Optimization of perturbative similarity renormalization group for Hamiltonians with asymptotic freedom and bound states

A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians, through adjustment of the generator of the similarity transformation. The improvement is measured by comparing the eigenvalues of perturbatively calculated renormalized Hamiltonians that couple only a relatively small number of effective basis states, with the exact bound state energy in the model. The improved perturbative calculus leads to a few-percent accuracy in a systematic expansion.Comment: 6 pages of latex, 4 eps figure

Limit cycles of effective theories

A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains a logarithmic ultraviolet divergence that is generated by both real and imaginary parts of the Hamiltonian matrix elements. Discussion of the example includes a connection between asymptotic freedom with one scale of bound states and the limit cycle with an entire hierarchy of bound states.Comment: 8 pages, 3 figures, revtex

Light-front Hamiltonians for heavy quarks and gluons

A boost-invariant light-front Hamiltonian formulation of canonical quantum chromodynamics provides a heuristic picture of the binding mechanism for effective heavy quarks and gluons.Comment: 10 pages, 6 figures, Invited talk at the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics (LC2005), Cairns, Australia, 7-15 Jul 200

Renormalized quark-antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD

In response to the growing need for theoretical tools that can be used in QCD to describe and understand the dynamics of gluons in hadrons in the Minkowski space-time, the renormalization group procedure for effective particles (RGPEP) is shown in the simplest available context of heavy quarkonia to exhibit a welcome degree of universality in the first approximation it yields once one assumes that beyond perturbation theory gluons obtain effective mass. Namely, in the second-order terms, the Coulomb potential with Breit-Fermi spin couplings in the effective quark-antiquark component of a heavy quarkonium, is corrected in one-flavor QCD by a spin-independent harmonic oscillator term that does not depend on the assumed effective gluon mass or the choice of the RGPEP generator. The new generator we use here is much simpler than the ones used before and has the advantage of being suitable for studies of the effective gluon dynamics at higher orders than the second and beyond the perturbative expansion.Comment: 8 pages, 2 figures, journal versio

Neutrino oscillations in the front form of Hamiltonian dynamics

Since future, precise theory of neutrino oscillations should include the understanding of the neutrino mass generation and a precise, relativistic description of hadrons, and observing that such a future theory may require Dirac's FF of Hamiltonian dynamics, we provide a preliminary FF description of neutrino oscillations using the Feynman--Gell-Mann-Levy version of an effective theory in which leptons interact directly with whole nucleons and pions, instead of with quarks via intermediate bosons. The interactions are treated in the lowest-order perturbative expansion in the coupling constants in the effective theory, including a perturbative solution of the coupled constraint equations. Despite missing quarks and their binding mechanism, the effective Hamiltonian description is sufficiently precise for showing that the standard oscillation formula results from the interference of amplitudes with different neutrinos in virtual intermediate states. This holds provided that the inherent experimental uncertainties of preparing beams of incoming and measuring rates of production of outgoing particles are large enough for all of the different neutrino intermediate states to contribute as alternative virtual paths through which the long-baseline scattering process can manifest itself. The result that an approximate, effective FF theory reproduces the standard oscillation formula at the level of transition rates for currently considered long-baseline experiments--even though the space-time development of scattering is traced differently and the relevant interaction Hamiltonians are constructed differently than in the commonly used IF of dynamics--has two implications. It shows that the common interpretation of experimental results is not the only one, and it opens the possibility of considering more precise theories taking advantage of the features of the FF that are not available in the IF.Comment: revtex4, 10 page

Asymptotic Freedom and Bound States in Hamiltonian Dynamics

We study a model of asymptotically free theories with bound states using the similarity renormalization group for hamiltonians. We find that the renormalized effective hamiltonians can be approximated in a large range of widths by introducing similarity factors and the running coupling constant. This approximation loses accuracy for the small widths on the order of the bound state energy and it is improved by using the expansion in powers of the running coupling constant. The coupling constant for small widths is order 1. The small width effective hamiltonian is projected on a small subset of the effective basis states. The resulting small matrix is diagonalized and the exact bound state energy is obtained with accuracy of the order of 10% using the first three terms in the expansion. We briefly describe options for improving the accuracy.Comment: plain latex file, 15 pages, 6 latex figures 1 page each, 1 tabl