Leptoproduction of Heavy Quarks II -- A Unified QCD Formulation of Charged and Neutral Current Processes from Fixed-target to Collider Energies

TL;DR

The paper develops a unified QCD framework for leptoproduction of heavy quarks across fixed-target to collider energies by adopting a variable flavor-number scheme that seamlessly combines flavor-excitation and flavor-creation mechanisms. It shows how CWZ-based renormalization and factorization, together with explicit subtraction to avoid double counting, resum large logarithms and greatly reduce scale dependence. Numerical results demonstrate the interplay between the two production mechanisms and the improved stability of the total structure function, validating the approach across a broad kinematic range. The work also clarifies the relationship to MSbar, threshold matching between 3- and 4-flavor schemes, and practical scale choices, laying the groundwork for more accurate heavy-quark phenomenology at charm and bottom masses.

Abstract

A unified QCD formulation of leptoproduction of massive quarks in charged current and neutral current processes is described. This involves adopting consistent factorization and renormalization schemes which encompass both vector-boson-gluon-fusion (flavor creation) and vector-boson-massive-quark-scattering (flavor excitation) production mechanisms. It provides a framework which is valid from the threshold for producing the massive quark (where gluon-fusion is dominant) to the very high energy regime when the typical energy scale μis much larger than the quark mass m_Q (where the quark-scattering should be prevalent). This approach effectively resums all large logarithms of the type (alpha_s(mu) log(mu^2/m_Q^2)^n which limit the validity of existing fixed-order calculations to the region mu ~ O(m_Q). We show that the (massive) quark-scattering contribution (after subtraction of overlaps) is important in most parts of the (x, Q) plane except near the threshold region. We demonstrate that the factorization scale dependence of the structure functions calculated in this approach is substantially less than those obtained in the fixed-order calculations, as one would expect from a more consistent formulation.

Figures (11)

• Figure 1: Amplitudes for heavy quark production: (a) order $\alpha _{s}^{0}$ quark-scattering; and (b) order $\alpha _{s}^{1}$ gluon-fusion contributions. At least one of the quarks, say $Q_{2}$, is "heavy" and corresponds to the "Q" used in the text. For flavor changing currents, the two quarks $Q_{1}$ and $Q_{2}$ are different. For neutral currents, they are the same.
• Figure 2: Regions of the $x-\mu _{{\it phy}}$ kinematic plane for a typical physical process involving a heavy quark with mass $m_{Q}$ and the natural QCD calculational schemes for each region.
• Figure 3: General lepton-hadron production amplitude for a heavy quark
• Figure 4: Graphical representation of the factorization formula, Eq. ( \ref{['HelGluFac']}).
• Figure 5: Graphical representation of the three terms which enter the master equation, Eq. ( \ref{['masterEq']}), for the physical structure functions: the subtraction term is placed in the middle to emphasize its similarity both to the quark-scattering (left) and to the gluon-fusion (right) contributions. The $\times$ on the internal quark line in the subtraction term indicates it is close to mass-shell and collinear to the gluon and the hadron momenta.