Abstract
With a key improvement, the auxiliary mass flow method is now able to compute Feynman integrals encountered in cutting-edge collider processes. We have successfully applied it to compute some integrals involved in two-loop electroweak corrections to $e^+e^-\to HZ$, two-loop QCD corrections to $3j$, $W/Z/H+2j$, $t\bar{t}H$ and $4j$ production at hadron colliders, and three-loop QCD corrections to $t\bar{t}$ production at hadron colliders, all of which are crucial for precision frontier in collider physics in the following decade. Our results are important building blocks and benchmarks for future studies of these processes.
Highlights
With the good performance of the LHC, the particle physics enters the era of precision
We have successfully applied it to compute some integrals involved in two-loop electroweak corrections to eþe− → HZ, two-loop QCD corrections to 3j, W=Z=H þ 2j, ttH and 4j production at hadron colliders, and three-loop QCD corrections to tt production at hadron colliders, all of which are crucial for precision frontier in collider physics in the following decade
We show that the auxiliary mass flow (AMF) method can provide high-precision boundary conditions for traditional differential equations (DEs) as well as provide a highly nontrivial selfconsistency check
Summary
With the good performance of the LHC, the particle physics enters the era of precision. One of the most important tasks for theorists is to compute higher-order corrections in perturbation theory to reduce theoretical uncertainties for important processes, such as two-loop electroweak corrections to HZ production at eþe− colliders, two-loop QCD corrections to 3j, W=Z=H þ 2j, ttH, 4j production, and three-loop QCD corrections to tt production at hadron colliders, and so on, where j means jet To carry out these urgently needed perturbative calculations, an important part is to calculate corresponding Feynman master integrals (MIs), which form a complete basis of general Feynman integrals. In the AMF method, MIs can be calculated by setting up and solving differential equations with respect to an auxiliary mass term η (denoted as η-DEs) with almost trivial boundary conditions at η → ∞. Our method and results provide a valuable component for current and future high-precision phenomenological studies
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