  We present a detailed analysis of the Horizontal Branch of the Carina Dwarf
Spheroidal Galaxy by means of synthetic modelling techniques, taking
consistently into account the star formation history and metallicity evolution
as determined from main sequence and red giant branch spectroscopic
observations. We found that a range of integrated red giant branch mass loss
values of 0.1-0.14 M, increasing with metallicity, is able to reproduce the
colour extension of the old Horizontal Branch. However, leaving the mass loss
as the only free parameter is not enough to match the detailed morphology of
Carina Horizontal Branch. We explored the role played by the star formation
history on the discrepancies between synthetic and observed Horizontal
Branches. We derived a toy bursty star formation history that reproduces the
horizontal branch star counts, and also matches qualitatively the red giant and
the turn off regions. This star formation history is made of a subset of age
and [M/H] components of the star formation history based on turn off and red
giants only, and entails four separate bursts of star formation of different
strenghts, centred at 2, 5, 8.6 and 11.5 Gyr, with mean [M/H] decreasing from
\sim -1.7 to \sim -2.2 for increasing ages, and a Gaussian spread of 0.1 dex.
The comparison between the metallicity distribution function of our star
formation history and the one measured from the infrared CaT feature using a
CaT-[Fe/H] calibration shows a qualitative agreement, once taken into account
the range of [Ca/Fe] abundances measured in a sample of Carina stars, that
biases the derived [Fe/H] distribution toward too low values. In conclusion, we
have shown how the information contained within the horizontal branch of Carina
(and dwarf galaxies in general) can be extracted and interpreted to refine the
star formation history derived from red giants and turn off stars only.
Abridged
