Open Heavy Flavor Production in QCD -- Conceptual Framework and Implementation Issues

TL;DR

The paper tackles heavy-flavor production in QCD by contrasting conventional fixed-flavor and zero-mass schemes, then advocates a unified VFNS based on Collins' factorization with massive partons. It introduces the ACOT($$) prescription, which uses a kinematic rescaling variable to enforce correct threshold behavior and stabilize predictions across energy scales. The approach yields robust, experimentally compatible results for charm production in DIS/HERA and is positioned as a practical tool for global QCD analyses, including potential non-perturbative heavy-flavor components. Overall, the work provides a theoretically solid, implementable framework for incorporating heavy-quark mass effects consistently in high-energy processes."

Abstract

Heavy flavor production is an important QCD process both in its own right and as a key component of precision global QCD analysis. Apparent disagreements between fixed-flavor scheme calculations of b-production rate with experimental measurements in hadro-, lepto-, and photo-production provide new impetus to a thorough examination of the theory and phenomenology of this process. We review existing methods of calculation, and place them in the context of the general PQCD framework of Collins. A distinction is drawn between scheme dependence and implementation issues related to quark mass effects near threshold. We point out a so far overlooked kinematic constraint on the threshold behavior, which greatly simplifies the variable flavor number scheme. It obviates the need for the elaborate existing prescriptions, and leads to robust predictions. It can facilitate the study of current issues on heavy flavor production as well as precision global QCD analysis.

Figures (6)

• Figure 1: Partonic processes for charm production to NLO in the 4-flavor scheme.
• Figure 2: Expected regions of applicability and uncertainty of the 4-flavor (a) and 3-flavor (b) schemes. Note: (i) the power of $\alpha_s$ for "NLO" is different in the two schemes due to the resummation of perturbation series; and (ii) the reliability of the calculation in each scheme depends on the scale $Q$.
• Figure 3: Partonic processes for charm production to NLO in the 3-flavor scheme.
• Figure 5: Comparison of the inclusive charm production data of Zeus ZeusF2c with: (i) order $\alpha_s^2$ 3-flavor (NLO) calculation (solid lines); and order $\alpha_s$ 4-flavor (also NLO) calculation ($m_c \neq 0$) in the general formalism (dashed lines). The various $Q$ bins are alternately put into two separate plots to avoid overlapping points and curves. Both schemes appear to be robust within the experimental kinematic range.
• Figure 6: Comparison of $F_2^c$ calculations vs. $Q^2$ with two different choices of $\mu$. The curve labelled "$c(\xi))$ TR" in (b), is the LO result using the prescription of Thorne-Roberts ThorneRob.