124 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
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
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
Hard Scattering Factorization from Effective Field Theory
In this paper we show how gauge symmetries in an effective theory can be used
to simplify proofs of factorization formulae in highly energetic hadronic
processes. We use the soft-collinear effective theory, generalized to deal with
back-to-back jets of collinear particles. Our proofs do not depend on the
choice of a particular gauge, and the formalism is applicable to both exclusive
and inclusive factorization. As examples we treat the pi-gamma form factor
(gamma gamma* -> pi^0), light meson form factors (gamma* M -> M), as well as
deep inelastic scattering (e- p -> e- X), Drell-Yan (p pbar -> X l+ l-), and
deeply virtual Compton scattering (gamma* p -> gamma(*) p).Comment: 35 pages, 4 figures, typos corrected, journal versio
Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum
We complete the leading-log renormalization group scaling of the NRQCD
Lagrangian at . The next-to-next-to-leading-log renormalization group
scaling of the potential NRQCD Lagrangian (as far as the singlet is concerned)
is also obtained in the situation . As a
by-product, we obtain the heavy quarkonium spectrum with the same accuracy in
the situation m\alpha_s^2 \simg \Lambda_{QCD}. When , this is equivalent to obtain the whole set of
terms in the heavy quarkonium spectrum.
The implications of our results in the non-perturbative situation are also mentioned.Comment: 16 pages, LaTeX. Minor changes. Final versio
Two-loop corrections to the decay rate of parapositronium
Order corrections to the decay rate of parapositronium are
calculated. A QED scattering calculation of the amplitude for electron-positron
annihilation into two photons at threshold is combined with the technique of
effective field theory to determine an NRQED Hamiltonian, which is then used in
a bound state calculation to determine the decay rate. Our result for the
two-loop correction is in units of times the
lowest order rate. This is consistent with but more precise than the result
of a previous calculation.Comment: 26 pages, 7 figure
NRQCD Analysis of Bottomonium Production at the Tevatron
Recent data from the CDF collaboration on the production of spin-triplet
bottomonium states at the Tevatron p \bar p collider are analyzed within the
NRQCD factorization formalism. The color-singlet matrix elements are determined
from electromagnetic decays and from potential models. The color-octet matrix
elements are determined by fitting the CDF data on the cross sections for
Upsilon(1S), Upsilon(2S), and Upsilon(3S) at large p_T and the fractions of
Upsilon(1S) coming from chi_b(1P) and chi_b(2P). We use the resulting matrix
elements to predict the cross sections at the Tevatron for the spin-singlet
states eta_b(nS) and h_b(nP). We argue that eta_b(1S) should be observable in
Run II through the decay eta_b -> J/psi + J/psi.Comment: 20 pages, 3 figure
Quenched charmonium spectrum
We study charmonium using the standard relativistic formalism in the quenched
approximation, on a set of lattices with isotropic lattice spacings ranging
from 0.1 to 0.04 fm. We concentrate on the calculation of the hyperfine
splitting between eta_c and J/psi, aiming for a controlled continuum
extrapolation of this quantity. The splitting extracted from the
non-perturbatively improved clover Dirac operator shows very little dependence
on the lattice spacing for fm. The dependence is much stronger for
Wilson and tree-level improved clover operators, but they still yield
consistent extrapolations if sufficiently fine lattices, fm (), are used. Our result for the hyperfine splitting is
77(2)(6) MeV (where Sommer's parameter, r_0, is used to fix the scale). This
value remains about 30% below experiment. Dynamical fermions and OZI-forbidden
diagrams both contribute to the remainder. Results for the eta_c and J/psi wave
functions are also presented.Comment: 22 pages, 7 figure
Mass spectra of doubly heavy Omega_QQ' baryons
We evaluate the masses of baryons composed of two heavy quarks and a strange
quark with account for spin-dependent splittings in the framework of potential
model with the KKO potential motivated by QCD with a three-loop beta-function
for the effective charge consistent with both the perturbative limit at short
distances and linear confinement term at long distances between the quarks. The
factorization of dynamics is supposed and explored in the nonrelativistic
Schroedinger equation for the motion in the system of two heavy quarks
constituting the doubly heavy diquark and the strange quark interaction with
the diquark. The limits of approach, its justification and uncertainties are
discussed. Excited quasistable states are classified by the quantum numbers of
heavy diquark composed by the heavy quarks of the same flavor.Comment: 14 pages, revtex4-file, 3 eps-figures, 5 tables, typos correcte
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