Periodic Reporting for period 1 - MultiScaleAmp (Multi-Scale Amplitudes For Collider Physics)
Período documentado: 2023-10-01 hasta 2026-03-31
The Large Hadron Collider (LHC) represents the frontier of exploration of nature at the smallest length scales. By colliding protons at near-light speeds, it produces short-lived particles whose decay patterns are recorded in complex detectors. Comparing these data to theoretical predictions has already led to the 2012 discovery of the Higgs boson and has firmly established the Standard Model (SM) as our current best description of fundamental interactions. Yet profound questions remain: the origin of dark matter, the stability of the vacuum, and the possibility of new physics at high energy scales. Because the Higgs boson couples broadly to other heavy SM particles, its properties offer a unique window into potential new phenomena. Exploiting this opportunity requires theoretical predictions of exceptional precision.
In the coming years, the LHC will enter into an era of precision measurements. Increased collision rates will yield vastly larger datasets, reducing experimental uncertainties for many observables to the percent level or below. To fully benefit from this wealth of data, theory must keep pace: the SM predictions used to interpret measurements must reach matching levels of accuracy. At the LHC, achieving this precision hinges on perturbative quantum chromodynamics (QCD), where observables are computed order-by-order in the strong coupling. While next-to-leading order calculations already describe many processes well, percent-level precision typically requires next-to-next-to-leading order (NNLO) accuracy. The central obstacle to NNLO predictions is the need for mathematical descriptions of multi-particle scattering processes: the so-called "scattering amplitude".
These amplitudes form a key building block of precision collider phenomenology, but they present a formidable challenge. Their analytic structure is highly intricate and traditional computational techniques struggle to cope with this complexity. As a result, many amplitudes essential for interpreting Higgs, top-quark, and electroweak measurements remain out of reach. A new paradigm has emerged in recent years that promises to overcome these barriers. This approach leverages deep physical and mathematical insights into the scattering amplitudes. By combining geometric tools, differential equations and modern understanding of Feynman integrals, MultiScaleAmp is pushing forward the frontiers in two-loop amplitude computation. The central idea is to reveal and exploit the underlying geometric structures that govern these amplitudes and enable computations far beyond the reach of conventional methods. This strategy will make it possible to handle processes involving many final state particles, delivering a broad class of two-loop amplitudes required for precision studies of jets, top quarks, vector bosons and the Higgs boson.
In the coming years, the LHC will enter into an era of precision measurements. Increased collision rates will yield vastly larger datasets, reducing experimental uncertainties for many observables to the percent level or below. To fully benefit from this wealth of data, theory must keep pace: the SM predictions used to interpret measurements must reach matching levels of accuracy. At the LHC, achieving this precision hinges on perturbative quantum chromodynamics (QCD), where observables are computed order-by-order in the strong coupling. While next-to-leading order calculations already describe many processes well, percent-level precision typically requires next-to-next-to-leading order (NNLO) accuracy. The central obstacle to NNLO predictions is the need for mathematical descriptions of multi-particle scattering processes: the so-called "scattering amplitude".
These amplitudes form a key building block of precision collider phenomenology, but they present a formidable challenge. Their analytic structure is highly intricate and traditional computational techniques struggle to cope with this complexity. As a result, many amplitudes essential for interpreting Higgs, top-quark, and electroweak measurements remain out of reach. A new paradigm has emerged in recent years that promises to overcome these barriers. This approach leverages deep physical and mathematical insights into the scattering amplitudes. By combining geometric tools, differential equations and modern understanding of Feynman integrals, MultiScaleAmp is pushing forward the frontiers in two-loop amplitude computation. The central idea is to reveal and exploit the underlying geometric structures that govern these amplitudes and enable computations far beyond the reach of conventional methods. This strategy will make it possible to handle processes involving many final state particles, delivering a broad class of two-loop amplitudes required for precision studies of jets, top quarks, vector bosons and the Higgs boson.
In its early phase, the project has already achieved several advances towards its goal of developing methods for perturbative computations to aid particle-physics research at the Large Hadron Collider (LHC).
A key focus has been improving theoretical predictions for how Higgs bosons are produced together with top-quark pairs. The project delivered the first predictions for this process at a new level of precision. These results will help experimental teams extract more information from LHC data and sharpen searches for new physics. Another major achievement is the progress on the Drell–Yan process, a cornerstone reaction for testing the Standard Model. The project carried out the first computation of a challenging class of two-loop corrections and performed high-precision studies for both charged- and neutral-current versions of the process.
In addition, the project achieved a world-first calculation of a complex family of two-loop integrals relevant for multi-particle scattering. This breakthrough opens the door to precision predictions for a wide range of LHC processes that were previously out of reach. Further results include a public tool that connects two simulation frameworks, making it possible to generate fast and reliable interpolation grids at NNLO accuracy, as well as new analytic calculations of photon and jet production involving heavy quark loops, offering fresh insights into the mathematical structures underlying particle interactions. Finally, the project has advanced the mathematical foundations of Feynman-integral reduction by uncovering a new class of geometrically significant relations, known as “critical syzygies,” which promise to make future precision calculations more efficient.
A key focus has been improving theoretical predictions for how Higgs bosons are produced together with top-quark pairs. The project delivered the first predictions for this process at a new level of precision. These results will help experimental teams extract more information from LHC data and sharpen searches for new physics. Another major achievement is the progress on the Drell–Yan process, a cornerstone reaction for testing the Standard Model. The project carried out the first computation of a challenging class of two-loop corrections and performed high-precision studies for both charged- and neutral-current versions of the process.
In addition, the project achieved a world-first calculation of a complex family of two-loop integrals relevant for multi-particle scattering. This breakthrough opens the door to precision predictions for a wide range of LHC processes that were previously out of reach. Further results include a public tool that connects two simulation frameworks, making it possible to generate fast and reliable interpolation grids at NNLO accuracy, as well as new analytic calculations of photon and jet production involving heavy quark loops, offering fresh insights into the mathematical structures underlying particle interactions. Finally, the project has advanced the mathematical foundations of Feynman-integral reduction by uncovering a new class of geometrically significant relations, known as “critical syzygies,” which promise to make future precision calculations more efficient.
Among the results beyond the state-of-the-art that have been produced and are already published or under peer review (all also accessible on the arXiv) are:
- QED contributions to the two-loop electroweak corrections to the Drell-Yan process.
- Soft contributions to heavy quark production.
- An interface of PDF interpolation grids with NNLO cross-section codes.
- NNLO predictions for ttH production cross sections, matched with NNLL resummation and EW corrections.
- Mixed QCD-EW corrections to the neutral-current Drell-Yan process
- Precise predictions for inclusive cross section and differential distributions for ttH production at the LHC.
- Two-loop mixed QCD-EW corrections to charged current Drell-Yan.
- Analytic two-loop amplitudes for di-jet and γ + jet production mediated by a heavy-quark loop.
- Analytic two-loop amplitudes for diphoton production mediated by a heavy-quark loop at the LHC.
- Two-loop six-point Feynman integrals.
- Novel methods for the reduction of Feynman integrals.
- QED contributions to the two-loop electroweak corrections to the Drell-Yan process.
- Soft contributions to heavy quark production.
- An interface of PDF interpolation grids with NNLO cross-section codes.
- NNLO predictions for ttH production cross sections, matched with NNLL resummation and EW corrections.
- Mixed QCD-EW corrections to the neutral-current Drell-Yan process
- Precise predictions for inclusive cross section and differential distributions for ttH production at the LHC.
- Two-loop mixed QCD-EW corrections to charged current Drell-Yan.
- Analytic two-loop amplitudes for di-jet and γ + jet production mediated by a heavy-quark loop.
- Analytic two-loop amplitudes for diphoton production mediated by a heavy-quark loop at the LHC.
- Two-loop six-point Feynman integrals.
- Novel methods for the reduction of Feynman integrals.