The Heavy Quark Parton Oxymoron -- A mini-review of Heavy Quark Production theory in PQCD

Conventional perturbative QCD calculations on the production of a heavy quark ``$H$'' consist of two contrasting approaches: the usual QCD parton formalism uses the zero-mass approximation ($m_H=0$) once above threshold, and treats $H$ just like the other light partons; on the other hand, most recent ``NLO'' heavy quark calculations treat $m_H$ as a % large parameter and always consider $H$ as a heavy particle, never as a parton, irrespective of the energy scale of the physical process. By their very nature, both these approaches are limited in their regions of applicability. This dichotomy can be resolved in a unified general-mass variable-flavor-number scheme, which retains the $m_H$ dependence at all energies, and which naturally reduces to the two conventional approaches in their respective region of validity. Recent applications to lepto- and hadro-production of heavy quarks are briefly summarized.Comment: Talk given at DIS97, Chicago; 8 pages; Latex, use aipproc.st

Charm Production in Deep Inelastic Scattering from Threshold to High $Q^{2}

Charm final states in deep inelastic scattering constitute $\sim 25$ of the inclusive cross-section at small $x$ as measured at HERA. These data can reveal important information on the charm and gluon structure of the nucleon if they are interpreted in a consistent perturbative QCD framework which is valid over the entire energy range from threshold to the high energy limit. We describe in detail how this can be carried out order-by-order in PQCD in the generalized \msbar formalism of Collins (generally known as the ACOT approach), and demonstrate the inherent smooth transition from the 3-flavor to the 4-flavor scheme in a complete order $\alpha_s$ calculation, using a Monte Carlo implementation of this formalism. This calculation is accurate to the same order as the conventional NLO $F_2$ calculation in the limit $\frac{Q}{m_c} >> 1$. It includes the resummed large logarithm contributions of the 3-flavor scheme (generally known in this context as the fixed-flavor-number or FFN scheme) to all orders of $\alpha_s\ln(m_c^2/Q^2)$. For the inclusive structure function, comparison with recent HERA data and the existing FFN calculation reveals that the relatively simple order-$\alpha_s$ (NLO) 4-flavor ($m_c \neq 0$) calculation can, in practice, be extended to rather low energy scales, yielding good agreement with data over the full measured $Q^2$ range. The Monte Carlo implementation also allows the calculation of differential distributions with relevant kinematic cuts. Comparisons with available HERA data show qualitative agreement; however, they also indicate the need to extend the calculation to the next order to obtain better description of the differential distributions.Comment: 22 pages (LATEX), 8 figures (EPS); A few clarifying changes made; version published in JHE

Collider Inclusive Jet Data and the Gluon Distribution

Inclusive jet production data are important for constraining the gluon distribution in the global QCD analysis of parton distribution functions. With the addition of recent CDF and D0 Run II jet data, we study a number of issues that play a role in determining the up-to-date gluon distribution and its uncertainty, and produce a new set of parton distributions that make use of that data. We present in detail the general procedures used to study the compatibility between new data sets and the previous body of data used in a global fit. We introduce a new method in which the Hessian matrix for uncertainties is ``rediagonalized'' to obtain eigenvector sets that conveniently characterize the uncertainty of a particular observable.Comment: Published versio

The Parton Structure of the Nucleon and Precision Determination of the Weinberg Angle in Neutrino Scattering

A recently completed next-to-leading-order program to calculate neutrino cross sections, including power-suppressed mass correction terms, has been applied to evaluate the Paschos-Wolfenstein relation, in order to quantitatively assess the validity and significance of the NuTeV anomaly. In particular, we study the shift of $\sin^2 \theta_{\mathrm{W}}$ obtained in calculations with a new generation of PDF sets that allow $s(x)\neq \bar{s}(x)$, enabled by recent neutrino dimuon data from CCFR and NuTeV, as compared to the previous $s = \bar{s}$ parton distribution functions like CTEQ6M. The extracted value of $\sin^2 \theta_{\mathrm{W}}$ is closely correlated with the strangeness asymmetry momentum integral $\int_{0}^{1}x[s(x)-\bar{s}(x)] dx$. We also consider isospin violating effects that have recently been explored by the MRST group. The results of our study suggest that the new dimuon data, the Weinberg angle measurement, and other data sets used in global QCD parton structure analysis can all be consistent within the Standard Model.Comment: 4 page