New solutions of Heun general equation

We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behavior at only one of the singular points of the equation; the sum, however, has correct behavior

Top quark physics in hadron collisions

The top quark is the heaviest elementary particle observed to date. Its large mass makes the top quark an ideal laboratory to test predictions of perturbation theory concerning heavy quark production at hadron colliders. The top quark is also a powerful probe for new phenomena beyond the Standard Model of particle physics. In addition, the top quark mass is a crucial parameter for scrutinizing the Standard Model in electroweak precision tests and for predicting the mass of the yet unobserved Higgs boson. Ten years after the discovery of the top quark at the Fermilab Tevatron top quark physics has entered an era where detailed measurements of top quark properties are undertaken. In this review article an introduction to the phenomenology of top quark production in hadron collisions is given, the lessons learned in Tevatron Run I are summarized, and first Run II results are discussed. A brief outlook to the possibilities of top quark research a the Large Hadron Collider, currently under construction at CERN, is included.Comment: 84 pages, 32 figures, accepted for publication by Reports on Progress in Physic

A Pedagogical Review of Electroweak Symmetry Breaking Scenarios

We review different avenues of electroweak symmetry breaking explored over the years. This constitutes a timely exercise as the world's largest and the highest energy particle accelerator, namely, the Large Hadron Collider (LHC) at CERN near Geneva, has started running whose primary mission is to find the Higgs or some phenomena that mimic the effects of the Higgs, i.e. to unravel the mysteries of electroweak phase transition. In the beginning, we discuss the Standard Model Higgs mechanism. After that we review the Higgs sector of the Minimal Supersymmetric Standard Model. Then we take up three relatively recent ideas: Little Higgs, Gauge-Higgs Unification, and Higgsless scenarios. For the latter three cases, we first present the basic ideas and restrict our illustration to some instructive toy models to provide an intuitive feel of the underlying dynamics, and then discuss, for each of the three cases, how more realistic scenarios are constructed and how to decipher their experimental signatures. Wherever possible, we provide enough pedagogical details, which the beginners might find useful.Comment: 45 pages, Review based on a series of lectures; v2: 63 pages, substantially expanded, references added, to appear in `Reports on Progress in Physics