6. Katsumi Sugita, Yoshiwo Okamoto, Matsuo Sekine, CP Violation via a Noncommutative SU(2)‐Bundle Internal Structure

$25.00 each

Volume 19: Pages 55-57, 2006

CP Violation via a Noncommutative SU(2)Bundle Internal Structure

Katsumi Sugita 1, Yoshiwo Okamoto 2, Matsuo Sekine 3

1Sun Tech. Information Technology Laboratory, Sun Techno College, 19995, Ryuoshinmachi, Kaishi, Yamanashi, Japan

2Department of Electrical Engineering, Chiba Institute of Technology, 2171, Tsudanuma, Narashinoshi, Chiba, Japan

3Department of Communications Engineering, National Defense Academy, 11020, Hashirimizu, Yokosukashi, Kanagawa, Japan

CP is violated in only one family of u and d quarks by considering an internal structure described by a noncommutative SU(2)bundle. The u and d quark states are represented by the internal structure coordinates. These states are noncommutative. As a result, the phase factor cannot be eliminated by redefining such states, and CP is violated in one family of u and d quarks.

Keywords: CP violation, noncommutative SU(2)bundle, noncommutative geometry, one family of u and d quarks, standard model, twodimensional torus

Received: October 8, 2004; Published online: December 15, 2008