Glueball scattering cross section in lattice SU(2) Yang-Mills theory. (arXiv:1910.07756v2 [hep-lat] UPDATED)

Glueball scattering cross section in lattice SU(2) Yang-Mills theory. (arXiv:1910.07756v2 [hep-lat] UPDATED)
<a href="http://arxiv.org/find/hep-lat/1/au:+Yamanaka_N/0/1/0/all/0/1">Nodoka Yamanaka</a>, <a href="http://arxiv.org/find/hep-lat/1/au:+Iida_H/0/1/0/all/0/1">Hideaki Iida</a>, <a href="http://arxiv.org/find/hep-lat/1/au:+Nakamura_A/0/1/0/all/0/1">Atsushi Nakamura</a>, <a href="http://arxiv.org/find/hep-lat/1/au:+Wakayama_M/0/1/0/all/0/1">Masayuki Wakayama</a>

We calculate the scattering cross section between two $0^{++}$ glueballs in
$SU(2)$ Yang-Mills theory on lattice at $beta = 2.1, 2.2, 2.3, 2.4$, and 2.5
using the indirect (HAL QCD) method. We employ the cluster-decomposition error
reduction technique and use all space-time symmetries to improve the signal. In
the use of the HAL QCD method, the centrifugal force was subtracted to remove
the systematic effect due to nonzero angular momenta of lattice discretization.
From the extracted interglueball potential we determine the low energy glueball
effective theory by matching with the one-glueball exchange process. We then
calculate the scattering phase shift, and derive the relation between the
interglueball cross section and the scale parameter $Lambda$ as $sigma_{phi
phi} = (2 – 51) Lambda^{-2}$ (stat.+sys.). From the observational constraints
of galactic collisions, we obtain the lower bound of the scale parameter, as
$Lambda > 60$ MeV. We also discuss the naturalness of the Yang-Mills theory as
the theory explaining dark matter.

We calculate the scattering cross section between two $0^{++}$ glueballs in
$SU(2)$ Yang-Mills theory on lattice at $beta = 2.1, 2.2, 2.3, 2.4$, and 2.5
using the indirect (HAL QCD) method. We employ the cluster-decomposition error
reduction technique and use all space-time symmetries to improve the signal. In
the use of the HAL QCD method, the centrifugal force was subtracted to remove
the systematic effect due to nonzero angular momenta of lattice discretization.
From the extracted interglueball potential we determine the low energy glueball
effective theory by matching with the one-glueball exchange process. We then
calculate the scattering phase shift, and derive the relation between the
interglueball cross section and the scale parameter $Lambda$ as $sigma_{phi
phi} = (2 – 51) Lambda^{-2}$ (stat.+sys.). From the observational constraints
of galactic collisions, we obtain the lower bound of the scale parameter, as
$Lambda > 60$ MeV. We also discuss the naturalness of the Yang-Mills theory as
the theory explaining dark matter.

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