Particle Physics Theory Group

Lattice Gauge Theory

P.A. Boyle, L. Del Debbio, N. Garron, R. Horsley, A.D. Kennedy, R.D. Kenway, B.J. Pendleton, J. Zanotti

In Lattice QCD, the Group plays a major part in the UKQCD consortium, a national collaboration involving seven universities.

Non-abelian gauge theories display asymptotic freedom. The converse of asymptotic freedom at high scales, is non-linear slavery at low energies. Lattice gauge theory performs the Feynman path integral for quantum field theory numerically, and is the only model independent tool for making predictions about field theory in the non-linear low energy regime.

Certain hadronic properties are needed to both determine fundamental constants of nature, and search for new laws of physics with collider experiments.

We have used a five dimensional Fermion approach known as domain wall fermions. The physical fermion modes appear as four dimensional surface states and develop a chiral symmetry. This chiral symmetry is key to developing a programme of precise weak matrix elements because the V-A couplings to W-bosons are chirally structured.

Much of our QCD research is performed as part of the international (US/UK/Japan) RBC-UKQCD collaboration and the QCDSF (Germany/UK) collaboration. Some of our research areas are listed below:

Neutral Kaon mixing (Boyle, Garron)

Neutral Kaon oscillations are mediated through the quark-W couplings of the Cabbibo-Kobayashi-Maskawa matrix (Nobel prize 2008).

These are the source of CP violation in the Standard Model of particle physics. In fact decay of a K_L neutral kaon to a "wrong" CP two pion state was the process by which CP violation was discovered by Cronin and Fitch in 1964 (Nobel prize 1980). The image on right displays a recent measurement at CPLEAR of the two lifetimes in these two pion decays.

Precise theoretical computation of the Kaon matrix element $B_K$ of the Weak four quark operator is required to use the experimental measurement of the Kaon decay asymmetry $\epsilon_K$ to constrain the vertex unitarity triangle (left).

Our work has reduced the uncertainty in the B_K matrix element from 15% to 3.6% in the last four years.

Semi-leptonic kaon decays (Boyle, Zanotti)

The beta decay of the Kaon proceeds via the CKM matrix element $V_{us}$. Determining $V_{us}$ from experimental decay rates requires a theoretical calculation of the hadronic form factor $f_+^{\pi K}$.

Our programme of research has determined this form factor to 0.5% precision and provides the best theoretical constraint on this fundamental constant.

In future we hope to improve this to a 0.1% precision with calculations at physical quark masses.

Non-perturbative Renormalisation (Boyle, Arthur, Garron)

We have recently developed a new non-perturbative approach to match operators in the lattice regularisation with their counterparts in the perturbative MS scheme.

This approach will allow the momentum scale at which perturbation theory must be applied to be run non-perturbatively to very high scales and will enhance the precision of matrix element calculations.

B physics (Boyle, Del Debbio)

We will use the precision methods developed for our neutral Kaon mixing calculations to calculate the much heavier neutral B-meson mixing amplitudes.

This is a key input to the LHC-b experimental constraints on the CKM matrix and consequently on searches for new physics at the LHC.

Non-perturbative models of new physics (Del Debbio)

We have simulated models of nonperturbative BSM physics, and also studied QCD matrix elements for BSM search channels. In particular we study candidate models for dynamical electroweak symmetry breaking, providing novel insights on the existence of near-conformal theories. We have also studied quantitatively the 1/N corrections to the orientifold planar equivalence between supersymmetric and nonsupersymmetric theories. Our calculations have combined string techniques and lattice computations in extra-dimensional theories. The work is a first step to define four-dimensional massless scalar-gauge theories on the lattice as the low-energy limit of extra-dimensional pure gauge theories.

Nucleon structure (Horsley, Zanotti)

Understanding the internal structure of nucleons (proton and neutron) in terms of quarks and gluons is one of the outstanding problems in particle physics which has attracted the attention of both theory and experiment for many years. For example, mapping out the distribution of electric and magnetic charge inside the proton is a prime objective of the Jefferson Laboratory's experimental research program. We have started investigating new directions in understanding the effects of different quark masses (flavour symmetry breaking) in the structure of hadrons through lattice simulations with 2+1 quark flavours. As an example of these flavour symmetry breaking effects, we show in the figure a `fan' plot of the masses of the SU(3) baryon octet that results from increasing the amount of flavour symmetry breaking in our simulations.

Algorithms (Kennedy, Pendleton)

Kennedy and Pendleton developed the standard HMC algorithm for the simulation of virtual quark loops in Lattice gauge theory.

Kennedy also developed the RHMC algorithm for simulation with odd numbers of flavours, and has developed a new class of force-gradient integrators for Hybrid Monte Carlo computations that can be optimized with a novel algorithm. He has also studied an improved algorithm for on-shell chiral fermions.

High Performance Computing (Boyle, Kenway)

In 2001 the UKQCD consortium was awarded £ 6.6 M for the design, construction and installation at Edinburgh of a multi-Teraflops scale computer, QCDOC. We developed the chip for this computer in collaboration with Columbia University and IBM T J Watson research center.

The computer was run in Edinburgh from 2004 until 2009 with world leading scientific impact. For example, three most cited published in the hep-lat arXiv preprint server in 2009 were produced with QCDOC computers

Our Watson collaborators went on to develop the BlueGene supercomputer line. QCDOC's network has more recently influenced the design of a 10Pflop/s Fujitsu supercomputer.

Boyle has worked with our IBM collaborators and Columbia University to jointly develop the next generation BlueGene supercomputer design.

In 2009 the UKQCD consortium was awarded an HPC grant by STFC to replace QCDOC with several computers, the largest of which is a next generation BlueGene prototype and will be installed in Edinburgh.

This gives us a unique opportunity to achieve a world lead for the next few years.