Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice extraction of $ K \to \pi \pi $ amplitudes to NLO in partially
  quenched and in full chiral perturbation theory   We show that it is possible to construct $\epsilon^\prime/\epsilon$ to NLO
using partially quenched chiral perturbation theory (PQChPT) from amplitudes
that are computable on the lattice. We demonstrate that none of the needed
amplitudes require three-momentum on the lattice for either the full theory or
the partially quenched theory; non-degenerate quark masses suffice.
Furthermore, we find that the electro-weak penguin ($\Delta I=3/2$ and 1/2)
contributions to $\epsilon^\prime/\epsilon$ in PQChPT can be determined to NLO
using only degenerate ($m_K=m_\pi$) $K\to\pi$ computations without momentum
insertion. Issues pertaining to power divergent contributions, originating from
mixing with lower dimensional operators, are addressed. Direct calculations of
$K\to\pi\pi$ at unphysical kinematics are plagued with enhanced finite volume
effects in the (partially) quenched theory, but in simulations when the sea
quark mass is equal to the up and down quark mass the enhanced finite volume
effects vanish to NLO in PQChPT. In embedding the QCD penguin left-right
operator onto PQChPT an ambiguity arises, as first emphasized by Golterman and
Pallante. With one version (the "PQS") of the QCD penguin, the inputs needed
from the lattice for constructing $K\to\pi\pi$ at NLO in PQChPT coincide with
those needed for the full theory. Explicit expressions for the finite
logarithms emerging from our NLO analysis to the above amplitudes are also
given.

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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: stat