and therefore are considered separately, whereas the fluxes of muon neutrinos and anti-neutrinos from the GC are identical.

The optimisation procedure provides a set of optimum values of angular separation to the GC, $\rm \Psi$, for each mass of the WIMP and for each benchmark channel. The distributions of $\rm \Psi$ as a function of the WIMP mass, $\rm M_{WIMP}$, are given in Tables \[tab:qresultsone\]+\[tab:qresultstwo\] and \[tab:qresultsthree\]+\[tab:qresultsfour\]. Regardless of self-annihilation channels and reconstruction algorithms, an optimised angular separation $\rm \Psi$ to the GC is wider for low $\rm M_{WIMP}$ due to the degradation of the angular resolution $\rm \tilde{\alpha}$ at low neutrino energy (Figure \[angresfig\]). Moreover, the optimimum $\rm \Psi$ for a given $\rm M_{WIMP}$ depends on the softness of the self-annihilation channel, $\rm \Psi$ being wider the softer the channel.

An example of the acceptance $\rm \bar{A}_{eff}(M_{\rm WIMP}) \times T_{eff}$ is shown in Figure \[aeffmwimpfig\]. The visibility of the GC and the data-taking periods from 2007 to 2012 are included. The $\rm QFit$ (dashed lines) and $\rm \Lambda Fit$ (solid lines) are compared for each self-annihilation channel, inside their respective angular separations, $\rm \Psi = 10^{\circ}$ and $\rm \Psi = 2^{\circ}$, that are typical over all the WIMP masses 