Amplitude-Based IR-Improvement in Precision LHC$/$FCC Physics

We present recent results based on the IR-improvement of unintegrable singularities in the infrared regime via amplitude-based resummation in $QED \times QCD \subset SU(2)_L \times U_1 \times SU(3)_c$. In the context of precision LHC$/$FCC physics, we focus on specific examples, such as the removal of QED contamination in PDFs evolved from data at ${Q_0}^2 \sim 2\; {\text{GeV}}^2$ and used in the evaluating precision observables in $pp \rightarrow Z + X \rightarrow \ell\bar{\ell} + X'$, in which we discuss new results and new issues.

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