Zazen Boys is a real Japanese rock band. There's a bit in the live drama Let's Go! which is probably a joke on them: Yui suggests changing HTT's name to "ZA ZENME" ("The All-Rice"). In turn, that's probably why they're in this comic.
Uuuh~Hey, I'm going to the music store. Do you want to come with?Well...I have some free time, but...Ritsu?If I go, I'll surely feel like buying something...Oh, this band has a new album out!Ritsu, you said you like them, right?I'll...I'll buy it, but......y-yeah...Are you going to buy it?