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

Abstract

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 ($m_c\ne 0$) 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.

arXiv comment22 pages (LATEX), 8 figures (EPS); A few clarifying changes made; version published in JHEP

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