Estimating QCD uncertainties in Monte Carlo event generators for gamma-ray dark matter searches

Motivated by the recent galactic center gamma-ray excess identified in the Fermi-LAT data, we perform a detailed study of QCD fragmentation uncertainties in the modeling of the energy spectra of gamma-rays from Dark-Matter (DM) annihilation. When Dark-Matter particles annihilate to coloured final states, either directly or via decays such as $W^{(*)}\to q\bar{q}'$, photons are produced from a complex sequence of shower, hadronisation and hadron decays. In phenomenological studies, their energy spectra are typically computed using Monte Carlo event generators. These results have however intrinsic uncertainties due to the specific model used and the choice of model parameters, which are difficult to asses and which are typically neglected. We derive a new set of hadronisation parameters (tunes) for the \textsc{Pythia~8.2} Monte Carlo generator from a fit to LEP and SLD data at the $Z$ peak. For the first time, we also derive a conservative set of uncertainties on the shower and hadronisation model parameters. Their impact on the gamma-ray energy spectra is evaluated and discussed for a range of DM masses and annihilation channels. The spectra and their uncertainties are also provided in tabulated form for future use. The fragmentation-parameter uncertainties may be useful for collider studies as well.