UKQCD DWF

Figure 1. This figure displays the new result for the neutral kaon mixing amplitude BK in green. This new result was calculated in the continuum limit and directly at physical quark masses. The line and the curve represent two fits to previous data points wich were used to extrapolate to quark masses. With our new algorithm and greater machine power we have been able to both eliminate the systematic extrapolation error and simultaneously reduce the statistical error on this important result.

We have carried out simulations of lattice QCD including up, down and strange quark loops using a chiral fermion discretization which is unique in fully preserving the meaning of left handed spin orientation. The W boson only interacts with left handed fermions, and so preserving this symmetry is deeply important to the calculation of the complex weak matrix elements required to support the experiments such as the Large Hadron Collider.

One important example of these is our determination of the two pion decay amplitudes of the Kaon. This is the process in which the asymmetry between matter and antimatter was discovered. Our calculations, which won the 2012 International Ken Wilson Lattice Award, involve mixing between many operators in the effective weak Hamiltonian. The calculation is only tractable with chiral Fermions, but gives rise to a wholly new constraint on the difference between matter and anti-matter in the standard model. Such constraints enable experiments to search for the effects of undiscovered physics beyond the standard model. Our calculation was updated in journal papers, one of which observed in detail a numerical cancellation that explains a long standing puzzle about the likelihood of decay into different pion charges known as the ΔI=1/2 rule – a case of numerical simulation leading to deeper understanding.

This progress over the last year has only been possible due to the powerful DiRAC BlueGene/Q supercomputer in Edinburgh, which our scientists helped IBM to develop, to simulate chiral fermions at the quark masses seen in nature and with spacings for the space-time grid (including all effects up to energy scales of 1.75 and 2.3 GeV). This has allowed us to predict continuum physics with the complete elimination of systematic errors arising from mass extrapolation. The calculation was shared between UKQCD and our USJapan international collaborators in the Riken-Brookhaven-Columbia collaboration, and also made use of BlueGene/Q systems at Argonne and Brookhaven National Laboratories in the US.

Our calculations on neutral kaon mixing are also relevant to CP violation. We presented both the precise continuum results for the standard model process at physical quark masses and for processes that only arise beyond the standard model.