Infrared divergences and non-lightlike eikonal lines in Sudakov processes

We propose a method to analyze infrared contributions to non-inclusive processes in QCD. We use the one-loop Sudakov form factor as a working example. Borrowing techniques from renormalization theory, we construct counterterms for the contributions from the soft and collinear regions, and we relate them to eikonal Wilson lines taken along non-lightlike directions.Comment: Latex, 1 postscript figure. Version 2: presentation improved and typos corrected, results unchange

Leading-twist Single-transverse-spin asymmetries: Drell-Yan and Deep-Inelastic Scattering

Recently, Brodsky, Hwang and Schmidt have proposed a new mechanism that gives a transverse spin symmetry at leading twist in semi-inclusive deep-inelastic scattering. I show that the new mechanism is compatible with factorization and is due to an transverse-spin asymmetry in the k_T distribution of quarks in a hadron (the "Sivers asymmetry"). An earlier proof that the Sivers asymmetry vanishes because of time-reversal invariance is invalidated by the path-ordered exponential of the gluon field in the operator definition of parton densities. Instead, the time-reversal argument shows that the Sivers asymmetry is reversed in sign in hadron-induced hard processes (e.g., Drell-Yan), thereby violating naive universality of parton densities. Previous phenomenology with time-reversal-odd parton densities is therefore validated.Comment: 12 pages latex. V.2: references corrected. V.3: references added, misprints correcte

Proof of Factorization of Fragmentation Function in Non-Equilibrium QCD

In this paper we prove factorization of fragmentation function in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. We use the background field method of QCD in a pure gauge in path integral approach to prove factorization of fragmentation function in non-equilibrium QCD. Our proof is valid in any arbitrary gauge fixing parameter $\alpha$. This may be relevant to study hadron production from quark-gluon plasma at high energy heavy-ion colliders at RHIC and LHC.Comment: 13 pages latex, (Final Published Version, Annals of Physics

A Unified Theory for the Effects of Stellar Perturbations and Galactic Tides on Oort Cloud Comets

We examine the effects of passing field stars on the angular momentum of a nearly radial orbit of an Oort cloud comet bound to the Sun. We derive the probability density function (PDF) of the change in angular momentum from one stellar encounter, assuming a uniform and isotropic field of perturbers. We show that the total angular momentum follows a Levy flight, and determine its distribution function. If there is an asymmetry in the directional distribution of perturber velocities, the marginal probability distribution of each component of the angular momentum vector can be different. The constant torque attributed to Galactic tides arises from a non-cancellation of perturbations with an impact parameter of order the semimajor axis of the comet. When the close encounters are rare, the angular momentum is best modeled by the stochastic growth of stellar encounters. If trajectories passing between the comet and sun occur frequently, the angular momentum exhibits the coherent growth attributed to the Galactic tides.Comment: 8 pages, 2 figures; accepted to A

Hard Scattering in QCD with Polarized Beams

I show that factorization for hard processes in QCD is also valid when the detected particles are polarized, and that the proof of the theorem determines the operator form for the parton densities. Particular attention is given to the case of transversely polarized incoming hadrons.Comment: 37 pages + 4 figures (postscript available), plain TeX, PSU/TH/10

Over egging the pudding? Comments on Ojala and Thorpe

In a recent paper in ISCJ, Ojala and Thorpe offered a culturally based observation that questions the role and application of coaching in action sports. Their critique is focused on the action sport of snowboarding which, despite its’ comparatively recent inclusion in the Olympics, retains a different, almost collaborative rather than competitive culture more akin to other action sports such as skateboarding and surfing. Ojala and Thorpe then present Problem Based Learning (PBL) as the solution to many of these perceived ills, describing the positive characteristics of the approach and promoting its cultural fit with action sport environments and performers. In this paper we offer a different perspective, which questions the veracity of the data presented and the unquestioningly positive view of PBL as the answer. Our alternative, data-driven perspective suggests that action sport athletes are increasingly positive, or even desirous of good coaching, of which PBL is a possible approach; suitable for some athletes some of the time

Parton Distributions in Light-Cone Gauge: Where Are the Final-State Interactions?

We show that the final-state interaction effects in the single target spin asymmetry discovered by Brodsky et al. can be reproduced by either a standard light-cone gauge definition of the parton distributions with a prescription of the light-cone singularities consistent with the light-cone gauge link, or a modified light-cone gauge definition with a gauge link involving the gauge potential at the spatial infinity.Comment: 9 pages, 2 figures, additional results are adde

Sudakov Logarithm Resummation in Transverse Momentum Space for Electroweak Boson Production at Hadron Colliders

A complete description of W and Z boson production at high-energy hadron colliders requires the resummation of large Sudakov double logarithms which dominate the transverse momentum (q_T) distribution at small q_T. We compare different prescriptions for performing this resummation, in particular implicit impact parameter space resummation versus explicit transverse momentum space resummation. We argue that the latter method can be formulated so as to retain the advantages of the former, while at the same time allowing a smooth transition to finite order dominance at high q_T.Comment: 32 pages, Latex, epsfig, 17 figure

Effects of QCD Resummation on Distributions of Leptons from the Decay of Electroweak Vector Bosons

We study the distributions of leptons from the decay of electroweak vector bosons produced in hadron collisions. The effects of the initial state multiple soft-gluon emission, using the Collins--Soper resummation formalism, are included. The resummed results are compared with the next-to-leading-order results for the distributions of the transverse momentum, rapidity asymmetry, and azimuthal angle of the decay leptons.Comment: 12 pages, 3 figures uuencoded, LaTeX, uses epsf.tex for figures. (Was replaced on 5/2/95 because of mailer problems.

Attitudes towards science: a review of the literature and its implications

This article offers a review of the major literature about attitudes to science and its implications over the past 20 years. It argues that the continuing decline in numbers choosing to study science at the point of choice requires a research focus on students? attitudes to science if the nature of the problem is to be understood and remediated. Starting from a consideration of what is meant by attitudes to science, it considers the problems inherent to their measurement and what is known about students' attitudes towards science and the many factors of influence such as gender, teachers, curricula, cultural and other variables. The literature itself points to the crucial importance of gender and the quality of teaching. Given the importance of the latter we argue that there is a greater need for research to identify those aspects of science teaching that make school science engaging for pupils. In particular, a growing body of research on motivation offers important pointers to the kind of classroom environment and activities that might raise pupils' interest in studying school science and a focus for future research