Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice QCD Inputs for Nuclear Double Beta Decay   Second order beta-decay processes with and without neutrinos in the final
state are key probes of nuclear physics and of the nature of neutrinos.
Neutrinoful double-beta decay is the rarest Standard Model process that has
been observed and provides a unique test of the understanding of weak nuclear
interactions. Observation of neutrinoless double-beta decay would reveal that
neutrinos are Majorana fermions and that lepton number conservation is violated
in nature. While significant progress has been made in phenomenological
approaches to understanding these processes, establishing a connection between
these processes and the physics of the Standard Model and beyond is a critical
task as it will provide input into the design and interpretation of future
experiments. The strong-interaction contributions to double-beta decay
processes are non-perturbative and can only be addressed systematically through
a combination of lattice Quantum Chromoodynamics (LQCD) and nuclear many-body
calculations. In this review, current efforts to establish the LQCD connection
are discussed for both neutrinoful and neutrinoless double-beta decay. LQCD
calculations of the hadronic contributions to the neutrinoful process $nn\to pp
e^- e^- \bar\nu_e\bar\nu_e$ and to various neutrinoless pionic transitions are
reviewed, and the connections of these calculations to the phenomenology of
double-beta decay through the use of effective field theory (EFTs) is
highlighted. At present, LQCD calculations are limited to small nuclear
systems, and to pionic subsystems, and require matching to appropriate EFTs to
have direct phenomenological impact. However, these calculations have already
revealed qualitatively that there are terms in the EFTs that can only be
constrained from double-beta decay processes themselves or using inputs from
LQCD. Future prospects for direct calculations in larger nuclei are also
discussed.

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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph