Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the amplitudes for the CP-conserving
  $K^\pm(K_S)\to\pi^\pm(\pi^0)\ell^+\ell^-$ rare decay modes   The amplitudes for the rare decay modes $K^\pm\to\pi^\pm\ell^+\ell^-$ and
$K_S\to\pi^0\ell^+\ell^-$ are studied with the aim of obtaining predictions for
them, such as to enable the possibility to search for violations of
lepton-flavour universality in the kaon sector. The issue is first addressed
from the perspective of the low-energy expansion, and a two-loop representation
of the corresponding form factors is constructed, leaving as unknown quantities
their values and slopes at vanishing momentum transfer. In a second step a
phenomenological determination of the latter is proposed. It consists of the
contribution of the resonant two-pion state in the $P$ wave, and of the leading
short-distance contribution determined by the operator-product expansion. The
interpolation between the two energy regimes is described by an infinite tower
of zero-width resonances matching the QCD short-distance behaviour. Finally,
perspectives for future improvements in the theoretical understanding of these
amplitudes are discussed.

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The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
5
The categories of this paper are: gr-qc