15 research outputs found
Ultrasoft Renormalization in Non-Relativistic QCD
For Non-Relativistic QCD the velocity renormalization group correlates the
renormalization scales for ultrasoft, potential and soft degrees of freedom.
Here we discuss the renormalization of operators by ultrasoft gluons. We show
that renormalization of soft vertices can induce new operators, and also
present a procedure for correctly subtracting divergences in mixed
potential-ultrasoft graphs. Our results affect the running of the
spin-independent potentials in QCD. The change for the NNLL t-tbar cross
section near threshold is very small, being at the 1% level and essentially
independent of the energy. We also discuss implications for analyzing
situations where mv^2 ~ Lambda_QCD.Comment: 31 pages, 11 fig
Three particles in a finite volume: The breakdown of spherical symmetry
Lattice simulations of light nuclei necessarily take place in finite volumes,
thus affecting their infrared properties. These effects can be addressed in a
model-independent manner using Effective Field Theories. We study the model
case of three identical bosons (mass m) with resonant two-body interactions in
a cubic box with periodic boundary conditions, which can also be generalized to
the three-nucleon system in a straightforward manner. Our results allow for the
removal of finite volume effects from lattice results as well as the
determination of infinite volume scattering parameters from the volume
dependence of the spectrum. We study the volume dependence of several states
below the break-up threshold, spanning one order of magnitude in the binding
energy in the infinite volume, for box side lengths L between the two-body
scattering length a and L = 0.25a. For example, a state with a three-body
energy of -3/(ma^2) in the infinite volume has been shifted to -10/(ma^2) at L
= a. Special emphasis is put on the consequences of the breakdown of spherical
symmetry and several ways to perturbatively treat the ensuing partial wave
admixtures. We find their contributions to be on the sub-percent level compared
to the strong volume dependence of the S-wave component. For shallow bound
states, we find a transition to boson-diboson scattering behavior when
decreasing the size of the finite volume.Comment: 21 pages, 4 figures, 2 table
Renormalization group scaling in nonrelativistic QCD
We discuss the matching conditions and renormalization group evolution of
non-relativistic QCD. A variant of the conventional MS-bar scheme is proposed
in which a subtraction velocity nu is used rather than a subtraction scale mu.
We derive a novel renormalization group equation in velocity space which can be
used to sum logarithms of v in the effective theory. We apply our method to
several examples. In particular we show that our formulation correctly
reproduces the two-loop anomalous dimension of the heavy quark production
current near threshold.Comment: (27 pages, revtex
Renormalization group analysis of the QCD quark potential to order v^2
A one-loop renormalization group analysis of the order v^2 relativistic
corrections to the static QCD potential is presented. The velocity
renormalization group is used to simultaneously sum ln(m/mv) and ln(m/mv^2)
terms. The results are compared to previous calculations in the literature.Comment: 13 pages. important change: running of soft Lagrangian include
The QCD heavy-quark potential to order v^2: one loop matching conditions
The one-loop QCD heavy quark potential is computed to order v^2 in the color
singlet and octet channels. Several errors in the previous literature are
corrected. To be consistent with the velocity power counting, the full
dependence on |p' + p|/|p' - p| is kept. The matching conditions for the NRQCD
one-loop potential are computed by comparing the QCD calculation with that in
the effective theory. The graphs in the effective theory are also compared to
terms from the hard, soft, potential, and ultrasoft regimes in the threshold
expansion. The issue of off-shell versus on-shell matching and gauge dependence
is discussed in detail for the 1/(m k) term in the potential. Matching on-shell
gives a 1/(m k) potential that is gauge independent and does not vanish for
QED.Comment: 28 pages, References added and minor changes to section III, results
unchange
Effective theory of the Delta(1232) in Compton scattering off the nucleon
We formulate a new power-counting scheme for a chiral effective field theory
of nucleons, pions, and Deltas. This extends chiral perturbation theory into
the Delta-resonance region. We calculate nucleon Compton scattering up to
next-to-leading order in this theory. The resultant description of existing
p cross section data is very good for photon energies up to about 300
MeV. We also find reasonable numbers for the spin-independent polarizabilities
and .Comment: 29 pp, 9 figs. Minor revisions. To be published in PR