Did Umar ibn al-Khattab bury his daughter alive in the days of jahilliyah?

In a Nutshell: The claims that Umar (ra) buried his daughter alive are quite likely fabricated, not appearing in any hadith collection, seerah text or history book. This story is widespread, cited by orators, activists and teachers, however I can find no authentic report in any scholarly work, books of hadith, seerah or history. It is typically reported as follows: Umar ibn al-Khattab (ra) was sitting with some of the companions. He suddenly laughed and then started crying. When asked why he did this, he said: "When we were in jahiliyyah, we used to make an idol out of ajwa dates, we used to worship it then eat it. This is what made me laugh. As for my crying, I used to have a daughter and I wanted to bury her alive so I took her with me and I dug a hole for her, she then began to play with my beard so I buried her whilst she was alive." This is a fabricated story which has been falsely attributed to Umar Ibn al-Khattab (ra). Further considerations also suggest this story is fabricated: 1. It is known Umar's (ra) first wife was Uthman's (ra) sister, Zaynab bint Madh'oon (ra). Their children were: Hafsah, Abdullah and Abd al-Rahman. (Ibn Kathir, al-Bidayah wa al-Nihaya) Hafsa (ra) was born five years before revelation, so was the oldest daughter of Umar (ra) resulting in his kunya, Abu Hafsa. Umar (ra) said: "Hafsa was born whilst the Quraysh were building the Ka'bah. This was before the prophethood by five years." (al-Hakim) It is unusual why Umar (ra) did not bury his eldest daughter Hafsa (ra) as she was his eldest daughter. Furthermore, there is no recorded information regarding the daughter he allegedly buried. None of his relatives mentioned this story, neither is she mentioned along with his other children. (Ibn Hajar al-Asqalani, Al-Isabah, Vol. 7 p. 582) 2. Umar's (ra) tribe, the Banu Adiy, are not known to have ever buried any of their daughters alive.  This is illustrated by the fact Umar's (ra) sister Fatimah (ra) growing up to marry their cousin Sa'eed Ibn Zayd (ra). Likewise Hafsa (ra) survived childhood to grow up. 3. A review of the books of hadith, takhreej and seerah cite no narrations except some books of the Shi'a. Ni'matullah al-Jazairee who wrote al-Anwaar al-Nu'maniyyah citing this story does not state the narrator he relied on claiming 'it has been narrated…' References Ibn Kathir, al-Bidayah wa al-Nihayah Ibn Hajar al-Asqalani, al-Isabah Ni'matullah al-Jazairee, al-Anwaar al-Nu'maniyyah