This paper examines how a specific theoretical improvement affects our knowledge of proton structure. The authors study the transverse momentum spectrum of Z bosons produced at the Large Hadron Collider (LHC). They add a small‑transverse‑momentum resummation correction — a way of summing many small contributions that matter when the Z boson moves slowly across the detector — to high‑precision calculations and then re-fit parton distribution functions (PDFs). PDFs describe how the proton’s momentum is shared among its quarks and gluons.

The study uses Z‑boson measurements from the ATLAS and CMS experiments at centre‑of‑mass energies of 8 and 13 tera‑electronvolts (TeV). The 8 TeV datasets have integrated luminosities of about 20 fb−1 (ATLAS) and 19.7 fb−1 (CMS). The new 13 TeV measurements use about 36 fb−1 each. The ATLAS 13 TeV data are especially precise at low transverse momentum (per‑mille level). The authors include these measurements in PDF fits built with the NNPDF methodology. They compute the baseline theory at next‑to‑next‑to‑leading order (NNLO) in quantum chromodynamics (QCD) using stable fixed‑order codes (NNLOjet is used for the NNLO part) and store results in fast interpolation grids (PineAPPL) to make the fits practical.

Why resummation matters: at low Z transverse momentum the fixed‑order expansion in the strong force develops many large logarithmic terms. Resummation adds up those terms to all orders and gives a reliable prediction in that region. The authors apply resummation at next‑to‑next‑to‑next‑to‑leading logarithmic accuracy (N3LL) using the RadISH tool. They also estimate missing higher‑order theory uncertainties by building a theory covariance matrix from renormalisation‑ and factorisation‑scale variations. (Those scales are internal choices in the calculation that probe how much the prediction can change when unknown higher‑order effects are varied.)