Glueball scattering cross section in lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> Yang-Mills theory
Nodoka Yamanaka, Hideaki Iida, Atsushi Nakamura, Masayuki Wakayama
Abstract
We calculate the scattering cross section between two ${0}^{++}$ glueballs in $SU(2)$ Yang-Mills theory on a lattice at $\ensuremath{\beta}=2.1$, 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 the 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 $\mathrm{\ensuremath{\Lambda}}$ as ${\ensuremath{\sigma}}_{\ensuremath{\phi}\ensuremath{\phi}}=(2--51){\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{-}2}$ ($\text{stat}+\text{sys}$). From the observational constraints of galactic collisions, we obtain the lower bound of the scale parameter as $\mathrm{\ensuremath{\Lambda}}>60\text{ }\text{ }\mathrm{MeV}$. We also discuss the naturalness of the Yang-Mills theory as the theory explaining dark matter.