Resummation structure for full off-shell MiNLO merging

Determine the relevant resummation structure for the complicated full off-shell pp → e⁺νₑ μ⁻ν̄μ τ⁺ντ bb̄ + X process with fiducial phase-space cuts, in order to enable the standard MiNLO merging procedure with the corresponding process-dependent Sudakov-form-factor modifications.

Background

The paper combines samples with different jet multiplicities to improve predictions for the full off-shell tt̄W⁺ process. Because the standard MiNLO merging procedure requires a merging-scale-independent treatment based on process-dependent modifications of the Sudakov form factors, its direct application depends on knowing the appropriate resummation structure for the process and fiducial cuts.

The authors state that this resummation structure is not known for the complicated full off-shell process considered. Consequently, they use a MiNLO ⊕ Direct sum procedure with an explicit merging-scale parameter rather than applying the standard MiNLO merging method. Determining the missing resummation structure would therefore allow a more formally complete implementation of the standard merging procedure.

References

However, for the complicated full off-shell $pp \to e+ \nu_e \mu- \bar{\nu}\mu \tau+ \nu\tau b\bar{b} + X$ process with fiducial phase-space cuts, the relevant resummation structure is not known.

— Improving predictions for the $pp \to t\bar{t}W^+$ process at the LHC with the MINLO method  (2609.31296 - Dimitrakopoulos, 25 Sep 2026) in Section 3, “Multi-jet merged predictions”