Sources used: discogs, youtube.
Note:
This is the first recording (1964). RCA did not release it because Sedaka had not recorded it at the RCA studios, which was required by his contract. (It was recorded at the Dick Charles studio.) Sedaka re-recorded it at RCA, but none of those takes was satisfactory. In the meantime, the Gene Pitney version was released. That performance was created by removing the Sedaka vocal tracks from his original "demo" and over-dubbing Pitney's voice. (Neither the backup band nor backing singers are identified on either the Sedaka performance or the Pitney performance. The backing singers included Sedaka's wife, Leba, Toni Wine, and Helen Miller, the lyricist. You can hear Sedaka in the background of the Pitney release. Sedaka is also the pianist.) The Sedaka performance was eventually released in 2003.
See,
https://books.google.com/books?id=hj0fAwAAQBAJ&pg=PA111&lpg=PA111&dq=%22it+hurts…=onepage&q=%22it%20hurts%20to%20be%20in%20love%22%20%22neil%20sedaka%22&f=false
http://www.spectropop.com/remembers/HelenMiller.htm
https://www.revolvy.com/page/Neil-Sedaka
Here's a clip of the Sedaka "original" and the Pitney performance on side-by-side synched tracks:
Other links to allow for verification:
See, generally,
https://en.wikipedia.org/wiki/It_Hurts_to_Be_in_Love