  Recent radial-velocity surveys for GK clump giants have revealed that planets
also exist around ~1.5-3 Msun stars. However, no planets have been found inside
0.6 AU around clump giants, in contrast to solar-type main-sequence stars, many
of which harbor short-period planets such as hot Jupiters. In this study we
examine the possibility that planets were engulfed by host stars evolving on
the red-giant branch (RGB). We integrate the orbital evolution of planets in
the RGB and helium burning (HeB) phases of host stars, including the effects of
stellar tide and stellar mass loss. Then we derive the critical semimajor axis
(or the survival limit) inside which planets are eventually engulfed by their
host stars after tidal decay of their orbits. Especially, we investigate the
impact of stellar mass and other stellar parameters on the survival limit in
more detail than previous studies. In addition, we make detailed comparison
with measured semimajor axes of planets detected so far, which no previous
study did. We find that the critical semimajor axis is quite sensitive to
stellar mass in the range between 1.7 and 2.1 Msun, which suggests a need for
careful comparison between theoretical and observational limits of existence of
planets. Our comparison demonstrates that all those planets are beyond the
survival limit, which is consistent with the planet-engulfment hypothesis.
However, on the high-mass side (> 2.1 Msun), the detected planets are orbiting
significantly far from the survival limit, which suggests that engulfment by
host stars may not be the main reason for the observed lack of short-period
giant planets. To confirm our conclusion, the detection of more planets around
clump giants, especially with masses > 2.5 Msun, is required.
