  The past decade has seen increasing efforts in detecting and characterising
exoplanets by high contrast imaging in the near/mid-infrared, which is the
optimal wavelength domain for studying old, cold planets. In this work, we
present deep AO imaging observations of the nearby Sun-like star $\epsilon$ Ind
A with NaCo ($L^{\prime}$) and NEAR (10-12.5 microns) instruments at VLT, in an
attempt to directly detect its planetary companion whose presence has been
indicated from radial velocity (RV) and astrometric trends. We derive
brightness limits from the non-detection of the companion with both
instruments, and interpret the corresponding sensitivity in mass based on both
cloudy and cloud-free atmospheric and evolutionary models. For an assumed age
of 5 Gyr for the system, we get detectable mass limits as low as 4.4 $M_{\rm
J}$ in NaCo $L^{\prime}$ and 8.2 $M_{\rm J}$ in NEAR bands at 1.5$\arcsec$ from
the central star. If the age assumed is 1 Gyr, we reach even lower mass limits
of 1.7 $M_{\rm J}$ in NaCo $L^{\prime}$ and 3.5 $M_{\rm J}$ in NEAR bands, at
the same separation. However, based on the dynamical mass estimate (3.25
$M_{\rm J}$) and ephemerides from astrometry and RV, we find that the
non-detection of the planet in these observations puts a constraint of 2 Gyr on
the lower age limit of the system. NaCo offers the highest sensitivity to the
planetary companion in these observations, but the combination with the NEAR
wavelength range adds a considerable degree of robustness against uncertainties
in the atmospheric models. This underlines the benefits of including a broad
set of wavelengths for detection and characterisation of exoplanets in direct
imaging studies.
