Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: O(6) algebraic theory of three nonrelativistic quarks bound by
  spin-independent interactions   We apply the newly developed theory of permutation-symmetric O(6)
hyperspherical harmonics to the quantum-mechanical problem of three
non-relativistic quarks confined by a spin-independent 3-quark potential. We
use our previously derived results to reduce the three-body Schr\"odinger
equation to a set of coupled ordinary differential equations in the
hyper-radius $R$ with coupling coefficients expressed entirely in terms of (i)
a few interaction-dependent O(6) expansion coefficients and (ii) O(6)
hyperspherical harmonics matrix elements, that have been evaluated in our
previous paper. This system of equations allows a solution to the eigenvalue
problem with homogeneous 3-quark potentials, which class includes a number of
standard Ans\"atze for the confining potentials, such as the Y- and
$\Delta$-string ones. We present analytic formulae for the $K = 2, 3, 4, 5$
shell states' eigen-energies in homogeneous three-body potentials, which
formulae we then apply to the Y- and $\Delta$-string, as well as the
logarithmic confining potentials. We also present numerical results for
power-law pair-wise potentials with the exponent ranging between -1 and +2. In
the process we resolve the 25 year-old Taxil and Richard vs. Bowler et al.
controversy regarding the ordering of states in the $K = 3$ shell, in favor of
the former. Finally, we show the first clear difference between the spectra of
$\Delta$- and Y-string potentials, which appears in $K \geq 3$ shells. Our
results are generally valid, not just for confining potentials, but also for
many momentum-independent permutation-symmetric homogenous potentials, that
need not be pairwise sums of two-body terms. The potentials that can be treated
in this way must be square-integrable under the O(6) hyperangular integral,
however, which class does not include the Dirac $\delta$-function.

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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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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: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: cs