2,613 research outputs found
Progress in three-particle scattering from LQCD
We present the status of our formalism for extracting three-particle
scattering observables from lattice QCD (LQCD). The method relies on relating
the discrete finite-volume spectrum of a quantum field theory with its
scattering amplitudes. As the finite-volume spectrum can be directly determined
in LQCD, this provides a method for determining scattering observables, and
associated resonance properties, from the underlying theory. In a pair of
papers published over the last two years, two of us have extended this approach
to apply to relativistic three-particle scattering states. In this talk we
summarize recent progress in checking and further extending this result. We
describe an extension of the formalism to include systems in which two-to-three
transitions can occur. We then present a check of the previously published
formalism, in which we reproduce the known finite-volume energy shift of a
three-particle bound state.Comment: 9 pages, 3 figures, proceedings for XIIth Quark Confinement and the
Hadron Spectrum (CONF12
Three-particle systems with resonant subprocesses in a finite volume
In previous work, we have developed a relativistic, model-independent
three-particle quantization condition, but only under the assumption that no
poles are present in the two-particle K matrices that appear as scattering
subprocesses. Here we lift this restriction, by deriving the quantization
condition for identical scalar particles with a G-parity symmetry, in the case
that the two-particle K matrix has a pole in the kinematic regime of interest.
As in earlier work, our result involves intermediate infinite-volume quantities
with no direct physical interpretation, and we show how these are related to
the physical three-to-three scattering amplitude by integral equations. This
work opens the door to study processes such as , in which the is rigorously treated as a resonance state.Comment: 46 pages, 9 figures, JLAB-THY-18-2819, CERN-TH-2018-21
Numerical study of the relativistic three-body quantization condition in the isotropic approximation
We present numerical results showing how our recently proposed relativistic
three-particle quantization condition can be used in practice. Using the
isotropic (generalized -wave) approximation, and keeping only the leading
terms in the effective range expansion, we show how the quantization condition
can be solved numerically in a straightforward manner. In addition, we show how
the integral equations that relate the intermediate three-particle
infinite-volume scattering quantity, , to the
physical scattering amplitude can be solved at and below threshold. We test our
methods by reproducing known analytic results for the expansion of the
threshold state, the volume dependence of three-particle bound-state energies,
and the Bethe-Salpeter wavefunctions for these bound states. We also find that
certain values of lead to unphysical finite-volume
energies, and give a preliminary analysis of these artifacts.Comment: 32 pages, 21 figures, JLAB-THY-18-2657, CERN-TH-2018-046; version 2:
corrected typos, updated references, minor stylistic changes---consistent
with published versio
Generalizing the relativistic quantization condition to include all three-pion isospin channels
We present a generalization of the relativistic, finite-volume,
three-particle quantization condition for non-identical pions in isosymmetric
QCD. The resulting formalism allows one to use discrete finite-volume energies,
determined using lattice QCD, to constrain scattering amplitudes for all
possible values of two- and three-pion isospin. As for the case of identical
pions considered previously, the result splits into two steps: The first
defines a non-perturbative function with roots equal to the allowed energies,
, in a given cubic volume with side-length . This function depends
on an intermediate three-body quantity, denoted ,
which can thus be constrained from lattice QCD input. The second step is a set
of integral equations relating to the physical
scattering amplitude, . Both of the key relations, and
, are shown to be
block-diagonal in the basis of definite three-pion isospin, ,
so that one in fact recovers four independent relations, corresponding to
. We also provide the generalized threshold expansion
of for all channels, as well as parameterizations
for all three-pion resonances present for and
. As an example of the utility of the generalized formalism,
we present a toy implementation of the quantization condition for
, focusing on the quantum numbers of the and
resonances.Comment: 46 pages, 4 figures. Updated to match erratum published in JHEP. Main
conclusions and results unchange
Multiple-channel generalization of Lellouch-Luscher formula
We generalize the Lellouch-Luscher formula, relating weak matrix elements in
finite and infinite volumes, to the case of multiple strongly-coupled decay
channels into two scalar particles. This is a necessary first step on the way
to a lattice QCD calculation of weak decay rates for processes such as D -> pi
pi and D -> KK. We also present a field theoretic derivation of the
generalization of Luscher's finite volume quantization condition to multiple
two-particle channels. We give fully explicit results for the case of two
channels, including a form of the generalized Lellouch-Luscher formula
expressed in terms of derivatives of the energies of finite volume states with
respect to the box size. Our results hold for arbitrary total momentum and for
degenerate or non-degenerate particles.Comment: 16 pages, 2 figures. v3: Added references, clarified relation to and
corrected comments about previous work, and minor stylistic improvements. v4:
Minor clarifications added, typos fixed, references updated---matches
published versio
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