Wudu after touching the private part

It is narrated from Urwah (may Allah have mercy on him); al-Zuhri says (and I did not hear it directly from him (Urwah)) that he used to narrate from Busrah bint Safwan and Sayyiduna Zayd bin Khalid al-Juhani (may Allah be pleased with him), and they from the Messenger of Allah (peace and blessings be upon him), that he (peace and blessings be upon him) said: "When any one of you touches his private part (the male organ), let him perform ablution."
Ibn Jurayj said: And Yahya bin Abi Kathir narrated through a man from the Ansar that the Messenger of Allah (peace and blessings be upon him) led the prayer, then returned to his gathering and performed ablution, then repeated the prayer and said: "I had touched my male organ (during the prayer), and I forgot."
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The second route (the route of Mu'adh bin Hisham):
It is narrated from Yahya bin Abi Kathir; he said: A man in the Prophet's Mosque (peace and blessings be upon him) narrated to me through Urwah, from the Mother of the Believers, Sayyidah Aishah al-Siddiqah (may Allah be pleased with her), that the Prophet (peace and blessings be upon him) said: "When any one of you touches his private part, let him perform ablution."

It is narrated from Amr bin Shu'ayb (may Allah have mercy on him); he said: I was in the company of Sa'id bin al-Musayyib (may Allah have mercy on him) when those present raised the issue of touching the private part. Sa'id bin al-Musayyib (may Allah have mercy on him) said: "Busrah bint Safwan (may Allah be pleased with her), who is one of my maternal aunts, related: I was present in the gathering of the Messenger of Allah (peace and blessings be upon him), and so-and-so and so-and-so and Sayyiduna Abdullah bin Amr (may Allah be pleased with him) were also there, until she mentioned six or seven people. Then the Messenger of Allah (peace and blessings be upon him) said: 'Whoever touches his private part, let him perform ablution.'"
As for its first chain, it is sahih (authentic) and connected (muttasil), and this hadith of Busrah (may Allah be pleased with her) is in the four Sunan. Imam Ahmad (may Allah have mercy on him) also recorded it as the hadith of Sayyiduna Zayd bin Khalid (may Allah be pleased with him), but that is through the narration of Ibn Ishaq from al-Zuhri, from Urwah, from Zayd bin Khalid (may Allah be pleased with him). The chain we have given here makes it clear that Imam al-Zuhri did not hear this narration directly from Urwah, so it appears that Ibn Ishaq committed tadlis al-taswiyah in it, because he explicitly stated in that narration that he heard it from al-Zuhri. Therefore I have mentioned it through this route for the sake of scholarly benefit, while the remaining routes mentioned here were not recorded by the other hadith scholars.

It is narrated from Sayyidah Busrah bint Safwan (may Allah be pleased with her); she relates: I asked the Messenger of Allah (peace and blessings be upon him) about the legal ruling of a woman who touches her private part (whether it breaks her ablution). He (peace and blessings be upon him) said: "She should perform ablution (again for the prayer)."
Imam al-Harith narrated this hadith in his Musnad. In its chain the narrator named Yahya bin Hashim is matruk (abandoned); however, this hadith is narrated with other reliable and sahih chains in Sunan Abi Dawud (181) and Sunan al-Tirmidhi (82), where Imam al-Tirmidhi declared it hasan sahih.

It is narrated from Sa'id bin al-Musayyib (may Allah have mercy on him) that he said: "Whoever touches his male organ is required to perform ablution."
The chain of this report (athar) is strong and all its narrators are thiqat (trustworthy) and reliable. This narration, in the chapter of purification, makes clear the juristic position of the eminent Successor Sa'id bin al-Musayyib (may Allah have mercy on him) that touching the male organ invalidates ablution.

It is narrated from Qatadah (may Allah have mercy on him) that he asked Sa'id bin al-Musayyib (may Allah have mercy on him) about touching the private part, and he said: "It is just a part of the body like your other limbs."
This report (athar) is sahih (authentic), and it states the juristic position of the eminent Successor Sa'id bin al-Musayyib (may Allah have mercy on him) that touching the private part does not invalidate ablution, because it too is an ordinary part of the body.

It is narrated from Sayyiduna Hudhayfah (may Allah be pleased with him) concerning touching the male organ that he said: "I do not care in the least whether I have touched it or my nose and my ear." The narrator Yahya said (out of doubt): "Or one of the two."
It is narrated from al-Bara' bin Qays that Sayyiduna Hudhayfah (may Allah be pleased with him) was asked about touching the private part, and he stated a similar position.

It is narrated from Sayf bin Ubaydullah al-Himyari: I and some other men with me came into the presence of Sayyidah Aishah (may Allah be pleased with her), and we asked her about a man who touches his private part and about a woman who touches her private part. She replied: I heard the Messenger of Allah (peace and blessings be upon him) say: "I do not care in the least whether I touch it (that is, my private part) or touch my nose."
The chain of this hadith is da'if (weak), because its narrators al-Mufaddal bin Thawab and Husayn bin Wadda' are majhul (unknown); however, in terms of its text this narration is evidence for those jurists who hold that touching the private part does not break ablution.