  We present an analytic model of nonlinear correlators of galaxy/halo
ellipticities in redshift space. The three-dimensional ellipticity field is not
affected by the redshift-space distortion (RSD) at linear order, but by the
nonlinear one, known as the Finger-of-God effect, caused by the coordinate
transformation from real to redshift space. Adopting a simple Gaussian damping
function to describe the nonlinear RSD effect and the nonlinear alignment model
for the relation between the observed ellipticity and underlying tidal fields,
we derive analytic formulas for the multipole moments of the power spectra of
the ellipticity field in redshift space expanded in not only the associated
Legendre basis, a natural basis for the projected galaxy shape field, but also
the standard Legendre basis, conventionally used in literature. The multipoles
of the corresponding correlation functions of the galaxy shape field are shown
to be expressed by a simple Hankel transform, as is the case for those of the
conventional galaxy density correlations. We measure these multipoles of the
power spectra and correlation functions of the halo ellipticity field using
large-volume N-body simulations. We then show that the measured alignment
signals can be better predicted by our nonlinear model than the existing linear
alignment model. The formulas derived here have already been used to place
cosmological constraints using from the redshift-space correlation functions of
the galaxy shape field measured from the Sloan Digital Sky Survey (Okumura and
Taruya, 2023).
