  We report the discovery of a radial velocity signal that can be interpreted
as a planetary-mass candidate orbiting the K dwarf HD26965, with an orbital
period of 42.364$\pm$0.015 days, or alternatively, as the presence of residual,
uncorrected rotational activity in the data. Observations include data from
HIRES, PFS, CHIRON, and HARPS, where 1,111 measurements were made over 16
years. Our best solution for HD26965 $b$ is consistent with a super-Earth that
has a minimum mass of 6.92$\pm$0.79 M$_{\oplus}$ orbiting at a distance of
0.215$\pm$0.008 AU from its host star. We have analyzed the correlation between
spectral activity indicators and the radial velocities from each instrument,
showing moderate correlations that we include in our model. From this analysis,
we recover a $\sim$38 day signal, which matches some literature values of the
stellar rotation period. However, from independent Mt. Wilson HK data for this
star, we find evidence for a significant 42 day signal after subtraction of
longer period magnetic cycles, casting doubt on the planetary hypothesis for
this period. Although our statistical model strongly suggests that the 42-day
signal is Doppler in origin, we conclude that the residual effects of stellar
rotation are difficult to fully model and remove from this dataset,
highlighting the difficulties to disentangle small planetary signals and
photospheric noise, particularly when the orbital periods are close to the
rotation period of the star. This study serves as an excellent test case for
future works that aim to detect small planets orbiting `Sun-like' stars using
radial velocity measurements.
