  LiteBIRD is a JAXA-led Strategic Large-Class mission designed to search for
the existence of the primordial gravitational waves produced during the
inflationary phase of the Universe, through the measurements of their imprint
onto the polarization of the cosmic microwave background (CMB). These
measurements, requiring unprecedented sensitivity, will be performed over the
full sky, at large angular scales, and over 15 frequency bands from 34GHz to
448GHz. The LiteBIRD instruments consist of three telescopes, namely the Low-,
Medium- and High-Frequency Telescope (respectively LFT, MFT and HFT). We
present in this paper an overview of the design of the Medium-Frequency
Telescope (89-224GHz) and the High-Frequency Telescope (166-448GHz), the
so-called MHFT, under European responsibility, which are two cryogenic
refractive telescopes cooled down to 5K. They include a continuous rotating
half-wave plate as the first optical element, two high-density polyethylene
(HDPE) lenses and more than three thousand transition-edge sensor (TES)
detectors cooled to 100mK. We provide an overview of the concept design and the
remaining specific challenges that we have to face in order to achieve the
scientific goals of LiteBIRD.
