Collider physics has entered into a precision era, where further insights into the fundamental laws of nature are derived from careful comparison of experimental measurements with the corresponding theoretical predictions. Such comparisons yield incrementally more conclusive results as the accuracy of the comparison improves.
At the forefront of experimental endeavors, the high-luminosity LHC is already pushing boundaries, achieving measurements with precision often surpassing the one percent mark. Looking ahead, projects like the FCC-ee promise to elevate this precision to the per mil level.
Aligning theoretical predictions with this level of experimental precision presents a formidable challenge, necessitating a unified effort across the field. An important component of these theoretical predictions is the perturbative expansion of the hard cross-section, which involves an enumeration of loop Feynman Diagrams.
Historically, the computation of such loop integrals has been fraught with obstacles, notably the emergence of intermediate divergences—infinities that seemingly undermine calculations but ultimately cancel out in the final tally. Our group is at the vanguard of surmounting these challenges through an innovative method dubbed "Local Unitarity." This approach ingeniously consolidates divergences at a local level into a finite, numerically integrable quantity.
Over the years, powerful techniques, mostly (semi-)analytical, have been developed to tackle the computation of such loop integrals. One particular hurdle is the presence of intermediate divergences — infinities that seemingly undermine calculations but ultimately cancel out in the final tally.
Our research pioneers a new approach to tackling these problems called "Local Unitarity", whereby all such divergences are combined locally into a finite quantity that can readily be integrated using numerical techniques.
The overarching objective of our research is two-fold:
- To improve theoretical predictions of perturbative cross-sections by adopting an entirely new and computational paradigm, tailored from the start for direct numerical evaluations.
- To deepen our understanding of Quantum Field Theory (QFT) by elucidating a comprehensive theoretical framework that captures the nature and cancellation mechanisms of singularities across all perturbative orders.
As our research matures, we plan on exploring the application of our findings to a diverse range of physics challenges related to loop computations; matching to resummation of logarithmic enhancements, Electro-Weak corrections, classical limits of gravity amplitudes, and finite temperature QFT to name a few.
More details and references on our work can be found on the official website of the group: alphaloop.
The research of our group is supported by the Swiss National Science Foundation Eccellenza grant entitled "A novel approach to perturbative computations in Quantum Field Theory".
