Precision calculations in the Standard Model and beyond are very important for the experimental programme of the LHC, planned high-energy colliders, and gravitational-wave detectors of the future. Following two years of pandemic-imposed virtual discussions, 25 invited experts gathered from 26 to 30 July at Cadenabbia on Lake Como, Italy, to present new results and discuss paths into the computational landscape of this year’s “Loop Summit”.
The conference surveyed topics relating to multi-loop and multi-leg calculations in quantum chromodynamics (QCD) and electroweak processes. In scattering processes, loops are closed particle lines and legs represent external particles. Both present computational challenges. Recent progress on many inclusive processes has been reported at three- or four-loop order, including for deep-inelastic scattering, jets at colliders, the Drell-Yan process, top-quark and Higgs-boson production, and aspects of bottom-quark physics. Much improved descriptions of scaling violations of parton densities, heavy-quark effects at colliders, power corrections, mixed QCD and electroweak corrections, and high-order QED corrections for e+e– colliders have also recently been obtained. These will be important for many processes at the LHC, and pave the way to physics at facilities such as the proposed Future Circular Collider (FCC).
Quantum field theory provides a very elegant way to solve Einsteinian gravity
Although merging black holes can have millions of solar masses, the physics describing them remains classical, and quantum gravity happened, if at all, shortly after the Big Bang. Nevertheless, quantum field theory provides an elegant way to solve Einsteinian gravity. At this year’s Loop Summit, perturbative approaches to gravity were discussed which use field-theoretic methods at the level of the 5th and 6th post-Newtonian approximations, where the nth post-Newtonian order corresponds to a classical n-loop calculation between black-hole world lines. These calculations allow predictions of the binding energy and periastron advance of spiralling-in pairs of black holes, and relate them to gravitational-wave effects. In these calculations, the classical loops all link to world lines in classical graviton networks within the framework of an effective-field-theory representation of Einsteinian gravity.
Other talks discussed important progress on advanced analytic computation technologies and new mathematical methods such as computational improvements in massive Dirac-algebra, new ways to calculate loop integrals analytically, new ways to deal consistently with polarised processes, the efficient reduction of highly connected systems of integrals, the solution of gigantic systems of differential equations, and numerical methods based on loop-tree duality. All these methods will decrease the theory errors for many processes due to be measured in the high-luminosity phase of the LHC, and beyond.
Half of the meeting was devoted to developing new ideas in subgroups. In-person discussions are invaluable for highly technical discussions such as these — there is still no substitute for gathering around the blackboard informally and jotting down equations and diagrams. The next Loop Summit in this triennial series will take place in summer 2024.