Basics of QCD Perturbation Theory: TASI 2000

This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. I also cover some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions.Comment: Lectures at TASI summer school, June 200

QCD and Monte Carlo event generators

Shower Monte Carlo event generators have played an important role in particle physics. Modern experiments would hardly be possible without them. In this talk I discuss how QCD physics is incorporated into the mathematical structure of these programs and I outline recent developments including matching between events with different numbers of hard jets and the inclusion of next-to-leading order effects.Comment: Plenary talk by D. Soper at XIV Workshop on Deep Inelastic Scattering (DIS2006

Parton distribution functions in the context of parton showers

When the initial state evolution of a parton shower is organized according to the standard "backward evolution'' prescription, ratios of parton distribution functions appear in the splitting probabilities. The shower thus organized evolves from a hard scale to a soft cutoff scale. At the end of the shower, one expects that only the parton distributions at the soft scale should affect the results. The other effects of the parton distributions should have cancelled. This means that the kernels for parton evolution should be related to the shower splitting functions. If the initial state partons can have non-zero masses, this requires that the evolution kernels cannot be the usual MSbar kernels. We work out what the parton evolution kernels should be to match the shower evolution contained in the parton shower event generator Deductor, in which the b and c quarks have non-zero masses.Comment: 33 pages, 6 figure

On the transverse momentum in Z-boson production in a virtuality ordered parton shower

Cross sections for physical processes that involve very different momentum scales in the same process will involve large logarithms of the ratio of the momentum scales when calculated in perturbation theory. One goal of calculations using parton showers is to sum these large logarithms. We ask whether this goal is achieved for the transverse momentum distribution of a Z-boson produced in hadron-hadron collisions when the shower is organized with higher virtuality parton splittings coming first, followed successively by lower virtuality parton splittings. We find that the virtuality ordered shower works well in reproducing the known QCD result.Comment: 60 pages with three figure

Summing threshold logs in a parton shower

When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in $\alpha_s$ that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.Comment: 83 pages, 8 figure

Structure of parton showers including quantum interference

It is useful to describe a leading order parton shower as the solution of a linear equation that specifies how the state of the partons evolves. This description involves an essential approximation of a strong ordering of virtualities as the shower progresses from a hard interaction to softer interactions. If this is to be the only approximation, then the partons should carry color and spin and quantum interference graphs should be included. We explain how the evolution equation for this kind of a shower can be formulated. We discuss briefly our efforts to implement this evolution equation numerically.Comment: Talk at 2008 Rencontre de Moriond, QCD session. Four page

Effects of subleading color in a parton shower

Parton shower Monte Carlo event generators in which the shower evolves from hard splittings to soft splittings generally use the leading color (LC) approximation, which is the leading term in an expansion in powers of 1/N_\Lc^2, where N_\Lc = 3 is the number of colors. In the parton shower event generator \textsc{Deductor}, we have introduced a more general approximation, the LC+ approximation, that includes some of the color suppressed contributions. In this paper, we explore the differences in results between the LC approximation and the LC+ approximation. Numerical comparisons suggest that, for simple observables, the LC approximation is quite accurate. We also find evidence that for gap-between-jets cross sections neither the LC approximation nor the LC+ approximation is adequate.Comment: 23 pages, 13 figures, published versio