## Final Report Summary - MM-PGT (Modern Methods for Perturbative Gauge Theories)

The Large Hadron Collider, operating a hundred meters below ground a few kilometers northwest of Geneva, Switzerland, is the world’s largest and most powerful particle accelerator. It collides two beams of protons at nearly the speed of light in opposite directions around a narrow vacuum tube 27 kilometers in circumference. Detectors, each the size of multi-story buildings, measure the energies of the thousands of particles emerging from each of the hundreds of millions of collisions every second. The LHC’s experimenters are seeking to understand what lies underneath the so-called Standard Model of particle physics, which describes all known data about particle physics. To do so, they seek rare deviations from the Standard Model’s predictions. In order to do so, one must first understand these latter predictions in detail, as they represent a voluminous “background” to the desired signal. Theoretical calculations play an important role in this understanding.

Calculating these processes requires calculating the scattering of the quark and gluon constituents of the proton. These can be calculated in a theory called quantum chromodynamics. The traditional tools for performing these calculations are Feynman diagrams, invented in the 1950s by the famous physicist Richard Feynman. For processes with many quarks and gluons emerging at short distances, however, the number of Feynman diagrams explodes, and the calculations become unmanageable. The years prior to the Project’s start saw the emergence of new techniques, called “on-shell methods,” for performing the required calculations. The new methods break the complicated problem of calculating quark and gluon interaction probabilities into smaller, simpler problems which also have physical meaning. The explicit and simple results for certain kinds of processes also planted the seeds of a new subfield of particle physics, called “Amplitudes”, devoted to the study of quantum scattering amplitudes.

The Project, in the framework of the BlackHat collaboration, has continued the development of on-shell methods. It refined the methods at the first quantum order (“one loop”) in a perturbative series and implemented them in a numerical software library. The collaboration then used these libraries in conjunction with other software packages to produce precise predictions for background processes. It pushed our capabilities for processes with many quarks and gluons dramatically beyond what had been possible earlier. Both the CMS and ATLAS experiments at the LHC have used these predictions in comparing with their data, improving our confidence in our detailed understanding of known physics.

The Project has also continued the theoretical work of developing on-shell methods. It has laid the foundation for extending the methods to the second quantum order (“two loops”), resolving a number of conceptual issues and refining mathematical tools for such calculations. The two-loop calculations will be needed to prepare yet-higher precision theoretical predictions. Experimenters will confront these predictions with future precision data. The Project has also participated in developing ideas which relate scattering processes in quantum gravity to those of gluons, and in calculations based on them. These calculations are on the path to answering an old, fundamental, and unresolved question: are any theories of quantum gravity, with the addition of supersymmetry, but without resort to string theory, fully consistent as quantum mechanical theories? The theoretical work in these directions promise a solid foundation for future applications to LHC physics and to fundamental questions in elementary particle physics.

Calculating these processes requires calculating the scattering of the quark and gluon constituents of the proton. These can be calculated in a theory called quantum chromodynamics. The traditional tools for performing these calculations are Feynman diagrams, invented in the 1950s by the famous physicist Richard Feynman. For processes with many quarks and gluons emerging at short distances, however, the number of Feynman diagrams explodes, and the calculations become unmanageable. The years prior to the Project’s start saw the emergence of new techniques, called “on-shell methods,” for performing the required calculations. The new methods break the complicated problem of calculating quark and gluon interaction probabilities into smaller, simpler problems which also have physical meaning. The explicit and simple results for certain kinds of processes also planted the seeds of a new subfield of particle physics, called “Amplitudes”, devoted to the study of quantum scattering amplitudes.

The Project, in the framework of the BlackHat collaboration, has continued the development of on-shell methods. It refined the methods at the first quantum order (“one loop”) in a perturbative series and implemented them in a numerical software library. The collaboration then used these libraries in conjunction with other software packages to produce precise predictions for background processes. It pushed our capabilities for processes with many quarks and gluons dramatically beyond what had been possible earlier. Both the CMS and ATLAS experiments at the LHC have used these predictions in comparing with their data, improving our confidence in our detailed understanding of known physics.

The Project has also continued the theoretical work of developing on-shell methods. It has laid the foundation for extending the methods to the second quantum order (“two loops”), resolving a number of conceptual issues and refining mathematical tools for such calculations. The two-loop calculations will be needed to prepare yet-higher precision theoretical predictions. Experimenters will confront these predictions with future precision data. The Project has also participated in developing ideas which relate scattering processes in quantum gravity to those of gluons, and in calculations based on them. These calculations are on the path to answering an old, fundamental, and unresolved question: are any theories of quantum gravity, with the addition of supersymmetry, but without resort to string theory, fully consistent as quantum mechanical theories? The theoretical work in these directions promise a solid foundation for future applications to LHC physics and to fundamental questions in elementary particle physics.