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(shorter version)The aim of this work is to search for planets aroundintermediate-mass stars in open clusters by using RV data obtained with HARPSfrom an extensive survey with more than 15 years of observations for a sampleof 142 giant stars in 17 open clusters. We present the discovery of a periodicRV signal compatible with the presence of a planet candidate in the 1.15 Gyropen cluster IC4651 orbiting the 2.06 M$_\odot$ star No. 9122. If confirmed,the planet candidate would have a minimum mass of 7.2 M$_{J}$ and a period of747 days. However, we also find that the FWHM of the CCF varies with a periodclose to the RV, casting doubts on the planetary nature of the signal. We alsoprovide refined parameters for the previously discovered planet around NGC2423No. 3 but show evidence that the BIS of the CCF is correlated with the RVduring some of the observing periods. This fact advises us that this might notbe a real planet and that the RV variations could be caused by stellar activityand/or pulsations. Finally, we show that the previously reported signal by abrown dwarf around NGC4349 No. 127 is presumably produced by stellar activitymodulation. The long-term monitoring of several red giants in open clusters hasallowed us to find periodic RV variations in several stars. However, we alsoshow that the follow-up of this kind of stars should last more than one orbitalperiod to detect long-term signals of stellar origin. This work warns thatalthough it is possible to detect planets around red giants, large-amplitude,long-period RV modulations do exist in such stars that can mimic the presenceof an orbiting planetary body. Therefore, we need to better understand how suchRV modulations behave as stars evolve along the RGB and perform a detailedstudy of all the possible stellar-induced signals (e.g. spots, pulsations,granulation) to comprehend the origin of RV variations.

Planets around evolved intermediate-mass stars in open clusters II. Are there really planets around IC4651No9122, NGC2423No3 and NGC4349No127?