  We study a mechanism of generating the trispectrum (4-point correlation) of
curvature perturbation through the dynamics of a spectator axion field and U(1)
gauge field during inflation. Owing to the Chern-Simons coupling, only one
helicity mode of gauge field experiences a tachyonic instability and sources
scalar perturbations. Sourced curvature perturbation exhibits parity-violating
nature which can be tested through its trispectrum. We numerically compute
parity-even and parity-odd component of the sourced trispectrum. It is found
that the ratio of parity-odd to parity-even mode can reach O(10%) in an exact
equilateral momentum configuration. We also investigate a quasi-equilateral
shape where only one of the momenta is slightly longer than the other three,
and find that the parity-odd mode can reach, and more interestingly, surpass
the parity-even one. This may help us to interpret a large parity-odd
trispectrum signal extracted from BOSS galaxy-clustering data.
