2,208 research outputs found
Implementing the three-particle quantization condition including higher partial waves
We present an implementation of the relativistic three-particle quantization
condition including both - and -wave two-particle channels. For this, we
develop a systematic expansion about threshold of the three-particle
divergence-free K matrix, , which is a
generalization of the effective range expansion of the two-particle K matrix,
. Relativistic invariance plays an important role in this
expansion. We find that -wave two-particle channels enter first at quadratic
order. We explain how to implement the resulting multichannel quantization
condition, and present several examples of its application. We derive the
leading dependence of the threshold three-particle state on the two-particle
-wave scattering amplitude, and use this to test our implementation. We show
how strong two-particle -wave interactions can lead to significant effects
on the finite-volume three-particle spectrum, including the possibility of a
generalized three-particle Efimov-like bound state. We also explore the
application to the system, which is accessible to lattice QCD
simulations, where we study the sensitivity of the spectrum to the components
of . Finally, we investigate the circumstances
under which the quantization condition has unphysical solutions.Comment: 57 pages, 12 figures, 3 tables (v2: Made minor clarifications,
updated a reference, fixed typos
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
Progress report on the relativistic three-particle quantization condition
We describe recent work on the relativistic three-particle quantization
condition, generalizing and applying the original formalism of Hansen and
Sharpe, and of Brice\~no, Hansen and Sharpe. In particular, we sketch three
recent developments: the generalization of the formalism to include K-matrix
poles; the numerical implementation of the quantization condition in the
isotropic approximation; and ongoing work extending the description of the
three-particle divergence-free K matrix beyond the isotropic approximation.Comment: 7 pages, 1 figure, Proceedings of Lattice 201
Entanglement properties in the Inhomogeneous Tavis-Cummings model
In this work we study the properties of the atomic entanglement in the
eigenstates spectrum of the inhomogeneous Tavis-Cummings Model. The
inhomogeneity is present in the coupling among the atoms with quantum
electromagnetic field. We calculate analytical expressions for the concurrence
and we found that this exhibits a strong dependence on the inhomogeneity.Comment: 5 pages, 5 figure
three-pion scattering amplitude from lattice QCD
We analyze the spectrum of two- and three-pion states of maximal isospin
obtained recently for isosymmetric QCD with pion mass MeV in
Ref. [1]. Using the relativistic three-particle quantization condition, we find
evidence for a nonzero value for the contact part of the
three- () scattering amplitude. We also compare our results to
leading-order chiral perturbation theory. We find good agreement at threshold,
and some tension in the energy dependent part of the three-scattering
amplitude. We also find that the two- () spectrum is fit well by an
-wave phase shift that incorporates the expected Adler zero.Comment: Update to match published versio
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