Is the Hadith narrated by Al-Hakim, in which the Prophet, peace and blessings be upon him, kissed some of his wives and then went out for prayer without performing ablution, authentic?

Al-Tirmidhi, Al-Nasa'i, Abu Dawud, Ibn Majah, and Ahmad narrated from Aisha that the Prophet kissed one of his wives and then prayed without performing ablution (wudu'). This indicates that touching a woman does not nullify ablution. The hadith was authenticated by Al-Albani and Al-Arna'oot. The nullification of ablution due to touching a woman is a matter of scholarly disagreement.