International Journal of Modern Physics A

The search for squarks in R-parity violating supersymmetry in ep collisions at HERA is reviewed. In the full data sample used by the H1 collaboration corresponding to about 0.5 fb^-1 no deviation from Standard Model predictions was observed and limits were set in phenomenological models. For example, for a R-parity violating coupling of electromagnetic strength λ′_11k = 0.3(k ∈ {1, 2}), the mass bound on the corresponding right-handed down-type squark is . The results are compared to other searches for supersymmetry. In particular, they are put in context with more recent results from the Large Hadron Collider (LHC). An outlook is given on search opportunities at a future ep collider.

With a bird's-eye view, we survey the landscape of Calabi–Yau threefolds, compact and noncompact, smooth and singular. Emphasis will be placed on the algorithms and databases which have been established over the years, and how they have been useful in the interaction between the physics and the mathematics, especially in string and gauge theories. A skein which runs through this review will be algorithmic and computational algebraic geometry and how, implementing its principles on powerful computers and experimenting with the vast mathematical data, new physics can be learnt. It is hoped that this interdisciplinary glimpse will be of some use to the beginning student.

We show that parity operator plays an interesting role in Dirac equation in (1+2) dimensions and can be used for defining chiral charges. Further the "anomalous" current induced by an external gauge field can be related to the anomalous divergence of an axial vector current which arises due to quantum radiative corrections provided by triangular loop Feynman diagrams in analogy with the corresponding axial anomaly in (1+3) dimensions. It is shown that the nonconservation of "chiral charge" due to anomaly is related with the topological Chern–Simons charge. As an application pair creation of massless fermions in electric field is discussed.

Generation of the neutrino masses and leptogenesis (LG) in the standard model extended by the heavy Majorana fermions is considered. Classification of LG scenarios according to the new fermion mass spectra is given, where singlet–triplet LG is considered for the first time. The upper bound on the CP asymmetry relevant for LG with hierarchical heavy neutrinos (Davidson–Ibarra bound) is revised, and shown that in the case of one massless neutrino it essentially depends on the type of the light neutrino mass hierarchy. The resonant scenarios, which help to avoid the problem of extremely high reheating temperature in the early universe, are discussed. In particular, we present new simplified, generalized and detailed formulation of freed LG, which violates Davidson–Ibarra bound in a special class of models.

The bottomonium states due to their varying binding energies dissolve at different temperatures and thus their nuclear modification factors and relative yields have potential to map the properties of Quark–Gluon Plasma (QGP). We estimate the suppression of bottomonia states due to color screening in an expanding QGP of finite lifetime and size with the conditions relevant for PbPb collisions at Large Hadron Collider. The properties of ϒ states and recent results on their dissociation temperatures have been used as ingredients in the study. The nuclear modification factors and the ratios of yields of ϒ states are then obtained as a function of transverse momentum and centrality. We compare our theoretical calculations with the bottomonia yields measured with CMS in PbPb collisions at . The model calculations explain the data very well.

In the context of F-theory, we study the related eight-dimensional super-Yang–Mills theory and reveal the underlying supersymmetric quantum mechanics algebra that the fermionic fields localized on the corresponding defect theory are related to. Particularly, the localized fermionic fields constitute a graded vector space, and in turn this graded space enriches the geometric structures that can be built on the initial eight-dimensional space. We construct the implied composite fiber bundles, which include the graded affine vector space and demonstrate that the composite sections of this fiber bundle are in one-to-one correspondence to the sections of the square root of the canonical bundle corresponding to the submanifold on which the zero modes are localized.

We apply Bogoliubov compensation principle to the problem of forward–backward asymmetry in production at TEVATRON. The nontrivial solution of compensation equation for anomalous four-fermion effective interaction of doublets of heavy and light quarks leads to possibility of existence of vector bound states (resonance). The coupling of the bound state to , u pair is calculated. With this result we obtain satisfactory description of totality of data on the effect of FB asymmetry including slope of effect dependence on invariant mass. Predictions for the resonance mass and production cross-section at LHC are presented.

For the newly proposed coupled (but equivalent) Lagrangians for the supersymmetric (SUSY) system of a one (0+1)-dimensional spinning relativistic particle, we derive the Noether conserved charges corresponding to its (super)gauge, Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST and ghost-scale symmetry transformations. We deduce the underlying algebra amongst the continuous symmetry operators and corresponding conserved charges. We point out a novel observation that emerges, for this specific SUSY system, when we discuss it within the framework of BRST formalism. In particular, the requirement of the physicality criteria with the (anti-)BRST charges leads to a completely new observation because, as it turns out, one of the primary constraints does not annihilate the physical state of the theory. We have never come across this kind of result in the realm of BRST approach to usual gauge theories. We provide the physical and theoretical reasons behind the above observation.

The Unruh effect for the rate of emission and absorption of neutral massive Majorana spinor particles — plausible constituents of the Dark Matter — in a Rindler space–time is thoroughly investigated. The corresponding Bogoliubov coefficients are explicitly calculated and the consistency with Fermi–Dirac statistics and the Pauli principle is actually verified.

The nonleptonic decays from and to an orbitally excited P-wave charmed meson are studied within the naive factorization hypothesis. Based on the Mandelstam formalism, and under the framework of the improved Bethe–Salpeter method, the hadronic matrix elements of the decays and are calculated, in which nonperturbative QCD effects are well considered by overlapping integral over the relativistic Salpeter wave functions of initial and final states. Some of these decays have sizable branching fractions and are expected to be detected in the current and near future experiments.

Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints has structure functions, and provides an algebraically consistent way of discretizing the Dirac first-class constraint algebra for general relativity. This paper successfully formulates the Wheeler–DeWitt scheme of quantization of the canonical tensor model; the ordering of operators in the constraints is determined without ambiguity by imposing Hermiticity and covariance on the constraints, and the commutation algebra of constraints takes essentially the same form as the classical Poisson algebra, i.e. is first-class. Thus one could consistently obtain, at least locally in the configuration space, wave functions of "universe" by solving the partial differential equations representing the constraints, i.e. the Wheeler–DeWitt equations for the quantum canonical tensor model. The unique wave function for the simplest nontrivial case is exactly and globally obtained. Although this case is far from being realistic, the wave function has a few physically interesting features; it shows that locality is favored, and that there exists a locus of configurations with features of beginning of universe.

Generalized field equations of linear gravity are formulated on the basis of octons. When compared to the other eight-component noncommutative hypercomplex number systems, it is demonstrated that associative octons with scalar, pseudoscalar, pseudovector and vector values present a convenient and capable tool to describe the Maxwell–Proca-like field equations of gravitoelectromagnetism in a compact and simple way. Introducing massive graviton and gravitomagnetic monopole terms, the generalized gravitational wave equation and Klein–Gordon equation for linear gravity are also developed.