A Panoramic Study of $K$-Factors for 111 Processes at the 14 TeV LHC

In this comprehensive study, we investigate $K$-factors ($K=\sigma_{\text{NLO}}/\sigma_{\text{LO}}\equiv 1+\delta K$) for a broad array of Standard Model processes at the 14 TeV LHC, which are pivotal for background assessments in Beyond the Standard Model (BSM) searches. Using MadGraph5_aMC@NLO, we calculate the leading-order and next-to-leading order (NLO) cross-sections and compute the corresponding $K$-factors for 111 processes. Our analysis reveals $K$-factors ranging from 1.005 for $pp \to jjj$ to 4.221 for $pp\to W^\pm \gamma\gamma\gamma$. Key findings include: (i) processes involving photons display significantly high $K$-factors, attributed to gluon-initiated processes at NLO; (ii) processes with multiple particle productions, particularly those involving vector bosons, exhibit elevated $K$-factors due to multiple real emission processes; (iii) there exists an inverse correlation between the number of jets and $\delta K$, indicating that the addition of jets generally leads to a decrease in $\delta K$. Additionally, our investigation into differential $K$-factors relative to transverse momentum and invariant mass shows notable increases with higher $p_T$, but minimal changes with invariant mass. This study highlights the indispensable role of precise $K$-factor evaluations for accurate interpretations of BSM search outcomes.