A Wilsonian approach to ππ scattering based in the Glazek-Wilson Similarity Renormalization Group (SRG) for Hamiltonians is analyzed in momentum space up to a maximal CM energy of √ s = 1.4 GeV. To this end, we identify the corresponding relativistic Hamiltonian by means of the 3D reduction of the Bethe-Salpeter equation in the Kadyshevsky scheme, introduce a momentum grid and provide an isospectral definition of the phase-shift based on a spectral shift of a Chebyshev angle. We also propose a new method to integrate the SRG equations based on the Crank-Nicolson algorithm with a single step finite difference so that isospectrality is preserved at any step of the calculations. We discuss issues on the unnatural high momentum tails present in the fitted interactions and reaching far beyond the maximal CM energy of √ s = 1.4 GeV and how these tails can be integrated out explicitly by using Block-Diagonal generators of the SRG.

In this article we re-derive the Boost operators in Coulomb Gauge Yang-Mills theory employing the path integral formalism and write down the complete operators for QCD. We immediately apply them to note that what are usually called the pion square, quartic . . . charge radii, defined from derivatives of the pion form factor at zero squared momentum transfer, are completely blurred out by relativistic and interaction corrections, so that it is not clear at all how to interpret these quantities in terms of the pion charge distribution. The form factor therefore measures matrix elements of powers of the QCD boost and Moeller operators, weighted by the charge density in the target's rest frame. In addition we remark that the decomposition of the η wave function in quarkonium, gluonium, . . . , components attempted by the KLOE Collaboration combining data from φ radiative decays, requires corrections due to the velocity of the final-state meson recoiling against a photon. This will be especially important if such decompositions are to be attempted with data from J/ψ decays.

We present a general formalism that uses the point form of relativistic Hamiltonian dynamics to describe the electroweak structure of heavy-light mesons within constituent quark models. We study the heavy quark limit (i.e. m Q → ∞) and check that the predictions of heavy quark symmetry are satisfied. A simple analytic expressions is given for the Isgur-Wise function. In addition, cluster properties and the relation of our approach to front form calculations are discussed.

We investigate electromagnetic and weak form factors of heavy-light mesons in the context of point-form relativistic quantum mechanics. To this aim we treat the physical processes from which such electroweak form factors are extracted by means of a coupled channel approach which accounts for the dynamics of the intermediate gauge bosons. It is shown that heavy-quark symmetry is respected by this formulation. A simple analytical expression is obtained for the Isgur-Wise function in the heavy-quark limit. Breaking of heavy-quark symmetry due to realistic values of the heavy-quark mass are studied numerically.

No abstract