146 research outputs found
Fitting two nucleons inside a box: exponentially suppressed corrections to the Luscher's formula
Scattering observables can be computed in lattice field theory by measuring
the volume dependence of energy levels of two particle states. The dominant
volume dependence, proportional to inverse powers of the volume, is determined
by the phase shifts. This universal relation (\Lu's formula) between energy
levels and phase shifts is distorted by corrections which, in the large volume
limit, are exponentially suppressed. They may be sizable, however, for the
volumes used in practice and they set a limit on how small the lattice can be
in these studies. We estimate these corrections, mostly in the case of two
nucleons. Qualitatively, we find that the exponentially suppressed corrections
are proportional to the {\it square} of the potential (or to terms suppressed
in the chiral expansion) and the effect due to pions going ``around the world''
vanishes. Quantitatively, the size of the lattice should be greater than
in order to keep finite volume corrections to the phase
less than for realistic pion mass.Comment: 18 pages, 5 figures, 6 figure
Adversarial Transformations for Semi-Supervised Learning
We propose a Regularization framework based on Adversarial Transformations
(RAT) for semi-supervised learning. RAT is designed to enhance robustness of
the output distribution of class prediction for a given data against input
perturbation. RAT is an extension of Virtual Adversarial Training (VAT) in such
a way that RAT adversarialy transforms data along the underlying data
distribution by a rich set of data transformation functions that leave class
label invariant, whereas VAT simply produces adversarial additive noises. In
addition, we verified that a technique of gradually increasing of perturbation
region further improve the robustness. In experiments, we show that RAT
significantly improves classification performance on CIFAR-10 and SVHN compared
to existing regularization methods under standard semi-supervised image
classification settings.Comment: Accepted by AAAI 202
Lattice QCD Simulations of Baryon Spectra and Development of Improved Interpolating Field Operators
Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum.
Because of the cubical discretization of space, the continuum rotational group is broken down to a finite point group.
Operators are classified according to the irreducible representations of the double octahedral group.
At first, three-quark quasi-local operators are constructed for each isospin and strangeness with suitable symmetry of Dirac indices.
Nonlocal baryon operators are formulated in a second
step as direct products of the quasi-local spinor structures together with lattice displacements.
Appropriate Clebsch-Gordan coefficients of the octahedral group are used to form linear combinations of such direct products.
The construction maintains maximal overlap with the continuum SU(2) group in order to provide a physically interpretable basis.
Nonlocal operators provide direct couplings to states
that have nonzero orbital angular momentum.
Monte Carlo simulations of nucleon and delta baryon spectra are carried out with anisotropic lattices of anisotropy 3.0 with .
Gauge configurations are generated by the Wilson gauge action in quenched approximation with space-time volumes (1.6\,\mbox{fm})^3\times 2.1\,\mbox{fm} and
(2.4\,\mbox{fm})^3\times 2.1\,\mbox{fm}.
The Wilson fermion action is used with pion mass \simeq 500\,\mbox{MeV}.
The variational method is applied to matrices of correlation functions constructed using improved operators in order to extract mass eigenstates
including excited states.
Stability of the obtained masses is confirmed by varying the dimensions of the matrices.
The pattern of masses for the low-lying states that we compute is consistent with the pattern that is observed in nature.
Ordering of masses is consistent for positive-parity excited states, but mass splittings are considerably larger than the physical values.
Baryon masses for spin states are obtained in these simulations.
Hyperfine mass splittings are studied for both parities.
No significant finite volume effect is seen at the quark mass that is used
Finite volume corrections to pi-pi scattering
Lattice QCD studies of hadron-hadron interactions are performed by computing
the energy levels of the system in a finite box. The shifts in energy levels
proportional to inverse powers of the volume are related to scattering
parameters in a model independent way. In addition, there are non-universal
exponentially suppressed corrections that distort this relation. These terms
are proportional to exp(-m_pi L) and become relevant as the chiral limit is
approached. In this paper we report on a one-loop chiral perturbation theory
calculation of the leading exponential corrections in the case of I=2 pi-pi
scattering near threshold.Comment: 17 pages, 2 figures, 1 table. Version published in PR
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