Quark, lepton mass matrices in the string theory on orbifolds》.pdf.pdf

Volume 184, number 4 PHYSICS LETTERS B 5 February 1987 QUARK, LEPTON MASS MATRICES IN THE STRING THEORY ON ORBIFOLDS Kei ITO Department of Physics, Faculty of Science, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan Received 4 June 1986 A selection rule of Yukawa couplings is derived in the string theory on the Z-orbifold, using the symmetries of six- and 16- dimensional internal space. A possible form of quark-lepton mass matrices is derived. The mixing pattern is not changed by gauge symmetry breaking. In a previous note [ 1 ] we found a selection rule of the Yukawa couplings in heterotic string - pactified on a Z-orbifold [2] and showed that some qualitative features of quark, lepton masses and mix- ings can be reproduced as a consequence of this rule. There we derived the rule based on a group-theoret- ical argument. Since in heterotic string theory [3 ] Lie groups arise from symmetries of the extra 16 dimen- sions, the rule is considered to be a consequence of the symmetries of these dimensions. Therefore, in this letter, we first study the selection rule starting from translational invariance of 16-dimensional space. However, we have to consider not only the symmetry of 16 dimensions, but also that of six dimensions. From the latter, we find that allowed types of Yukawa couplings are further restricted. It turns out that the structure of the fermion mass matrix is constr