Transverse lattice

Abstract

The transverse lattice approach to non-perturbative light-front hamiltonian QCD is described. Preliminary results on the π −ρ system are presented, at fixed DLCQ and Tamm-Dancoff cut-offs. A renormalised, approximately Lorentz covariant light-front hamiltonian is found to leading order of the colour-dielectric expansion, compatible with a massless pion. The π light-front wavefunction is compared with experiment. Exclusive processes agree reasonably well, given the approximations, but inclusive processes, sensitive to higher Fock state structure, still exhibit large cut-off artifacts.

A study of heavy-light mesons on the transverse lattice

“…Our main sources of systematic errors are the Fock space truncation (in combination with a truncation of the transverse lattice Hamiltonian [9]), the truncation of the Hilbert space within each Fock component and the extrapolation to the M b → ∞ limit. The uncertainties from Hilbert space truncations are well under control since we used basis function techniques and extrapolated the results in the dimension of the Hilbert space.…”

“…For example, it would be very useful to repeat this study for B s mesons. While the ub meson calculations that we performed here could make use of light-quark parameters determined in previous works [11,9], such a study involving s quarks would first require determination of hopping parameters for s quarks using techniques similar to the used in Refs. [11,9].…”

“…[12] and was previously applied to mesons containing only light quarks in Refs. [9,11], and we refer the reader to these works for more details. Here we restrict ourselves to a more qualitative description of the degrees of freedom that enter the Hamiltonian and some of the details of how heavy quarks are incorporated in this framework.…”

“…The first approximation that we use is the same light front Tamm-Dancoff truncation of the Fock state expansion that was used in Refs. [9,11], namely, a truncation upto and including the 3-particle sector. After reminding oneself that the fermion degrees of freedom (quarks and antiquarks) always occupy the lattice (transverse) sites and the gauge degrees of freedom (link fields) reside on the lattice spacings, it is easy to understand the following two direct consequences of the aforementioned truncation:…”

“…More recent applications of the color dielectric transverse lattice formulation to mesons at large N C can be found in Refs. [9][10][11], where more details regarding the transverse lattice approach approach can be found.…”