Dynamical implications of gluonic excitations in meson-meson systems

Abstract

We study meson-meson interactions using an extended $q^2\bar{q}^2(g)$ basis that allows calculating coupling of an ordinary meson-meson system to a hybrid-hybrid one. We use a potential model matrix in this extended basis which at quark level is known to provide a good fit to numerical simulations of a $q^2\bar{q}^2$ system in pure gluonic theory for static quarks in a selection of geometries. We use a combination of resonating group method formalism and Born approximation to include the quark motion using wave functions of a $q\bar{q}$ potential within a cluster. This potential is taken to be quadratic for ground states and has an additional smeared $\frac{1}{r}$ (Gaussian) for the matrix elements between hybrid mesons. For the parameters of this potential, we use values chosen to 1) minimize the error resulting from our use of a quadratic potential and 2) best fit the lattice data for differences of $\Sigma_{g}$ and $\Pi_{u}$ configurations of the gluonic field between a quark and an antiquark. At the quark (static) level, including the gluonic excitations was noted to partially replace the need for introducing many-body terms in a multi-quark potential. We study how successful such a replacement is at the (dynamical) hadronic level of relevance to actual hard experiments. Thus we study effects of both gluonic excitations and many-body terms on mesonic transition amplitudes and the energy shifts resulting from the second order perturbation theory (i.e. from the respective hadron loops). The study suggests introducing both energy and orbital excitations in wave functions of scalar mesons that are modelled as meson-meson molecules or are supposed to have a meson-meson component in their wave functions.