arXiv subjects

Pan-Feng Li

Publications and source records attributed to Pan-Feng Li.

3 recordsLinked to original sources

arXiv2026

Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \rightarrow Z H$

For the two-loop next-to-leading-order electroweak (NLO EW) corrections to $gg \rightarrow ZH$, the light-fermion contributions can be classified into eight distinct topologies. Using the canonical differential-equations method, we perform an analytic computation of the master integrals (MIs) associated with the four planar topologies. Canonical bases are constructed using the Magnus-expansion method, and the resulting alphabets consist of algebraic symbol letters involving nontrivial radicals. We develop a systematic framework for identifying the radical structures of the canonical MIs, enabling their organization into suitable subsystems and, whenever possible, their representation in terms of Goncharov polylogarithms (GPLs) up to $\mathcal{O}(\epsilon^4)$. Only a few MIs at $\mathcal{O}(\epsilon^3)$ and $\mathcal{O}(\epsilon^4)$ are instead represented as one-fold integrals over GPLs, due to the presence of nested square roots that obstruct the simultaneous rationalization of all radicals.

hep-ph↗

arXiv2024

Two-loop planar master integrals for NNLO QCD corrections to W-pair production in quark-antiquark annihilation

The planar two-loop scalar Feynman integrals contributing to the massive NNLO QCD corrections for $W$-boson pair production via quark-antiquark annihilation can be classified into three family branches, each of which is reduced to a distinct set of master integrals (MIs), totaling $27$, $45$ and $15$, respectively. These MIs are analytically calculated using the method of differential equations, with solutions expanded as Taylor series in the dimensional regulator $\epsilon$. For the first two family branches, the differential systems can be successfully transformed into canonical form by adopting appropriate bases of MIs. This enables the MIs of these family branches to be expressed either as Goncharov polylogarithms (GPLs) or as one-fold integrals over GPLs, up to $\mathcal{O}(\epsilon^4)$. In contrast, the differential system for the third family branch can only be cast into a form linear in $\epsilon$ due to the presence of elliptic integrals. The solution to this linear-form differential system is expressed in an iterated form owing to the strictly lower-triangular structure of the coefficient matrices at $\epsilon = 0$. Our analytic expressions for these MIs are verified with high accuracy against the numerical results from the \texttt{AMFlow} package.

hep-ph↗

arXiv2023

Next-to-next-to-leading order $\text{QCD} \otimes \text{EW}$ corrections to $Z$-boson pair production at electron-positron colliders

We present a comprehensive analytic calculation of the next-to-next-to-leading order $\text{QCD} \otimes \text{EW}$ corrections to $Z$-boson pair production at electron-positron colliders. The two-loop master integrals essential to this calculation are evaluated using the differential equation method. In this work, we detail the formulation and solution of the canonical differential equations for the two-loop three-point master integrals with two on-shell $Z$-boson external legs and a massive internal quark in the loops. These canonical master integrals are systematically expanded as Taylor series in the dimensional regulator, $\epsilon = (4-d)/2$, up to the order of $\epsilon^4$, with coefficients expressed in terms of Goncharov polylogarithms up to weight four. Upon applying our analytic expressions of these master integrals to the phenomenological analysis of $Z$-pair production, we observe that the $\mathcal{O}(\alpha \alpha_s)$ corrections manifest at a level of approximately one percent compared to the leading-order predictions, underscoring their significance for comparisons with future high-precision experimental data.

hep-ph↗