Lattice QCD tests Standard Model at high precision

Lattice QCD tests Standard Model at high precision

Figure 1: Fermilab g-2 Experiment (Photo: Wikipedia/Glukicov)

We have recently studied the properties of the electron’s heavier sibling, the muon. Its anomalous magnetic moment, aμ, quantifies how vacuum fluctuations contribute when it interacts with an external magnetic field. With accuracy of the order of 1ppm, aμ is one of the most precisely determined quantities in experimental as well as theoretical particle physics. Since its value is sensitive to contributions from yet unknown new physics, the persistent 3−4σ tension between experiment and theory is generating a lot of interest within the particle physics community. Is this really a first sign of new and yet unknown physics? Two new experiments at Fermilab (USA, see Figure 1) and J-PARC (Japan), respectively, are trying to address this question. Both efforts are expected to reduce the uncertainty on the experimental value by a factor of around four, down to 140ppb. This puts much pressure on the theory community to match this precision – only the combination of theory and experiment will be able to answer this important question.

 Figure 2: Summary of results for the HVP [4] – RBC/UKQCD 2018 are the results addressed in the text – note the tension with the “No new physics data point”. Green points are other lattice determinations, magenta points are phenome-nological determinations.

On the theory side the error budget is dominated by hadronic uncertainties, in particular uncertainties on predictions for vacuum polarisation effects due to the strong interaction. DiRAC has enabled the first-ever computation of these effects starting from first principles, i.e. from the Standard Model Lagrangian by allowing simulations of Lattice Quantum Chromodynamics including effects of Quantum Electrodynamics. In a series of papers [1-4] researchers from the Universities of Edinburgh and Southampton, together with their collaborators in the US, have developed the required theoretical understanding and the numerical and algorithmic techniques needed to complete their ambitious and state-of-the-art program. In Lattice Quantum Chromodynamics one performs the calculation by constructing a discrete four-dimensional space-time grid (the lattice) on which one numerically solves the QCD equations of motion. Such lattice QCD simulations are the only known method to address the above questions without having to rely on ad hoc assumptions. This type of computation crucially relies on access to the world’s fastest parallel supercomputers like DiRAC’s Extreme Scaling system.

There is still some way to go until a full theoretical computation will match experimental precision. The DiRAC researchers have however developed a method that allows to get very close to the required precision by combining complementary experimental data and their numerical simulations. It will be exciting to compare to new experimental results expected by end of 2018!

Bibliography:[1] Calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment, Blum et al., Phys.Rev.Lett. 116 (2016) no.23, 232002 [2] Lattice calculation of the leading strange quark-connected contribution to the muon g–2, RBC/UKQCD Collaboration, Blum et al., JHEP 1604 (2016) 063 [3] Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study, Boyle et al., JHEP 1709 (2017) 153 [4] Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, Blum et al., arXiv:1801.07224