arXiv subjects
Publications and source records attributed to Davison E. Soper.
Calculations of observables in quantum chromodynamics are typically performed using a method that combines numerical integrations over the momenta of final state particles with analytical integrations over the momenta of virtual particles. I describe the most important steps of a method for performing all of the integrations numerically.
Calculations in Quantum Chromodynamics are typically performed using a method pioneered by Ellis, Ross and Terrano in 1981. In this method, one combines numerical integrations over the momenta of final state particles with analytical integrations over the momenta of virtual particles. I discuss a more flexible method in which one performs all of the integrations numerically.
We show that existing proofs of factorization imply the cancellation of certain multiladder contributions that Gotsman, Levin, and Maor had suggested would invalidate the basic factorization theorem in QCD. No modifications of the original argument are necessary, although the details of the example offer useful insight into the mechanisms of factorization.
Calculations of observables in Quantum Chromodynamics are typically performed using a method that combines numerical integrations over the momenta of final state particles with analytical integrations over the momenta of virtual particles. I discuss a method for performing all of the integrations numerically.
The total cross section for scattering virtual photons at high energy is sensitive to pomeron physics. If the photons are sufficiently virtual, QCD perturbation theory applies, so that the reaction probes the short distance pomeron. We study this reaction for present and future e+/- e- colliders.
I review some of the results presented in the working group on diffraction at DIS97, with a particular emphasis on the theory of diffractive hard scattering.
I discuss the one jet inclusive jet cross section, d sigma /dE_T emphasizing the concept of infrared safety and the cone definition of jets. Then I estimate the size of power corrections to the jet cross section, which become important at smaller values of E_T.
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.
Jet production in high energy hadron-hadron collisions can serve as a probe for new physics. I review recent data from CDF and D0 on the high E_T jet cross section. Reporting on recent work of the CTEQ collaboration, I argue that the apparent excess seen in the CDF data may be due to the gluon distribution function used in the theoretical calculation being too small at large x. I discuss data on the dijet angular distribution, which shows no sign of a new physics signal.
Parton distribution functions give the probability to find partons (quarks and gluons) in a hadron as a function of the fraction x of the proton's momentum carried by the parton. They are conventionally defined in terms of matrix elements of certain operators. They are determined from experimental results on short distance scattering of the partons. Integrals of these functions weighted with x^n are calculable using lattice QCD. Some simple models for their behavior have implications that could also be tested in lattice QCD.
Measurement of the distribution of hadronic energy in the final state in deeply inelastic electron scattering at HERA can provide a good test of our understanding of perturbative QCD. For this purpose, we consider the energy distribution function, which can be computed without needing final state parton fragmentation functions. We compute this distribution function for finite transverse momentum q_T at order alpha_s, and use the results to sum the perturbation series to obtain a result valid for both large and small values of transverse momentum.
We study the perturbative QCD series for the hadronic width of the Z boson. We sum a class of large ``pi^2 terms'' and reorganize the series so as to minimize ``renormalon'' effects. We also consider the renormalization scheme-scale ambiguity of the perturbative results. We find that, with three nontrivial known terms in the perturbative expansion, the treatment of the pi^2 terms is quite important, while renormalon effects are less important. The measured hadronic width of the Z is often used to determine the value of alpha_s(M_Z^2). A standard method is to use the perturbative expansion for the width truncated at order alpha_s^3 in the MS-bar scheme with scale mu = M_Z. We estimate that the determined value of alpha_s(M_Z^2) should be increased by 0.6% compared to the value extracted with this standard method. After this adjustment for pi^2 and renormalon effects, we estimate that the uncertainty in alpha_s(M_Z^2) arising from QCD theory is about 0.4%. This is, of course, much less than the experimental uncertainty of about 5%.
Diffractive parton distribution functions give the probability to find a parton in a hadron if the hadron is diffractively scattered. We provide an operator definition of these functions and discuss their relation to diffractive deeply inelastic scattering and to photoproduction of jets at HERA. We perform a calculation in the style of ``constituent counting rules'' for the behavior of these functions when the detected parton carries almost all of the longitudinal momentum transferred from the scattered hadron.
We review the current status of the high order perturbative QCD evaluation of the hadronic decay rates of the Z and Higgs bosons. A systematic classification of the various types of QCD corrections to $O(α_s^2)$ and $O(α_s^3)$ is made and their numerical status is clarified.
The main topics covered in this summary talk are the Large Hadron Collider, heavy ion collisions, renormalons, parton distribution functions, measurements of the strong coupling and the top quark. Of special interest this year was the discovery of the top quark by the CDF and D0 groups at Fermilab. I conclude that the evidence is compelling and that the best fit of the Standard Model top hypothesis to the data gives a top mass of $170 +/- 9 GeV with a good chisquared.
We discuss cross sections for hadron + hadron to 2 jets + anything in which three jet variables are measured. Such cross sections are useful especially for determining parton distributions. We define a new cross section d sigma/dX_A dX_B d eta_* for which the perturbation theory is nicely behaved even in the kinematic regime where the parton distributions are probed at large momentum fractions. The cross section dσ/dE_{T1}\, dη_1\, dη_2, which has been used in the past, is not so well behaved in this region. We calculate these cross sections at order $α_s^3$ in QCD.
The CTEQ and MRS parton distributions involve a substantial number (~30) of parameters that are fit to a large number (~900) of data. Typically, these groups produce fits that represent a good fit to the data, but there is no substantial attempt to determine the errors associated with the fits. Determination of errors would involve consideration of the experimental statistical and systematic errors and also the errors in the theoretical formulas that relate the measured cross sections to parton distributions. We discuss the principles that would be needed in such an error analysis. These principles are standard. However, certain aspects of the principles appear counter-intuitive in the case of a large number of data. Accordingly, we strive to devote careful attention to the logic behind the methods.
We evaluate the effect of a virtual top quark on the coefficient of $α_{s}^{2}$ in the decay rates $Γ(Z \rightarrow {\rm hadrons})$ and $Γ(Z \rightarrow b\overline{b} )$. We treat the dependence on the top quark mass exactly instead of using a large mass expansion. The present work completes the evaluation of the $α_{s}^{2}$ contributions to these quantities. The calculation uses both the $\overline{\rm MS}$ and Collins-Wilczek-Zee renormalization prescriptions. The results can be applied to the hadronic decays of the $τ$-lepton.