TRANSVERSE MOMENTUM DISTRIBUTIONS FROM EFFECTIVE FIELD THEORY

We present a factorization theorem for the low transverse momentum (pT) and rapidity (Y) distribution of the Higgs and electroweak gauge bosons using the Soft-Collinear Effective Theory. In the region M ≫ pT ≫ ΛQCD, where M denotes the mass of the electroweak object, the factorization formula is given in terms of perturbatively calculable functions and the standard PDFs. For pT ~ ΛQCD, the factorization theorem is given in terms of non-perturbative Impact-parameter Beam Functions (iBFs) and an Inverse Soft Function (iSF). The iBFs correspond to completely unintegrated PDFs and can be interesting probes of momentum distributions in the nucleon. The iBFs and the iSF are grouped together and written as a product of a gauge invariant and non-perturbative Transverse Momentum Function (TMF) with the standard PDFs. We present results of NLL resummation for the Higgs and Z-boson distributions and give a comparison with Tevatron data.

BAND EDGE EIGENFUNCTIONS AND EIGENVALUES FOR PERIODIC POTENTIALS THROUGH THE QUANTUM HAMILTON–JACOBI FORMALISM

We demonstrate the procedure of finding the band edge eigenfunctions and eigenvalues of periodic potentials, through the quantum Hamilton–Jacobi formalism. The potentials studied here are the Lamé and associated Lamé, which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function p, obeying a Riccati type equation in the complex x-plane. Essential use is made of suitable conformal transformations, which lead to the eigenvalues and the eigenfunctions corresponding to the band edges, in a straightforward manner. Our study reveals interesting features about the singularity structure of p, underlying the band edge states.

BOUND STATE WAVE FUNCTIONS THROUGH THE QUANTUM HAMILTON–JACOBI FORMALISM

The bound state wave functions for a wide class of exactly solvable potentials are found by utilizing the quantum Hamilton–Jacobi formalism of Leacock and Padgett. It is shown that, exploiting the singularity structure of the quantum momentum function, until now used only for obtaining the bound state energies, one can straightforwardly find both the eigenvalues and the corresponding eigenfunctions. After demonstrating the working of this approach through a few solvable examples, we consider Hamiltonians, which exhibit broken and unbroken phases of supersymmetry. The natural emergence of the eigenspectra and the wave functions, in both unbroken and the algebraically nontrivial broken phase, demonstrates the utility of this formalism.

The Projected Performance Model: Relating Cognitive and Performance Antecedents of Psychological Momentum

Psychological momentum has been an elusive phenomenon in sport psychology research. The present study utilized a two-round free-throw shooting contest between pairs of participants to examine factors which influenced participants' perceptions of momentum and subsequent changes in performance. Factors hypothesized to contribute to perceptions of momentum were divided into three categories of Personal Variables, Situational Variables, and Self-ratings of Performance. Perceptions of momentum could be significantly predicted by both Situational Variables and Self-ratings of Performance. Changes in performance, however, were only significantly predicted by Situational Variables. These findings support the notion that attributions of positive and negative psychological momentum function simply as a labeling process in the evaluation of performance, with little or no effect on subsequent performance. Based on these findings and other research on psychological momentum, a theoretical model (Projected Performance Model) is proposed to conceptualize more clearly fluctuations in performance and their relationship to the construct of psychological momentum.

Energy Eigenvalues for a Class of One-Dimensional Potentials via Quantum Hamilton–Jacobi Formalism

Using quantum Hamilton–Jacobi formalism of Leacock and Padgett, we show how to obtain the known energy eigenvalues for a class of widely studied, solvable, one-dimensional potentials. An alternative method to the one given by us, is provided which unambiguously determines the quantum momentum function and hence the eigenvalues for these Hamiltonians.