24,178 research outputs found
Quarkonia in Hamiltonian Light-Front QCD
A constituent parton picture of hadrons with logarithmic confinement
naturally arises in weak coupling light-front QCD. Confinement provides a mass
gap that allows the constituent picture to emerge. The effective renormalized
Hamiltonian is computed to , and used to study charmonium and
bottomonium. Radial and angular excitations can be used to fix the coupling
, the quark mass , and the cutoff . The resultant hyperfine
structure is very close to experiment.Comment: 9 pages, 1 latex figure included in the text. Published version (much
more reader-friendly); corrected error in self-energ
Note on restoring manifest rotational symmetry in hyperfine and fine structure in light-front QED
We study the part of the renormalized, cutoff QED light-front Hamiltonian
that does not change particle number. The Hamiltonian contains interactions
that must be treated in second-order bound state perturbation theory to obtain
hyperfine structure. We show that a simple unitary transformation leads
directly to the familiar Breit-Fermi spin-spin and tensor interactions, which
can be treated in degenerate first-order bound-state perturbation theory, thus
simplifying analytic light-front QED calculations. To the order in momenta we
need to consider, this transformation is equivalent to a Melosh rotation. We
also study how the similarity transformation affects spin-orbit interactions.Comment: 17 pages, latex fil
Initial bound state studies in light-front QCD
We present the first numerical QCD bound state calculation based on a
renormalization group-improved light-front Hamiltonian formalism. The QCD
Hamiltonian is determined to second order in the coupling, and it includes
two-body confining interactions. We make a momentum expansion, obtaining an
equal-time-like Schrodinger equation. This is solved for quark-antiquark
constituent states, and we obtain a set of self-consistent parameters by
fitting B meson spectra.Comment: 38 pages, latex, 5 latex figures include
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Analytic Treatment of Positronium Spin Splittings in Light-Front QED
We study the QED bound-state problem in a light-front hamiltonian approach.
Starting with a bare cutoff QED Hamiltonian, , with matrix elements
between free states of drastically different energies removed, we perform a
similarity transformation that removes the matrix elements between free states
with energy differences between the bare cutoff, , and effective
cutoff, \lam (\lam < \Lam). This generates effective interactions in the
renormalized Hamiltonian, . These effective interactions are derived
to order in this work, with . is renormalized
by requiring it to satisfy coupling coherence. A nonrelativistic limit of the
theory is taken, and the resulting Hamiltonian is studied using bound-state
perturbation theory (BSPT). The effective cutoff, \lam^2, is fixed, and the
limit, 0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow
\infty, is taken. This upper bound on \lam^2 places the effects of
low-energy (energy transfer below \lam) emission in the effective
interactions in the sector. This lower bound on \lam^2
insures that the nonperturbative scale of interest is not removed by the
similarity transformation. As an explicit example of the general formalism
introduced, we show that the Hamiltonian renormalized to reproduces
the exact spectrum of spin splittings, with degeneracies dictated by rotational
symmetry, for the ground state through . The entire calculation is
performed analytically, and gives the well known singlet-triplet ground state
spin splitting of positronium, . We discuss remaining
corrections other than the spin splittings and how they can be treated in
calculating the spectrum with higher precision.Comment: 46 pages, latex, 3 Postscript figures included, section on remaining
corrections added, title changed, error in older version corrected, cutoff
placed in a windo
Perturbative Tamm-Dancoff Renormalization
A new two-step renormalization procedure is proposed. In the first step, the
effects of high-energy states are considered in the conventional (Feynman)
perturbation theory. In the second step, the coupling to many-body states is
eliminated by a similarity transformation. The resultant effective Hamiltonian
contains only interactions which do not change particle number. It is subject
to numerical diagonalization. We apply the general procedure to a simple
example for the purpose of illustration.Comment: 20 pages, RevTeX, 10 figure
Nonperturbative renormalization group in a light-front three-dimensional real scalar model
The three-dimensional real scalar model, in which the symmetry
spontaneously breaks, is renormalized in a nonperturbative manner based on the
Tamm-Dancoff truncation of the Fock space. A critical line is calculated by
diagonalizing the Hamiltonian regularized with basis functions. The marginal
() coupling dependence of the critical line is weak. In the broken
phase the canonical Hamiltonian is tachyonic, so the field is shifted as
. The shifted value is determined as a function of
running mass and coupling so that the mass of the ground state vanishes.Comment: 23 pages, LaTeX, 6 Postscript figures, uses revTeX and epsbox.sty. A
slight revision of statements made, some references added, typos correcte
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