We explore the electromagnetic contribution to the charge symmetry breaking in the octet baryon masses using a subtracted dispersion relation based on the Cottingham formula. For the protonneutron mass splitting we report a minor revision of the recent analysis of Walker-Loud, Carlson and Miller. For the electromagnetic structure of the hyperons we constrain our analysis, where possible, by a combination of lattice QCD and SU(3) symmetry breaking estimates. The results for the baryon mass splittings are found to be compatible with recent lattice QCD+QED determinations. The uncertainties in the dispersive analysis are dominated by the lack of knowledge of the hyperon inelastic structure.

We study isospin-1 P-wave ππ scattering in lattice QCD with two flavours of O(a) improved Wilson fermions. For pion masses ranging from m π = 265 MeV to m π = 437 MeV, we determine the energy spectrum in the centre-of-mass frame and in three moving frames. We obtain the scattering phase shifts using Lüscher's finite-volume quantisation condition. Fitting the dependence of the phase shifts on the scattering momentum to a Breit-Wigner form allows us to determine the resonance parameters m ρ and g ρππ . By combining the scattering phase shifts with the decay matrix element of the vector current, we calculate the timelike pion form factor, F π , and compare the results to the Gounaris-Sakurai representation of the form factor in terms of the resonance parameters. In addition, we fit our data for the form factor to the functional form suggested by the Omnès representation, which allows for the extraction of the charge radius of the pion. As a further application, we discuss the long-distance behaviour of the vector correlator, which is dominated by the two-pion channel. We reconstruct the long-distance part in two ways: one based on the finite-volume energies and matrix elements and the other based on F π . It is shown that this part can be accurately constrained using the reconstructions, which has important consequences for lattice calculations of the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment. * felix.erben@ed.ac.uk

Abstract.Results are presented from an ongoing study of the ρ resonance. The focus is on CLS 2-flavour ensembles generated using O(a) improved Wilson fermions with pion masses ranging from 265 to 437 MeV. The energy levels are extracted by solving the GEVP of correlator matrices, created with the distillation approach involving ρ and ππ interpolators. The study is done in the centre-of-mass frame and several moving frames. One aim of this work is to extract the timelike pion form factor after applying the Lüscher formalism. We therefore plan to integrate this study with the existing Mainz programme for the calculation of the hadronic vacuum polarization contribution to the muon g − 2.

The decays and mixing of K mesons are remarkably sensitive to the weak interactions of quarks and leptons at high energies. They provide important tests of the standard model at both first and second order in the Fermi constant G F and offer a window into possible new phenomena at energies as high as 1,000 TeV. These possibilities become even more compelling as the growing capabilities of lattice QCD make high-precision standard model predictions possible. Here we discuss and attempt to forecast some of these capabilities.

Results are presented from an ongoing study of the ρ resonance. The focus is on CLS 2-flavour ensembles generated using O(a) improved Wilson fermions with pion masses ranging from 265 to 437 MeV. The energy levels are extracted by solving the GEVP of correlator matrices, created with the distillation approach involving ρ and ππ interpolators. The study is done in the centre-of-mass frame and several moving frames. One aim of this work is to extract the timelike pion form factor after applying the Lüscher formalism. We therefore plan to integrate this study with the existing Mainz programme for the calculation of the hadronic vacuum polarization contribution to the muon g − 2.

Scattering at physical pion mass is still an exploratory field in lattice QCD. This generally involves the extraction of excited states through multi-particle correlators on systems with resonances. In that context, distillation has been demonstrated to be effective both as a smearing kernel and a computational tool. Motivated by the study of the smearing profile of the distillation operator, we compare stochastic and exact distillation cases for different numbers of Laplacian eigenvectors using a RBC-UKQCD N f = 2 + 1 domain-wall fermion lattice with a physical pion mass.

The decreasing uncertainties in theoretical predictions and experimental measurements of several hadronic observables related to weak processes, which in many cases are now smaller than O(1%), require theoretical calculations to include subleading corrections that were neglected so far. Precise determinations of leptonic and semi-leptonic decay rates, including QED and strong isospin-breaking effects, can play a central role in solving the current tensions in the first-row unitarity of the CKM matrix. In this work we present the first RBC/UKQCD lattice calculation of the isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muons and neutrinos. The calculation is performed at fixed lattice spacing (a−1 ≃ 1.730 GeV) on a 483× 96 volume with Nf = 2 + 1 dynamical quarks close to the physical point and domain wall fermions in the Möbius formulation are employed. Long-distance QED interactions are included according to the QEDL prescription and the crucial role of finite-volume electromagnetic corrections in the determination of leptonic decay rates, which produce a large systematic uncertainty, is extensively discussed. Finally, we study the different sources of uncertainty on |Vus|/|Vud| and observe that, if finite-volume systematics can be reduced, the error from isospin-breaking corrections is potentially sub-dominant in the final precision of the ratio of the CKM matrix elements.

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