I really need to know the name of the song that was playing during the torture scene of Migun and Jin in episode 1
thanks in advance

I compiled a list of the songs that played during each episode of Samurai Champloo, and so far there appears to be no record of the name of the song that you have asked for. Just like the themes that played during Mugen's trouble in the restaurant in episode 3, and his training on episode 10, this one also appears to be a mystery track.