Absorption and scattering of charged scalar waves by charged Horndeski black hole

We investigate the absorption and scattering of a charged massive scalar field by a charged Horndeski black hole using both the approximation or classical geometric method and the partial wave method and compare the numerical and analytical results, which are found to agree with each other very well. We observe that an increase in either the BH charge $Q$ or the field charge $q$ when $qQ>0$ leads to a smaller absorption cross section and a widening of the interference fringes in the scattering cross section, while the increase in the field mass enlarges the absorption cross section and the width of the interference fringes. Compared to the Reissner-Nordstr$\ddot{\rm{o}}$m BH with the same charge and other parameter settings, the absorption and scattering cross sections of the charged Horndeski BH are higher, and its interference fringes are narrower. We also investigate the effect of the field charge $q$ on the absorption and scattering cross sections when superradiance is triggered. It is shown that the total absorption cross section can be negative, and the scattering intensity can be significantly enhanced by superradiance.