Where do the Progenitors of Millisecond Pulsars come from?
  Observations of a large population of Millisecond Pulsars (MSPs) show a wide divergence in the orbital periods (from approximately hours to a few months). In the standard view, Low-Mass X-Ray Binaries (LMXBs) are considered as progenitors for some MSPs during the recycling process. We present a systematic study that combines different types of compact objects in binaries such as Cataclysmic Variables (CVs), LMXBs and MSPs. We plot them together in the so called Corbet diagram. Larger and different samples are needed to better constrain the result as a function of the environment and formations. A scale diagram showing the distribution of MSPs for different orbital periods and the aspects for their progenitors relying on Accretion Induced Collapse (AIC) of white dwarfs in binaries. Thus massive CVs (M >1.1M\odot) can play a vital role on binary evolution, as well as of the physical processes involved in the formation and evolution of neutron stars and their magnetic fields, and could turn into binary MSPs with different scales of orbital periods; this effect can be explained by the AIC process. This scenario also suggests that some fraction of isolated MSPs in the Galactic disk could be formed through the same channel, formingthe contribution of some CVs to the single-degenerate progenitors of Type Ia supernova. Furthermore, we have refined the statistical distribution and evolution by using updated data. This implies that the significant studies of compact objects in binary systems can benefit from the Corbet diagram. 
Ali Taani, Chengmin Zhang, Mashhoor Al-Wardat and Yongheng Zhao
astro-ph.HE