16M⁸ is shown to be removed.

Colour SU(3) symmetry is broken spontaneously by the introduction of coloured Higgs scalars in the standard SU(3)×SU(2)×U(1) model, so as to make the quarks integrally charged. The resulting couplings of the Higgs bosons with the gauge bosons are worked out.

We give plausible interpretations of the unusual events seen in the proton decay detector at Kolar Gold Fields indicating the existence of a massive (≳2GeV) long lived (10⁻⁸−10⁻⁹s) particle. We show that it is possible to accommodate the particle in the standard model as a fourth generation neutrino, or inE₆ grand unified theory as a neutral fermion occurring in27 representation or in supersymmetric theory as a scalar neutrino. However, there is a difficulty in explaining the large production rate for the particle.

We show how the position and residue of theS matrix pole can remain stable under changes in the form of the parametrization of theS matrix elements. We also derive a relation among the shifts in the Breit-Wigner resonance parameters under the same changes and verify the relation numerically for the case of Δ(1232). Despite its stability, the pole does not provide a unique definition of the resonance because of the existence of shadow poles.

We construct the algebra of the creation and destruction operators for spin 1/2 particles obeying a new exclusion principle which is “more exclusive” than Pauli’s exclusion principle: an orbital state shall not contain more than one particle, whether spin up or spin down. The consequences of this algebra are studied and applications to the Hubbard model in condensed matter physics are indicated.

We propose a new two-parameter deformation of the algebra of creation and destruction operators, which allows the construction of a new family of Hillbert spaces with positive definite inner product. This provides a continuous interpolation between two new forms of statistics named orthofermi and orthobose statistics. Positivity of the inner product over the two-parameter region is discussed.

A general analysis of bilinear algebras of creation and destruction operators is performed. Generalizing the earlier work on the single-parameterq-deformation of the Heisenberg algebra, we study two-parameter and four-parameter algebras. Two new forms of quantum statistics called orthofermi and orthobose statistics and aq-deformation interpolating between them have been found. In the Fock representation, quadratic relations among destruction operators, wherever they are allowed, are shown to follow from the bilinear algebra of creation and destruction operators. Postitivity of the Hilbert space for the four-parameter algebra has been studied in the two-particle sector, but for the two-parameter algebra, results are presented up to the four-particle sector.

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ‘infinite’, Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are: new algebras for infinite statistics,q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ‘doubly-infinite’ statistics, many representations of orthostatistics, Hubbard statistics and its variations.

The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.

We have identified some important and worthwhile physics opportunities with a possible neutrino detector located in India. Particular emphasis is placed on the geographical advantage with a stress on the complimentary aspects with respect to other neutrino detectors already in operation.

Some unusual and unexplained events (the so-called Kolar events) were interpreted in $\it{Pramana – J. Phys}$. $\bf{82}$, 609 (2014). This article is a corrigendum to it.

The upcoming 50 kt magnetized iron calorimeter (ICAL) detector at the India-based Neutrino Observatory (INO) is designed to study the atmospheric neutrinos and antineutrinos separately over a wide range of energies andpath lengths. The primary focus of this experiment is to explore the Earth matter effects by observing the energy and zenith angle dependence of the atmospheric neutrinos in the multi-GeV range. This study will be crucial toaddress some of the outstanding issues in neutrino oscillation physics, including the fundamental issue of neutrino mass hierarchy. In this document, we present the physics potential of the detector as obtained from realistic detector simulations.We describe the simulation framework, the neutrino interactions in the detector, and the expected responseof the detector to particles traversing it. The ICAL detector can determine the energy and direction of the muons to a high precision, and in addition, its sensitivity to multi-GeV hadrons increases its physics reach substantially. Itscharge identification capability, and hence its ability to distinguish neutrinos from antineutrinos, makes it an efficient detector for determining the neutrino mass hierarchy. In this report, we outline the analyses carried out for the determination of neutrino mass hierarchy and precision measurements of atmospheric neutrino mixing parameters at ICAL, and give the expected physics reach of the detector with 10 years of runtime. We also explore the potential of ICAL for probing new physics scenarios like CPT violation and the presence of magnetic monopoles.