What are the views of the four Islamic schools of thought (madhhabs) and their evidences regarding whether a man touching a non-mahram woman without desire invalidates wudu (ablution)?

Scholars differed regarding the nullification of ablution (wudu') by touching a woman without desire (shahwa). The Hanafis held that touching does not nullify ablution at all. The Malikis held that touching nullifies ablution under specific conditions related to intention and pleasure. The Shafi'is held that touching nullifies ablution absolutely if the skin of a man and a non-mahram woman who is desired meet, whether with desire or not. As for the Hanbalis, ablution is not nullified in their view except under two conditions: that there is no barrier, and that it is with desire. Ibn Taymiyyah chose the opinion that touching does not nullify ablution at all. Those who held the view of non-nullification cite as evidence what Aishah (may Allah be pleased with her) narrated: that the Prophet (peace be upon him) used to nudge her leg while she was asleep in front of him during his prostration, and that she missed him one night and her hand fell on the soles of his feet while he was prostrating. This indicates that touching without desire does not nullify ablution. As for the evidence of those who held the view of absolute nullification (the Shafi'is), it is the generality of Allah's statement: "or you have touched women" [An-Nisa: 43], and this is supported by Ibn Mas'ud's reading: "or you have touched." The preponderant view is that ablution is not nullified at all unless something is emitted.