  Pulsars are neutron stars that rotate rapidly. Most of the pulsars in binary
systems tend to spin faster than those in isolation. According to binary
evolution theory, radio pulsars in binary systems can have various types of
companion stars. However, binary radio pulsars with giant stars, helium stars,
and black holes as companions are lacking so far. We aim to investigate the
possible parameter space of binary radio pulsars with giant companions. We used
the MESA stellar evolution code to consider the effect of irradiation in binary
evolution and evolved a series of binary models. We present the potential
physical properties of binary radio pulsars with giant star companions in the
framework of the classical recycling scenario and the irradiation model. We
found that the parameter space of binary radio pulsars with giant companions
can be greatly expanded by the effect of irradiation. Moreover, when
irradiation is strong enough, submillisecond pulsars might be accompanied by
giant companion stars. We also demonstrate a correlation between the timescale
of the binary system as a low-mass X-ray binary and the irradiation efficiency.
The birthrate problem between millisecond pulsars and low-mass X-ray binaries
might not be resolved by the irradiation effect. A more detailed binary
population synthesis is necessary. Our findings may offer guidance for
observers that wish to locate binary radio pulsars with giant companions or
submillisecond pulsars.
