The formation of low-mass helium white dwarfs orbiting pulsars: Evolution of low-mass X-ray binaries below the bifurcation period

Millisecond pulsars (MSPs) are generally believed to be old neutron stars (NSs) that have been spun up to high rotation rates via accretion of matter from a companion star in a low-mass X-ray binary (LMXB). Here we investigate binary evolution in close LMXBs to study the formation of radio MSPs with low-mass helium white dwarf companions (He WDs) in tight binaries with orbital periods P[suborb][approx =]2-9 h. We find that severe fine-tuning is necessary to reproduce the observed MSPs in tight binaries with He WD companions of mass