As regards the question, it is a controversial issue among the Muslim jurists; but the opinion which carries more weight is that touching women with lust it breaks wudu’ (ablution).
In his Al-Fatwa, Imam Ibn Taymiyyah states:

“There are three juristic views regarding the issue of touching women and breaking wudu’.
The first view is attributed to Imam As-Shafi`i, who states that touching woman breaks wudu’ even if one does not have desire or lust as long as the woman he touches can arouse him. He bases his argument upon the Qur’anic verse that reads: “Or ye have touched women, and ye find not water, then go to high clean soil and rub your faces and your hands (therewith). Lo! Allah is Benign, Forgiving.” (An-Nisa’: 43)
The second view is ascribed to Imam Abu Hanifah, who maintains that touching women, even with lustful thought, does not invalidate wudu’.

The third view is held by the rest of jurists. They are of the opinion that if one touches women with lust it breaks wudu’, but if it is not a lustful touch, wudu’ would not be broken.

According to Ibn Taymiyyah, the third view is believed to be the most correct.”

The difference over the issue arises from the interpretation of the verse: “Or ye have touched women, and ye find not water, then go to high clean soil and rub your faces and your hands (therewith). Lo! Allah is Benign, Forgiving.” (An-Nisa’: 43)

While Imam Ash-Shafi`i bases his argument that touching women requires wudu’ on the apparent meaning of the word Lamastum which literally means “touch”, other jurists interpret the same term to mean sexual intercourse.

Putting many hadiths and verses of the Qur’an together, we would say that the last view is the most correct. To illustrate, in an authentic hadith narrated by `A’ishah (may Allah be pleased with her) she states: “The Prophet (peace and blessings be upon him) used to pray for long hours at night in their apartment, and that she used to sleep in front of him. Because the room was small, when the Prophet used to make sajdah (prostration) he would tap her calf with his hand and she would retract her legs so he could make sajdah. And when he stood up she would allow her feet to return to their original position.” (Reported by Al-Bukhari)

Another hadith narrated by `A’ishah (may Allah be pleased with her) as recorded in the Musnad of Imam Ahmad states that the Prophet (peace and blessings be upon him) used to kiss `A’ishah (may Allah be pleased with her) and then go to pray at the masjid without renewing his ablution.

It is clear from this evidence that touching those women whom Allah allows us to have contact with does not break our wudu’. As for the term lamastum, Ibn `Abbas states that whenever lamastum is used by Allah in the Qur’an in reference to males and females, it specifically means sexual intercourse.

Examples of the verses of the Qur’an where the term lamastum is used to refer to sexual intercourse:

In surat Al `Imran: 47, “She said: ‘O my Lord how shall I have a son when no man hath touched Me.’”, and in suratAl-Baqarah: 187, “But do not associate with your wives while ye are in retreat in the Mosques those are limits by Allah.” Thus the “touch” here means the private contact.

Ibn Taymiyyah argues: It is well-known that touching women is among the things that have become rampant and men always touch their wives. If touching one’s wife breaks wudu’ the Prophet (peace and blessings be upon him) would have told the people about it, and it would have been famous among the Companions of the Prophet (may Allah be pleased with them). No Companion of the Prophet has been reported to have renewed his wudu’ upon touching his wife or another woman, and there is no single hadith from the Prophet (peace and blessings be upon him) to support that.