1,318 research outputs found
Langevin equations with multiplicative noise: resolution of time discretization ambiguities for equilibrium systems
A Langevin equation with multiplicative noise is an equation schematically of
the form dq/dt = -F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose
amplitude e(q) depends on q itself. Such equations are ambiguous, and depend on
the details of one's convention for discretizing time when solving them. I show
that these ambiguities are uniquely resolved if the system has a known
equilibrium distribution exp[-V(q)/T] and if, at some more fundamental level,
the physics of the system is reversible. I also discuss a simple example where
this happens, which is the small frequency limit of Newton's equation d^2q/dt^2
+ e^2(q) dq/dt = - grad V(q) + e^{-1}(q) xi with noise and a q-dependent
damping term. The resolution does not correspond to simply interpreting naive
continuum equations in a standard convention, such as Stratanovich or Ito. [One
application of Langevin equations with multiplicative noise is to certain
effective theories for hot, non-Abelian plasmas.]Comment: 15 pages, 2 figures [further corrections to Appendix A
Production of the X(3872) at the Tevatron and the LHC
We predict the differential cross sections for production of the X(3872) at
the Tevatron and the Large Hadron Collider from both prompt QCD mechanisms and
from decays of b hadrons. The prompt cross section is calculated using the
NRQCD factorization formula. Simplifying assumptions are used to reduce the
nonperturbative parameters to a single NRQCD matrix element that is determined
from an estimate of the prompt cross section at the Tevatron. For X(3872) with
transverse momenta greater than about 4 GeV, the predicted cross section is
insensitive to the simplifying assumptions. We also discuss critically a recent
analysis that concluded that the prompt production rate at the Tevatron is too
large by orders of magnitude for the X(3872) to be a weakly-bound charm-meson
molecule. We point out that if charm-meson rescattering is properly taken into
account, the upper bound is increased by orders of magnitude and is compatible
with the observed production rate at the Tevatron.Comment: 29 pages, 5 figure
The Massive Thermal Basketball Diagram
The "basketball diagram" is a three-loop vacuum diagram for a scalar field
theory that cannot be expressed in terms of one-loop diagrams. We calculate
this diagram for a massive scalar field at nonzero temperature, reducing it to
expressions involving three-dimensional integrals that can be easily evaluated
numerically. We use this result to calculate the free energy for a massive
scalar field with a phi^4 interaction to three-loop order.Comment: 19 pages, 3 figure
Color-Octet Fragmentation and the psi' Surplus at the Tevatron
The production rate of prompt 's at large transverse momentum at the
Tevatron is larger than theoretical expectations by about a factor of 30. As a
solution to this puzzle, we suggest that the dominant production
mechanism is the fragmentation of a gluon into a pair in a pointlike
color-octet S-wave state, which subsequently evolves nonperturbatively into a
plus light hadrons. The contribution to the fragmentation function from
this process is enhanced by a short-distance factor of relative
to the conventional color-singlet contribution. This may compensate for the
suppression by , where is the relative momentum of the charm quark in
the . If this is indeed the dominant production mechanism at large
, then the prompt 's that are observed at the Tevatron should
almost always be associated with a jet of light hadrons.Comment: 9 pages, LaTe
Damping rate of plasmons and photons in a degenerate nonrelativistic plasma
A calculation is presented of the plasmon and photon damping rates in a dense
nonrelativistic plasma at zero temperature, following the resummation program
of Braaten-Pisarski. At small soft momentum , the damping is dominated by scattering processes corresponding to double longitudinal Landau
damping. The dampings are proportional to , where
is the Fermi velocity.Comment: 9 pages, 2 figure
Factorization in the Production and Decay of the X(3872)
The production and decay of the X(3872) are analyzed under the assumption
that the X is a weakly-bound molecule of the charm mesons D^0 \bar D^{*0} and
D^{*0} \bar D^0. The decays imply that the large D^0 \bar D^{*0} scattering
length has an imaginary part. An effective field theory for particles with a
large complex scattering length is used to derive factorization formulas for
production rates and decay rates of X. If a partial width is calculated in a
model with a particular value of the binding energy, the factorization formula
can be used to extrapolate to other values of the binding energy and to take
into account the width of the X. The factorization formulas relate the rates
for production of X to those for production of D^0 \bar D^{*0} and D^{*0} \bar
D^0 near threshold. They also imply that the line shape of X differs
significantly from that of a Breit-Wigner resonance.Comment: 23 pages, 8 figures, revtex4, typos correcte
The Renormalization Group Limit Cycle for the 1/r^2 Potential
Previous work has shown that if an attractive 1/r^2 potential is regularized
at short distances by a spherical square-well potential, renormalization allows
multiple solutions for the depth of the square well. The depth can be chosen to
be a continuous function of the short-distance cutoff R, but it can also be a
log-periodic function of R with finite discontinuities, corresponding to a
renormalization group (RG) limit cycle. We consider the regularization with a
delta-shell potential. In this case, the coupling constant is uniquely
determined to be a log-periodic function of R with infinite discontinuities,
and an RG limit cycle is unavoidable. In general, a regularization with an RG
limit cycle is selected as the correct renormalization of the 1/r^2 potential
by the conditions that the cutoff radius R can be made arbitrarily small and
that physical observables are reproduced accurately at all energies much less
than hbar^2/mR^2.Comment: 11 pages, 4 figure
Heavy Quark Fragmentation to Baryons Containing Two Heavy Quarks
We discuss the fragmentation of a heavy quark to a baryon containing two
heavy quarks of mass . In this limit the heavy quarks
first combine perturbatively into a compact diquark with a radius small
compared to , which interacts with the light hadronic
degrees of freedom exactly as does a heavy antiquark. The subsequent evolution
of this diquark to a baryon is identical to the fragmentation of a
heavy antiquark to a meson. We apply this analysis to the production of baryons
of the form , , and .Comment: 9 pages, 1 figure included, uses harvmac.tex and epsf.tex, UCSD/PTH
93-11, CALT-68-1868, SLAC-PUB-622
Gluon fragmentation to quarkonia
Gluon fragmentation to heavy quarkonia is studied herein. We
compute these D-wave states' polarized fragmentation functions and find that
they are enhanced by large numerical prefactors. The prospects for detecting
the lowest lying charmonium state at the Tevatron are discussed.Comment: 10 pages with 4 uuencoded figures, CALT-68-195
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