It is my understanding that many Torah authorities urge parents to refrain from this Spanking ones children. If it is permitted currently, are boy children, to be treated differently than girl children? If yes, why? If no, why not? Any good works available on this subject?

There is no blanket halachic prohibition against spanking one’s children for educational reasons (Rashi Masechet Makkot 8a; Shulchan Aruch HaRav Hilchot Nizkei Guf VaNefesh, article 4). The Vilna Gaon (commentary on Proverbs 19 18-19) writes that one should not spank his children when he is very angry so as not to punish them more than is necessary to achieve an educational purpose. The halacha forbids cruelty and requires that only a minimum amount of force, if and when necesssary, be used (see Shulchan Aruch Yoreh Deah 245 10 and Pitchei Teshuva Choshen Mishpat 424 4).