NLO heavy-quark contributions to DIS structure functions in the ACOT scheme

TL;DR

Problem: to provide precise NLO heavy-quark contributions to the DIS structure functions $F_4$ and $F_5$, which are suppressed for light leptons but become relevant in muon/tau and neutrino scattering. Approach: compute NLO heavy-quark corrections in the ACOT variable-flavor-number scheme and implement them in the APFEL++ framework using CT18NLO PDFs, with analytical results also derived for polarized functions $g_1$, $g_4$, $g_5$, $g_6$, and $g_7$. Key findings: $F_4$ first arises at NLO due to the Albright–Jarlskog relations, while $F_5$ exhibits sizable but smaller NLO corrections (up to ~10%), with strong low-$x$ sensitivity from heavy-quark dynamics; the gamma-Z interference becomes accessible with polarized beams at low $Q^2$. Significance: these results enable precise predictions for SHiP, IceCube, DUNE, and EIC measurements and support global QCD analyses; future work includes cross-checks across heavy-quark schemes and dedicated unpolarized and polarized studies.

Abstract

We present next-to-leading-order (NLO) calculations of heavy-quark contributions to deep-inelastic scattering (DIS) structure functions $F_4$ and $F_5$ within the Aivazis--Collins--Olness--Tung (ACOT) scheme, implemented in the open source library \texttt{APFEL++} using \texttt{CT18NLO} parton distribution functions. These structure functions, suppressed by lepton mass effects in light-lepton processes, become significant in muon, tau-lepton and neutrino scattering at facilities such as SHiP, IceCube, and DUNE. Our results reveal NLO corrections up to 10\% relative to leading order, with pronounced heavy-quark effects at low Bjorken-$x$, impacting gluon and strange quark distributions. In the unpolarized case, $F_{4/5}^{γZ}$ and $F_{4/5}^γ$ do not contribute to the cross section, while the $γZ$ interference becomes accessible with longitudinally polarized lepton beams at the Electron-Ion Collider (EIC), offering enhanced sensitivity at low $Q^2$ due to reduced $Z$-boson propagator suppression. Analytical NLO expressions have also been derived for the polarized structure functions $g_1$, $g_4$, $g_5$, $g_6$, and $g_7$ in the ACOT framework. These developments enable precise theoretical predictions for upcoming experimental programs and global QCD analyses.

Figures (1)

• Figure 1: Comparison of the structure functions $F_4$ (left) and $F_5$ (right) for $Q = 10\,\mathrm{GeV}$ as functions of the Bjorken variable $x$ in the range $10^{-3} \le x \le 1$. Solid lines correspond to next-to-leading order (NLO) results and dashed lines to leading order (LO), for both neutral-current and charged-current interactions.