FIRCLA, one-loop correction to e+ e- to nu anti-nu H and basis of Feynman integrals in higher dimensions

TL;DR

The paper tackles the challenge of efficiently evaluating one-loop multi-leg electroweak processes by introducing FIRCLA, a hybrid workflow that combines DIANA, FORM, and MAPLE and leverages Tarasov-type dimension-shifting recurrence to reduce tensor integrals to a scalar master-integral basis. It demonstrates the method on the process $e^+e^- \rightarrow \overline{\nu} \nu H$, handling 326 diagrams (including 15 pentagons) and achieving a dramatic reduction in the number of master integrals while preserving gauge invariance, with large intermediate outputs and ongoing work on bremsstrahlung. A central advance is the proposal to use master-integrals in higher dimensions to improve numerical stability, with relations that express $I^{(d)}_n$ in terms of $I^{(d+2)}_n$ (or higher) and yield more stable $n$-point integrals. This approach promises a more robust, scalable framework for precision one-loop calculations in theories with many external legs and varying masses, relevant for future $e^+e^-$ colliders.

Abstract

An approach for an effective computer evaluation of one-loop multi-leg diagrams is proposed. It's main feature is the combined use of several systems - DIANA, FORM and MAPLE. As an application we consider the one-loop correction to Higgs production in e+ e- to nu anti-nu H, which is important for future e+ e- colliders. To improve the stability of numerical evaluations a non-standard basis of integrals is introduced by transforming integrals to higher dimensions.