Leptoproduction of Heavy Quarks I-- General Formalism and Kinematics of Charged Current and Neutral Current Production Processes

TL;DR

The paper develops a mass-inclusive QCD framework for heavy-quark leptoproduction in both charged- and neutral-current DIS, using factorization and a helicity formalism to handle arbitrary quark and target masses. It provides a detailed leading-order calculation that preserves all masses, revealing substantial deviations from traditional slow-rescaling predictions and showing that mass effects modify both parton-level amplitudes and scaling variables. The helicity approach is shown to yield a cleaner, more physical factorization with simple relationships between hadron and parton helicity structure functions, setting the stage for a complete NLO treatment and phenomenology across fixed-target and collider experiments. Overall, the work establishes a consistent, interpolation-capable framework for heavy-flavor DIS that reconciles threshold and high-energy regimes and informs future analyses of charm and bottom production.

Abstract

Existing calculations of heavy quark production in charged-current and neutral current lepton-hadron scattering are formulated differently because of the artificial distinction of ``light'' and ``heavy'' quarks made in the traditional approach. A proper QCD formalism valid for a wide kinematic range from near threshold to energies much higher then the quark mass should treat these processes in a uniform way. We formulate a unified approach to both types of leptoproduction processes based on the conventional factorization theorem. In this paper, we present the general framework with complete kinematics appropriate for arbitrary masses, emphasizing the simplifications provided by the helicity formalism. We illustrate this approach with an explicit calculation of the leading order contribution to the quark structure functions with general masses. This provides the basis for a complete QCD analysis of charged current and neutral current leptoproduction of charm and bottom quarks to be presented in subsequent papers.

Figures (7)

• Figure 1: The general lepton-hadron scattering process: $N(P) + \ell_1 \rightarrow X(P_X) + \ell_2$ via the exchange of a vector boson, $B(q)$. The lepton momenta are $\ell_{i}$ while the initial and final hadronic momenta are $P$ and $P_{X}$, respectively.
• Figure 2: Pictorial representation of the factorization theorem for the hadron structure functions for inclusive deeply inelastic scattering. The process on the left is $N(P) + B(q) \rightarrow X(P_X)$, and the factorized process on the right is $N(P) \rightarrow a(k_1)$ (represented by the parton distribution function, $f_N^a$) with the successive hard scattering interaction $a(k_1) + B(q)$ (represented by $\omega_{\mu\nu}^a$). The vertical lines indicate an inclusive sum over the final states, $X(P_X)$.
• Figure 3: Leading order hard-scattering amplitude for heavy quark production.
• Figure 4: Percent deviation of leading-order cross section between the "slow-rescaling," Eq. (\ref{['eq:slowresxsii']}), and and complete, Eq. (\ref{['eq:dsdxynu']}), for $E_\nu=80GeV$, $m_c=1.5GeV$: (a) $d\sigma/dy(\nu+s\to c)$ integrated in $x$ over the range $x=[0.1,0.6]$; (b) $d\sigma/dx(\nu+s\to c)$ integrated in $y$ over the range $y=[0.1,0.8]$
• Figure 5: Basic process for inclusive boson B(q) nucleon N(P) scattering: $N(P) + B(q) \rightarrow X(P_X)$, summed over the final state, $X(P_X)$