The "radiative Delta -> N gamma" decay in light cone QCD

The "g_{Delta N gamma}" coupling for the "Delta -> N gamma" decay is calculated in framework of the light cone QCD sum rules and is found to be g_{Delta N gamma} = (1.6 pm 0.2) GeV^(-1). Using this value of g_{Delta N gamma} we estimate the branching ratio of the Delta^+ -> N gamma decay, which is in a very good agreement with the experimental result.Comment: 9 pages, 1figures, LaTeX formatte

Two-photon physics

It is reviewed how Compton scattering sum rules relate low-energy nucleon structure quantities to the nucleon excitation spectrum. In particular, the GDH sum rule and recently proposed extensions of it will be discussed. These extensions are sometimes more calculationally robust, which may be an advantage when estimating the chiral extrapolations of lattice QCD results, such as for anomalous magnetic moments. Subsequently, new developments in our description of the nucleon excitation spectrum will be discussed, in particular a recently developed chiral effective field theory framework for the $\Delta(1232)$-resonance region. Within this framework, we discuss results on $N$ and $\Delta$ masses, the $\gamma N \Delta$ transition and the $\Delta$ magnetic dipole moment.Comment: 10 pages, prepared for proceedings of Symposium on 20 Years of Physics at the Mainz Mikrotro

The pion photoproduction in the \Delta(1232) region

We investigate the pion photoproduction in the \Delta(1232) region in the framework of an effective Lagrangian including pions, nulceon and \Delta(1232). We work to third order in a small scale expansion with both $m_{\pi}$ and $M_{\Delta}-M_N$ treated as light scales. We note that in the $\Delta$ region, straightward power counting breaks as the amplitudes become very large, to deal with this problem, we suggest that the appropriate way to compare theoretical calculations with experimental data is via weighted integrals of the amplitudes through the $\Delta$ region.Comment: 34 pages and 5 figures,new counterterms arr adde

Computational determination of the largest lattice polytope diameter

A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. Let {\delta}(d, k) be the largest diameter over all lattice (d, k)-polytopes. We develop a computational framework to determine {\delta}(d, k) for small instances. We show that {\delta}(3, 4) = 7 and {\delta}(3, 5) = 9; that is, we verify for (d, k) = (3, 4) and (3, 5) the conjecture whereby {\delta}(d, k) is at most (k + 1)d/2 and is achieved, up to translation, by a Minkowski sum of lattice vectors

Computational determination of the largest lattice polytope diameter

A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. Let {\delta}(d, k) be the largest diameter over all lattice (d, k)-polytopes. We develop a computational framework to determine {\delta}(d, k) for small instances. We show that {\delta}(3, 4) = 7 and {\delta}(3, 5) = 9; that is, we verify for (d, k) = (3, 4) and (3, 5) the conjecture whereby {\delta}(d, k) is at most (k + 1)d/2 and is achieved, up to translation, by a Minkowski sum of lattice vectors