215,439 research outputs found

### $\pi N \sigma$ Term and Quark Spin Content of the Nucleon

We report results of our calculation on the $\pi N\sigma$ term and quark spin
content of the nucleon on the quenched $16^3 \times 24$ lattice at $\beta =
6.0$. The disconnected insertions which involve contributions from the sea
quarks are calculated with the stochastic $Z_2$ noise algorithm. As a physical
test of the algorithm, we show that the forward matrix elements of the vector
and pseudoscalar currents for the disconnected insertions are indeed consistent
with the known results of zero. We tried the Wuppertal smeared source and found
it to be more noisy than the point source. With unrenormalized
$m_q=4.42(17)$MeV, we find the $\pi N\sigma$ term to be $39.2\pm 5.2$ MeV. The
strange quark condensate in the nucleon is large, i.e. $\langle
N|\bar{s}s|N\rangle = 1.16 \pm 0.54$. For the quark spin content, we find
$\Delta u =0.78\pm 0.07$, $\Delta d =-0.42\pm 0.07$, and $\Delta s = -0.13\pm
0.06$. The flavor-singlet axial charge $g_A^1 = \Delta \Sigma =0.22\pm 0.09$.Comment: contribution to Lattice '94; 3 page uuencoded ps fil

### Tensor products of strongly graded vertex algebras and their modules

We study strongly graded vertex algebras and their strongly graded modules,
which are conformal vertex algebras and their modules with a second, compatible
grading by an abelian group satisfying certain grading restriction conditions.
We consider a tensor product of strongly graded vertex algebras and its tensor
product strongly graded modules. We prove that a tensor product of strongly
graded irreducible modules for a tensor product of strongly graded vertex
algebras is irreducible, and that such irreducible modules, up to equivalence,
exhaust certain naturally defined strongly graded irreducible modules for a
tensor product of strongly graded vertex algebras. We also prove that certain
naturally defined strongly graded modules for the tensor product strongly
graded vertex algebra are completely reducible if and only if every strongly
graded module for each of the tensor product factors is completely reducible.
These results generalize the corresponding known results for vertex operator
algebras and their modules.Comment: 26 pages. For the sake of readability, I quote certain necessary
technical definitions from earlier work of Y.-Z. Huang, J. Lepowsky and L.
Zhang [arXiv:0710.2687, arXiv:1012.4193, arXiv:math/0609833

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