Treatment of Heavy Quarks in Deeply Inelastic Scattering

TL;DR

The paper tackles the challenge of incorporating heavy-quark mass effects in deeply inelastic scattering by developing a Collins-inspired Simplified ACOT (S-ACOT) prescription that interpolates between FFN near threshold and ZM-VFN at high Q^2. It provides a clear factorization framework across multiple active-flavor schemes, identifies and resolves the factorization ambiguity, and demonstrates that S-ACOT yields the same results as ACOT at O(α_s) with greatly simplified calculations. Numerical comparisons show consistent matching between prescriptions near threshold and convergence to massless behavior at large Q^2, supporting the use of MS parton distributions in global analyses. The findings lay the groundwork for higher-order implementations and practical heavy-quark treatments in global parton-density fits.

Abstract

We investigate a simplified version of the ACOT prescription for calculating deeply inelastic scattering from Q^2 values near the squared mass M_H^2 of a heavy quark to Q^2 much larger than M_H^2.

Figures (5)

• Figure 1: CTEQ4L charm quark density $f_{H/p}(x,Q)$ and the approximate form $\tilde{f}_{H/p}(x,Q)$, Eq. (\ref{['pdfmatch']}), at $x=0.05$ as function of $Q$. Since Eq. (\ref{['pdfmatch']}) is an order $\alpha_s^1$ perturbative approximation and the evolution kernel for the CTEQ4L parton distribution is also order $\alpha_s^1$, these curves match closely at threshold.
• Figure 2: CTEQ4M charm quark density $f_{H/p}(x,Q)$ and the approximate form $\tilde{f}_{H/p}(x,Q)$, Eq. (\ref{['pdfmatch']}), at $x=0.05$ as function of $Q$. Since Eq. (\ref{['pdfmatch']}) is an order $\alpha_s^1$ perturbative approximation while the evolution kernel for the CTEQ4M parton distribution includes order $\alpha_s^2$ terms, these curves do not match closely at threshold.
• Figure 3: CTEQ4M charm quark density $f_{H/p}(x,Q)$ and an approximate form $\tilde{f}_{H/p}^{(2)}(x,Q)$ at $x=0.05$ as function of $Q$. The approximate form is based on an analogue of Eq. (\ref{['pdfmatch']}) in which appropriate order $\alpha_s^2$ terms are added. Since the calculation of $\tilde{f}_{H/p}^{(2)}(x,Q)$ uses the second order evolution kernel used for the CTEQ4M parton distributions, these curves match closely at threshold.
• Figure 4: $F_2^c$ for $x=0.1$ as a function of $Q$ as calculated using the ZM-VFN, FFN, ACOT, and S-ACOT prescriptions. The hard scattering coefficients are calculated to order $\alpha_s^1$. Plot a) uses CTEQ4L parton densities and Plot b) uses CTEQ4M parton densities.
• Figure 5: $F_2^c$ for $x=0.001$ as a function of $Q$ as calculated using the ZM-VFN, FFN, ACOT, and S-ACOT prescriptions. The hard scattering coefficients are calculated to order $\alpha_s^1$. Plot a) uses CTEQ4L parton densities and Plot b) uses CTEQ4M parton densities.