RUI: Advancing the Constructive Standard Model: Efficient Techniques for High-Multiplicity Amplitude Calculations

This award funds the research activities of Professor Neil Christensen at Illinois State University. At the Large Hadron Collider (LHC), protons are accelerated to near-light speeds and smashed together to potentially create new massive particles that have never been seen before. These particles could reveal new fundamental laws that govern the universe. However, these rare events occur in less than 1 in ten million million collisions, necessitating ultra-precise calculations that would allow us to identify new physics signals amid the mountain of background noise. As part of his research, Professor Christensen will perform such calculations. The new calculational methods developed in this research will advance the national interest by significantly increasing the efficiency and accuracy of these background calculations. This improvement will allow scientists to use data from the LHC more effectively in order to discover new physics that was previously out of reach. Additionally, this research keeps the United States at the forefront of theoretical progress, deepening our understanding of the fundamental particles, fields, and laws that govern the universe. This project also supports education and workforce development by training the next generation of physicists in cutting-edge techniques. At a more technical level, this project extends the development of a “constructive” technique for calculating scattering amplitudes, potentially replacing Feynman diagrams. Constructive amplitudes eliminate the unphysical degrees of freedom present in Feynman diagrams, ensuring trivial gauge invariance without the need for a gauge symmetry to cancel unphysical effects. Consequently, every diagram is physically meaningful, and the expressions are typically more compact and numerically efficient. However, the interactions are non-local, and on-shell identities must be used at intermediate stages to obtain correct results. This method is still relatively new for massive theories such as the Standard Model, and this research actively extends it to uncalculated amplitudes, higher multiplicity final states, and higher loops. As we develop this technique, we aim to create a comprehensive algorithm that can be faithfully followed and integrated into computational tools in order to automate these calculations. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.