A viable D-term hybrid inflation
  We propose a new model of the D-term hybrid inflation in the framework of
supergravity. Although our model introduces, analogously to the conventional
D-term inflation, the inflaton and a pair of scalar fields charged under a
$U(1)$ gauge symmetry, we study the logarithmic and exponential dependence on
the inflaton field, respectively, for the K\"ahler and superpotential. This
results in a characteristic one-loop scalar potential consisting of linear and
exponential terms, which realizes the small-field inflation dominated by the
Fayet-Iliopoulos term. With the reasonable values for the coupling coefficients
and, in particular, with the $U(1)$ gauge coupling constant comparable to that
of the Standard Model, our D-term inflation model can solve the notorious
problems in the conventional D-term inflation, namely, the CMB constraints on
the spectral index and the generation of cosmic strings.
