A multi-wavelength view of the multiple activity cycles of $\epsilon$~Eridani

$\epsilon$ Eridani is a highly active young K2 star with an activity cycle of about three years established using Ca II H & K line index measurements (S_MWO). This relatively short cycle has been demonstrated to be consistent with X-ray and magnetic flux measurements. Recent work suggested a change in the cyclic behaviour. Here we report new X-ray flux and S_MWO measurements and also include S_MWO measurements from the historical Mount Wilson program. This results in an observational time baseline of over 50 years for the S_MWO data and of over 7 years in X-rays. Moreover, we include Ca II infrared triplet (IRT) index measurements (S_IRT) from 2013-2022 in our study. With the extended X-ray data set, we can now detect the short cycle for the first time using a periodogram analysis. Near-simultaneous S_MWO data and X-ray fluxes, which are offset by 20 days at most, are moderately strongly correlated when only the lowest activity state (concerning short-term variability) is considered in both diagnostics. In the S_MWO data, we find strong evidence for a much longer cycle of about 34 years and an 11-year cycle instead of the formerly proposed $12$-year cycle in addition to the known 3-year cycle. The superposition of the three periods naturally explains the recent drop in S_MWO measurements. The two shorter cycles are also detected in the S_IRT data, although the activity cycles exhibit lower amplitudes in the S_IRT than in the S_MWO data. Finally, the rotation period of $\epsilon$Eri can be found more frequently in the S_MWO as well as in the S_IRT data for times near the minimum of the long cycle. This may be explained by a scenario in which the filling factor for magnetically active regions near cycle maximum is too high to allow for notable short-term variations.