Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elastic pion-nucleon scattering in chiral perturbation theory: Explicit
  $\Delta$(1232) degrees of freedom   For the first time, elastic pion-nucleon scattering is analyzed in the
framework of chiral perturbation theory up to fourth order with explicit
$\Delta$ degrees of freedom. The analysis is performed within the heavy-baryon
expansion as well as in a covariant approach based on an extended on-mass-shell
renormalization scheme. The renormalization of low-energy constants in both
chiral approaches is discussed in detail and the explicit expressions to cancel
both power-counting breaking as well as decoupling breaking terms are given.
The low-energy constants from the $2\pi \bar{N}N$ interaction as well as
additional constants from the $\Delta$ sector are reliably constrained by fits
to experimental data. The traditional $K$-matrix unitarization is employed in
the near threshold region, whereas a complex mass approach is used to extend
the applicability of the theory up to the $\Delta$ pole region. Additionally,
we estimate a theoretical error based on the truncation of the chiral series as
employed in recent analyses of nuclear forces as well as pion-nucleon
scattering. The obtained results provide a clear evidence that the explicit
inclusion of $\Delta$ degrees of freedom is fundamental to describe
pion-nucleon physics at threshold. The resulting predictions for the
subthreshold and threshold parameters as well as phase shifts are in excellent
agreement with the ones determined by the recent Roy-Steiner analysis of
pion-nucleon scattering.

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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat