5,557 research outputs found
Enhanced chiral logarithms in partially quenched QCD
I discuss the properties of pions in ``partially quenched'' theories, i.e.
those in which the valence and sea quark masses, and , are
different. I point out that for lattice fermions which retain some chiral
symmetry on the lattice, e.g. staggered fermions, the leading order prediction
of the chiral expansion is that the mass of the pion depends only on , and
is independent of . This surprising result is shown to receive corrections
from loop effects which are of relative size , and which thus
diverge when the valence quark mass vanishes. Using partially quenched chiral
perturbation theory, I calculate the full one-loop correction to the mass and
decay constant of pions composed of two non-degenerate quarks, and suggest
various combinations for which the prediction is independent of the unknown
coefficients of the analytic terms in the chiral Lagrangian. These results can
also be tested with Wilson fermions if one uses a non-perturbative definition
of the quark mass.Comment: 14 pages, 3 figures, uses psfig. Typos in eqs (18)-(20) corrected
(alpha_4 is replaced by alpha_4/2
Applications of Partially Quenched Chiral Perturbation Theory
Partially quenched theories are theories in which the valence- and sea-quark
masses are different. In this paper we calculate the nonanalytic one-loop
corrections of some physical quantities: the chiral condensate, weak decay
constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude,
using partially quenched chiral perturbation theory. Our results for weak decay
constants and masses agree with, and generalize, results of previous work by
Sharpe. We compare B_K and the K+ decay amplitude with their real-world values
in some examples. For the latter quantity, two other systematic effects that
plague lattice computations, namely, finite-volume effects and unphysical
values of the quark masses and pion external momenta are also considered. We
find that typical one-loop corrections can be substantial.Comment: 22 pages, TeX, refs. added, minor other changes, version to appear in
Phys. Rev.
Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit
The linear stability of freely propagating, adiabatic, planar premixed
ames is investigated in the context of a simple chain-branching
chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed
by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and
contrasted with those from a previous purely thermal-di�usive constant density linear stability study. It is shown that when thermal
expansion is properly accounted for, a region of stable
ames predicted by the constant density model disappears, and instead the
ame
is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak
e�ect on the critical fuel Lewis number required for instability. These e�ects of thermal expansion on the two-step chain-branching
ame
are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in
the limit that the chain-branching crossover temperature tends to the adiabatic
ame temperature, the two-step model can be described
to leading order by the one-step model with a suitably de�ned e�ective activation energy
Constraint on the Low Energy Constants of Wilson Chiral Perturbation Theory
Wilson chiral perturbation theory (WChPT) is the effective field theory
describing the long- distance properties of lattice QCD with Wilson or
twisted-mass fermions. We consider here WChPT for the theory with two light
flavors of Wilson fermions or a single light twisted-mass fermion.
Discretization errors introduce three low energy constants (LECs) into
partially quenched WChPT at O(a^2), conventionally called W'_6, W'_7 and W'_8 .
The phase structure of the theory at non-zero a depends on the sign of the
combination 2W'_6 + W'_8, while the spectrum of the lattice Hermitian
Wilson-Dirac operator depends on all three constants. It has been argued, based
on the positivity of partition functions of fixed topological charge, and on
the convergence of graded group integrals that arise in the epsilon-regime of
ChPT, that there is a constraint on the LECs arising from the underlying
lattice theory. In particular, for W'_6 = W'_7 = 0, the constraint found is
W'_8 \le 0. Here we provide an alternative line of argument, based on mass
inequalities for the underlying partially quenched theory. We find that W'_8
\le 0, irrespective of the values of W'_6 and W'_7. Our constraint implies that
2W'_6 > |W'_8| if the phase diagram is to be described by the first-order
scenario, as recent simulations suggest is the case for some choices of action.Comment: 10 pages, no figure
Finite-volume two-pion energies and scattering in the quenched approximation
We investigate how L\"uscher's relation between the finite-volume energy of
two pions at rest and pion scattering lengths has to be modified in quenched
QCD. We find that this relation changes drastically, and in particular, that
``enhanced finite-volume corrections" of order and occur at
one loop ( is the linear size of the box), due to the special properties of
the in the quenched approximation. We define quenched pion scattering
lengths, and show that they are linearly divergent in the chiral limit. We
estimate the size of these various effects in some numerical examples, and find
that they can be substantial.Comment: 22 pages, uuencoded, compressed postscript fil
Unphysical Operators in Partially Quenched QCD
We point out that the chiral Lagrangian describing pseudo-Goldstone bosons in
partially quenched QCD has one more four-derivative operator than that for
unquenched QCD with three flavors. The new operator can be chosen to vanish in
the unquenched sector of the partially quenched theory. Its contributions begin
at next-to-leading order in the chiral expansion. At this order it contributes
only to unphysical scattering processes, and we work out some examples. Its
contributions to pseudo-Goldstone properties begin at next-to-next-to-leading
order, and we determine their form. We also determine all the zero and two
derivative operators in the partially quenched chiral Lagrangian,
finding three more than in unquenched QCD, and use these to give the general
form of the analytic next-to-next-to-leading order contributions to the
pseudo-Goldstone mass and decay constant. We discuss the general implications
of such additional operators for the utility of partially quenched simulationsComment: 13 pages, 11 figures Version 2: Additional footnote and parenthesis
in section
Heavy-Meson Observables at One-Loop in Partially Quenched Chiral Perturbation Theory
I present one-loop level calculations of the Isgur-Wise functions for B ->
D^{(*)} + e + nu, of the matrix elements of isovector twist-2 operators in B
and D mesons, and the matrix elements for the radiative decays D^* -> D + gamma
in partially quenched heavy quark chiral perturbation theory. Such expressions
are required in order to extrapolate from the light quark masses used in
lattice simulations of the foreseeable future to those of nature.Comment: 13 pages, 3 fig
On Lattice Computations of K+ --> pi+ pi0 Decay at m_K =2m_pi
We use one-loop chiral perturbation theory to compare potential lattice
computations of the K+ --> pi+ pi0 decay amplitude at m_K=2m_pi with the
experimental value. We find that the combined one-loop effect due to this
unphysical pion to kaon mass ratio and typical finite volume effects is still
of order minus 20-30%, and appears to dominate the effects from quenching.Comment: 4 pages, revte
Chiral perturbation theory for partially quenched twisted mass lattice QCD
Partially quenched Quantum Chromodynamics with Wilson fermions on a lattice
is considered in the framework of chiral perturbation theory. Two degenerate
quark flavours are associated with a chirally twisted mass term. The pion
masses and decay constants are calculated in next-to-leading order including
terms linear in the lattice spacing .Comment: 7 pages, LaTeX2e, final published versio
Quenched Chiral Perturbation Theory for Vector Mesons
We develop quenched chiral perturbation theory for vector mesons made of
light quarks, in the limit where the vector meson masses are much larger than
the pion mass. We use this theory to extract the leading nonanalytic dependence
of the vector meson masses on the masses of the light quarks. By comparing with
analogous quantities computed in ordinary chiral perturbation theory, we
estimate the size of quenching effects, observing that in general they can be
quite large. This estimate is relevant to lattice simulations, where the
mass is often used to set the lattice spacing.Comment: 18 pages, 8 figures, uses REVTeX and epsf.st
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