Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mechanisms of the isospin-breaking decay $f_1(1285)\to
  f_0(980)\pi^0\to\pi^+\pi^-\pi^0$   Estimated are the contributions of the following mechanisms responsible for
the decay $f_1(1285)\to f_0(980)\pi^0\to\pi^+\pi^-\pi^0$: 1) the contribution
of the $a^0_0(980)-f_0(980)$ mixing, $f_1(1285)\to a_0(980)\pi^0\to
(K^+K^-+K^0\bar K^0)\pi^0\to f_0(980)\pi^0\to\pi^+\pi^-\pi^0$, 2) the
contribution of the transition $f_1(1285)\to(K^+K^-+K^0\bar K^0)\pi^0\to f_0
(980)\pi^0\to\pi^+\pi^-\pi^0$, arising due to the pointlike decay $f_1
(1285)\to K\bar K\pi^0$, 3) the contribution of the transition
$f_1(1285)\to(K^*\bar K+\bar K^*K)\to(K^+K^-+K^0\bar K^0)\pi^0\to
f_0(980)\pi^0\to \pi^+\pi^-\pi^0$, where $K^*=K^*(892)$, and 4) the
contribution of the transition $f_1(1285)\to(K^*_0\bar K+\bar
K^*_0K)\to(K^+K^-+K^0\bar K^0)\pi^0\to f_0(980)\to\pi^+ \pi^-\pi^0$, where
$K^*_0=K^*_0(800)$ (or $\kappa$) and $K^*_0(1430)$. These mechanisms break the
conservation of the isospin due to the nonzero mass difference of the $K^+$ and
$K^0$ mesons. They result in the appearance of the narrow resonance structure
in the $\pi^+\pi^-$ mass spectrum in the region of the $K\bar K$ thresholds,
with the width $\approx2m_{K^0}-2m_{K^+}\approx8$ MeV. The observation of such
a structure in experiment is the direct indication on the $K\bar K$ loop
mechanism of the breaking of the isotopic invariance. We point out that
existing data should be more precise, and it is difficult to explain them using
the single specific mechanism from those listed above. Taking the decay
$f_1(1285)\to f_0(980)\pi^0 \to\pi^+\pi^-\pi^0$ as the example, we discuss the
general approach to the description of the $K\bar K$ loop mechanism of the
breaking of isotopic invariance.

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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: physics