Estimating power corrections for the Drell-Yan Process

We study power corrections in the Drell-Yan (DY) process using state-of-the-art predictions for both neutral and charged current production. For both types of DY processes, we account for power corrections arising from bottom and charm quark effects within a variable flavor number scheme. Our results show that these corrections become significant in the low-$Q$ region. We also ensure proper treatment of overlapping contributions by carefully applying matching procedures to eliminate any double counting.

💡 Research Summary

This paper investigates power‑suppressed corrections in Drell‑Yan (DY) production, focusing on both neutral‑current (NC) and charged‑current (CC) channels, by combining state‑of‑the‑art fixed‑order predictions with heavy‑quark mass effects. The authors employ the Massive Variable Flavour Number Scheme (MVFNS), which merges the massless 5‑flavour scheme (5FS) – where bottom and charm quarks are treated as massless partons with PDFs – with massive 4‑flavour (4FS) and 3‑flavour (3FS) calculations that retain the full dependence on the bottom (m_b) and charm (m_c) masses.

The theoretical framework starts from the QCD factorisation theorem, expressing the differential cross‑section in terms of parton luminosities and partonic coefficient functions expanded in the strong coupling a_s = α_s/π. In the 5FS, large collinear logarithms of the form ln(Q²/m_Q²) are resummed into the PDFs, but genuine mass effects are omitted. Conversely, the 4FS/3FS retain the exact mass dependence, avoiding collinear divergences but leaving potentially large logarithms that can spoil perturbative convergence.

To avoid double counting, the MVFNS defines the total cross‑section as
dσ_MVFNS = dσ^(5) + Σ_{i=c,b} dσ^(5){i,pc},
where dσ^(5) is the massless N³LO (NC) or NNLO (CC) result obtained from the public code n3loxs, and dσ^(5){i,pc} are the power‑suppressed pieces extracted from the massive calculations. These pieces are further decomposed into three contributions: (i) nf‑terms, which are the massless limit of the heavy‑quark contributions; (ii) logarithmic terms, constructed from decoupling relations for the PDFs and α_s, involving operator‑matrix‑elements (OMEs) A_{ij}; and (iii) genuine power corrections that vanish as m_Q → 0. The OME‑based PDF transformation (f^(5) = Σ_j K_{ij} ⊗ f^(4)) generates the logarithmic pieces, while the power terms are obtained analytically using PolyLogTools and numerically with GiNaC.

Numerical results are presented for the invariant‑mass distribution Σ(n_f,κ)(Q_min,Q_max) = ∫_{Q_min}^{Q_max} dQ² dσ/dQ². For NC‑DY, the authors consider the low‑mass region Q ∈