Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
According to the correct opinion of the scholars, touching a woman does not invalidate Wudu, unless it causes an emission from the male's penis.
It is confirmed that the Prophet (Sallallahu Alaihi wa Sallam) kissed some of his wives and then prayed without making Wudu again. Reported by Ahmed and Ashab Al-Sunan form the Hadith narrated by Aisha, may Allah be pleased with her.
Similarly, touching a woman does not require Ghusl (ceremonial bath).
We draw the attention of the questioner to the fact that it is not permissible for a man to deliberately touch an alien woman, i.e. a woman not a Maharim (non-marriageable) women.
The Prophet (Sallallahu Alaihi wa Sallam) said: "If one of you were to be stabbed in the head with an iron needle, it would be better for him than touching a woman whom he is not permitted to him."
Bukhari and Muslim reported that Aisha, may Allah be pleased with her, said: "I swear by Allah that his hand-(meaning the Prophet (Sallallahu Alaihi wa Sallam)) never touched a woman."
Allah says: "Indeed in the Messenger of Allâh (Muhammad-(Sallallahu Alaihi wa Sallam) you have a good example to follow for him who hopes in (the Meeting with) Allâh and the Last Day and remembers Allâh much." (Al-Ahzab 33:21)
Because touching woman other than Maharim is a cause of Fitnah (affliction) and the Islamic Shariah came to block the reasons leading to what Allah has forbidden.
However, if that happens by mistake, then it is forgiven, as the Prophet (Sallallahu Alaihi wa Sallam) said: ""The pen is lifted (prevented from writing the sins) of three people: the child until becoming mature, the sleeping person until waking up, the mad person until recovering." Reported by Tabrani and others; Al-Nawawi classified it as a sound Hadith, and Al-Albani classified it as a Sahih Hadith, in Sahih Al-Jamii."
Allah knows best.