In the second of our featured project series, we hear from Professor Christine Davies and Dr Judd Harrison on their work in High Precision Quantum Chromodynamics (HPQCD).
The Standard Model (SM) of particle physics successfully describes all known elementary particles and their interactions through the weak, strong and electromagnetic forces. However, it doesn’t include gravity or dark matter; both the symmetries that underlie the SM and the values of the parameters that appear in it are unexplained. We believe there is a more complete theory of fundamental physics out there, waiting to be found. It will show up when SM predictions for some sensitive observables differ significantly from experimental values, but high precision from both theory and experiment is needed to uncover these differences because they are so small.
The theoretical challenge is to tame strong interactions: for this, we need the machinery of Lattice QCD (LQCD). The elementary quarks of the SM bind together through the strong interaction into hadrons such as the protons and neutrons that make up atomic nuclei. It is the hadrons, not the quarks, that are seen in experiments, and it is only through LQCD that we can obtain a complete description. The HPQCD team, working towards this goal, is mainly based in the UK, divided between Cambridge, Glasgow, and Plymouth. The research group comprises 4 academics, 2 postdoctoral researchers and 2 PhD students, as well as collaborators in the USA, Canada and Europe.
LQCD approximates continuous spacetime using a finite grid so that the integrals defining the full theory can be evaluated numerically. This is computationally very challenging but, thanks to facilities like DiRAC, LQCD has become the gold standard for predicting the properties of hadrons. Our project uses state-of-the-art methods to make these predictions at the high level of precision needed to maximise the impact of experimental results from the Large Hadron Collider (LHC). The calculations involve repeatedly solving the Dirac equation, describing how quark motion is affected by absorption and emission of gluons as they interact with other quarks, by inverting a huge O(10⁶ x 10⁶) matrix. The solution is made more efficient by using a highly optimised discretisation we have developed known as “Highly Improved Staggered Quarks” (HISQ). Our project uses the Data Intensive Peta4 supercomputer at Cambridge (CSD3), well suited to our typical CPU and memory usage. The data from our calculations is analysed statistically using Bayesian methods to extract hadronic properties such as masses and decay amplitudes.
The project has delivered many results permitting stringent tests of the SM. One example is that of understanding how the muon, a heavier cousin of the electron, is affected by interacting with quarks. The muon is a spinning electric charge and hence behaves like a little magnet. The strength of this magnet is sensitive to the muon’s interaction with all of the particles that can pop in and out of the vacuum, including quarks. It can also be measured extraordinarily precisely, most recently by the Muon g-2 experiment at Fermilab near Chicago. This gives the possibility of pinning down a discrepancy between experiment and the SM that would arise from particles not included in the SM. Current LQCD calculations, such as ours, are just now reaching the level of precision required to determine whether there is a discrepancy or not.
The team has also been at the forefront of calculations of the properties of hadrons containing bottom quarks, which are much heavier than the up and down quarks from which protons and neutrons are built. They appear fleetingly at the LHC and decay through rare weak interaction processes which provide a window into possible new physics. Several possible anomalies have been seen but pinning these down requires an even more detailed and precise understanding of the structure of these hadrons using LQCD.
Christine Davies studied physics at Cambridge University, earning a Ph.D. in theoretical particle physics under the supervision of Bryan Webber. She subsequently did post-doctoral research at Cornell University before taking up an Advanced Fellowship at the University of Glasgow, where she ultimately became professor and head of the theory group. Over the course of her career her research has helped lattice QCD develop from a numerical model offering insight into certain theoretical issues into a precision tool relied upon for both analysis and planning of particle physics experiments. She was the first chair of DiRAC’s Project Board, helping to secure funding for phase 2 of the facility. She is a Fellow of both the Royal Society of Edinburgh and the Institute of Physics and was awarded the OBE in 2006 for services to science.
Dr. Judd Harrison studied heavy quark physics for his Ph.D. at Cambridge University, staying within the HPQCD collaboration when moving to Glasgow as a post-doc, where he has worked on adapting the HISQ approach to heavy quarks. He became a Stephen Hawking Fellow at Glasgow in 2021.
Bc→J/ψ form factors for the full q2 range from lattice QCD
HPQCD Collaboration: J. Harrison, C.T.H. Davies and A. Lytle, Phys.Rev.D 102 (2020) 9, 094518
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.102.094518
Hadronic-vacuum-polarization contribution to the muon’s anomalous magnetic moment from four-flavor lattice QCD
Fermilab Lattice and LATTICE-HPQCD and MILC Collaborations: C.T.H. Davies et al.
Phys.Rev.D 101 (2020) 3, 034512
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.101.034512
