84 research outputs found
Relativistic, model-independent, multichannel transition amplitudes in a finite volume
We derive formalism for determining
infinite-volume transition amplitudes from finite-volume matrix elements.
Specifically, we present a relativistic, model-independent relation between
finite-volume matrix elements of external currents and the physically
observable infinite-volume matrix elements involving two-particle asymptotic
states. The result presented holds for states composed of two scalar bosons.
These can be identical or non-identical and, in the latter case, can be either
degenerate or non-degenerate. We further accommodate any number of
strongly-coupled two-scalar channels. This formalism will, for example, allow
future lattice QCD calculations of the -meson form factor, in which the
unstable nature of the is rigorously accommodated.Comment: 35 pages, 11 figure
Heavy Meson Masses in the \epsilon-Regime of HM\chi PT
The pseudoscalar and vector heavy meson masses are calculated in the
\epsilon-regime of Heavy Meson Chiral Perturbation Theory to order \epsilon^4.
The results of this calculation will allow the determination of low-energy
coefficients (LECs) directly from Lattice QCD calculations of the heavy mesons
masses for lattices that satisfy the \epsilon-regime criteria. In particular,
the LECs that parametrize the NLO volume dependance of the heavy meson masses
are necessary for evaluating the light pseudoscalar meson (\pi, K, \eta) and
heavy meson ({D^0, D^+, D^+_s}, {B^-,\bar{B}^0,\bar{B}^0_s}) scattering phase
shifts.Comment: 16 pages, 6 figure
Nuclear Reactions from Lattice QCD
One of the overarching goals of nuclear physics is to rigorously compute
properties of hadronic systems directly from the fundamental theory of strong
interactions, Quantum Chromodynamics (QCD). In particular, the hope is to
perform reliable calculations of nuclear reactions which will impact our
understanding of environments that occur during big bang nucleosynthesis, the
evolution of stars and supernovae, and within nuclear reactors and high
energy/density facilities. Such calculations, being truly ab initio, would
include all two-nucleon and three- nucleon (and higher) interactions in a
consistent manner. Currently, lattice QCD provides the only reliable option for
performing calculations of some of the low- energy hadronic observables. With
the aim of bridging the gap between lattice QCD and nuclear many-body physics,
the Institute for Nuclear Theory held a workshop on Nuclear Reactions from
Lattice QCD on March 2013. In this review article, we report on the topics
discussed in this workshop and the path planned to move forward in the upcoming
years.Comment: 35 pages, 13 figures, 1 table, review article for the "Nuclear
Reactions from Lattice QCD" workshop hosted by the Institute for Nuclear
Theory on March 2013; version 2 includes updated references and extended
discussion of previous wor
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
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
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