What are the limits of the private parts (al-farj) that invalidate ablution (wudu') for males and females, and does the area between the private parts and the anus invalidate ablution?

Touching the private parts directly (without a barrier) invalidates ablution according to the majority of scholars. As for the extent of the private parts that invalidates ablution, it is the penis itself, the anus, and the labia in women. Touching other parts of the body apart from the two private parts, such as the testicles or the area between the buttocks, does not invalidate ablution.