Flavor physics and new physics searches from the lattice
Final Report Abstract
In our calculations of QCD + QED the strategy has been to simulate at an artificial coupling αEM = 0.1 and then interpolate between this point and pure QCD to the physical fine structure constant αEM = 1/137. This value was chosen so that electromagnetic effects can be easily seen, but are still small enough that we can expect them to scale linearly in αEM . To check that, and to extrapolate reliably to the physical point, we have added simulations at αEM = 0.05 as part of this project. To assess the CKM mixing matrix and reveal the signature for new physics, it is important to understand the pattern of flavor symmetry breaking in hadron matrix elements. In previous work we have presented a program to systematically investigate the pattern of symmetry breaking in meson and baryon masses involving u, d and s quarks. In this project the investigations have been extended to matrix elements of mesons and baryons. The strategy is to keep the average bare quark mass m = (mu + md + m s )/3 constant and expand the matrix elements about the flavor ¯ symmetric point mu = md = m s . Thus all mass dependence will be expressed as polynomials in δmq = mq − m, q = u, d, s. This is complementary to chiral expansions, which start at a ¯ numerically out-of-reach zero quark mass, rather than here where we start at the SU(3) flavor symmetry point. We have, for the first time, computed and resolved the broken isospin induced π0 − η mass splitting near an effective SU(3) symmetric point, as well as observed the qualitative effects of electromagnetism and broken isospin on the flavor compositions of the flavor-neutral pseudoscalar mesons. We have shown the efficacy of studying the flavor-neutral pseudoscalar mesons through the use of stochastic noise sources in combination with gauge-covariant Gaussian smearing and the variational method. Further, we have presented what appears to be a promising method for 13 studying the overlaps of the mesons with respect to the chosen interpolating operator basis, and shown that they can be further understood and extrapolated by appropriate parametrization. The major decay rates of the charged pion and kaon mesons are to the end states of a muon and neutrino. Analyzing this decay on the lattice could lead to improved values for the meson decay constants and the parameters Vud and Vus in the CKM matrix. High accuracy predictions will need to have electromagnetic effects included. Rather than correcting for QED effects perturbatively, we have developed an elegant way to compute electromagnetic corrections to hadronic processes, requiring background field configurations with dynamical photons, which makes our QCD + QED project the ideal laboratory for such calculations. We find the QED contribution to be 2 − 3%. We have obtained lattice QCD+QED results for the light baryon mass spectrum including both strong and electromagnetic isospin breaking effects. We find excellent agreement between our results for the mass splittings of the isospin partners, n − p, Σ− − Σ+ , Ξ− − Ξ0 , and those observed experimentally. Our procedure also allows for the decomposition of these isospin-dependent mass splittings into strong and electromagnetic contributions with the Dashen scheme. The principle focus is the determination of the isospin breaking effects in the decuplet baryon mass spectrum. The lattice estimates for the mass splittings within the different isospin multiplets of the decuplet baryons are in excellent agreement with the experimentally observed splittings.
