Following the canonical script for lattice conferences, yesterday was the day without plenaries. Instead, the morning was dedicated to parallel sessions (including my own talk), and the afternoon was free time with the option of taking one of several arranged excursions.
I went on the excursion to Salisbury cathedral (which is notable both for its fairly homogeneous and massive architectural ensemble, and for being home to one of four original copies of the Magna Carta) and Stonehenge (which in terms of diameter seems to be much smaller than I had expected from photos).
Today began with the traditional non-lattice theory talk, which was given by Monika Blanke, who spoke about the impact of lattice QCD results on CKM phenomenology. Since quarks cannot be observed in isolation, the extraction of CKM matrix elements from experimental results always require knowledge of the appropriate hadronic matrix elements of the currents involved in the measured reaction. This means that lattice results for the form factors of heavy-to-light semileptonic decays and for the hadronic parameters governing neutral kaon and B meson mixing are of crucial importance to CKM phenomenology, to the extent that there is even a sort of "wish list" to the lattice. There has long been a discrepancy between the values of both |Vcb| and |Vub| extracted from inclusive and exclusive decays, respectively, and the ratio |Vub/Vcb| that can be extracted from decays of Λb baryons only adds to the tension. However, this is likely to be a result of underestimated theoretical uncertainties or experimental issues, since the pattern of the discrepancies is not in agreement with that which would results from new physics effects induced by right-handed currents. General models of flavour violating new physics seems to favour the inclusive value for |Vub|. In b->s transitions, there is evidence for new physics effects at the 4σ level, but significant theoretical uncertainties remain. The B(s)->μ+μ- branching fractions are currently in agreement with the SM at the 2σ level, but new, more precise measurements are forthcoming.
Ran Zhou complemented this with a review talk about heavy flavour results from the lattice, where there are new results from a variety of different approaches (NRQCD, HQET, Fermilab and Columbia RHQ formalisms), which can serve as useful and important cross-checks on each other's methodological uncertainties.
Next came a talk by Amy Nicholson on neutrinoless double β decay results from the lattice. Neutrinoless double β decays are possible if neutrinos are Majorana particles, which would help to explain the small masses of the observed left-handed neutrinos through the see-saw mechanism pushing the right-handed neutrinos off to near the GUT scale. Treating the double β decay in the framework of a chiral effective theory, the leading-order matrix element required is a process π-->π+e-e-, for which there are first results in lattice QCD. The NLO process would have disconnected diagrams, but cannot contribute to the 0+->0+ transitions which are experimentally studied, whereas the NNLO process involves two-nucleon operators and still remains to be studied in greater detail on the lattice.
After the coffee break, Agostino Patella reviewed the hot topic of QED corrections to hadronic observables. There are currently two main methods for dealing with QED in the context of lattice simulations: either to simulate QCD+QED directly (usually at unphysically large electromagnetic couplings followed by an extrapolation to the physical value of α=1/137), or to expand it in powers of α and to measure only the resulting correlation functions (which will be four-point functions or higher) in lattice QCD. Both approaches have been used to obtain some already very impressive results on isospin-breaking QED effects in the hadronic spectrum, as shown already in the spectroscopy review talk. There are, however, still a number of theoretical issues connected to the regularization of IR modes that relate to the Gauss law constraint that would forbid the existence of a single charged particle (such as a proton) in a periodic box. The prescriptions to evade this problem all lead to a non-commutativity of limits requiring the infinite-volume limit to be taken before other limits (such as the continuum or chiral limits): QEDTL, which omits the global zero modes of the photon field, is non-local and does not have a transfer matrix; QEDL, which omits the spatial zero modes on each timeslice, has a transfer matrix, but is still non-local and renormalizes in a non-standard fashion, such that it does not have a non-relativistic limit; the use of a massive photon leads to a local theory with softly broken gauge symmetry, but still requires the infinite-volume limit to be taken before removing the photon mass. Going beyond hadron masses to decays introduces new IR problems, which need to be treated in the Bloch-Nordsieck way, leading to potentially large logarithms.
The 2016 Ken Wilson Lattice Award was awarded to Antonin Portelli for his outstanding contributions to our understanding of electromagnetic effects on hadron properties. Antonin was one of the driving forces behind the BMW collaboration's effort to determine the proton-neutron mass difference, which resulted in a Science paper exhibiting one of the most frequently-shown and impressive spectrum plots at this conference.
In the afternoon, parallel sessions took place, and in the evening there was a (very nice) conference dinner at the Southampton F.C. football stadium.
