Very large intermediate breaking scale in the Gepner/Schimmrigk three generation model

Abstract

A detailed study of the intermediate symmetry breaking scale, via the renormalization group equations, for a three generation heterotic string model arising from the N=2 superconformal construction is reported. The numerical study shows that the model admits a very large intermediate breaking scale > ∼ 1.0 × 10 16 GeV. The role of the gauge singlets in this model is studied, and it is found that these fields play a crucial role in determining the directions and the scale of the intermediate symmetry breaking. The importance of the mixing in generation space is also studied. The generation mixing terms are found to have special effects in the intermediate symmetry breaking. Remarkably these terms can produce some new Yukawa couplings (not present at the Planck scale) through loops. These couplings are in general very small compared to the ones with non-vanishing tree level values and thus offer a new mechanism to solve the lepton/quark mass hierarchy problem.

Is the Gepner three generation model phenomenologically viable?

“…After the decoupling of four generations of lepton-mirror-lepton pairs, we are left with five lepton (L,, i = 1,2, 3,8,9 ), two mirror-lepton (z7, 7=2,3), and three intact quark and conjugate-quark generations. Of all 52 independent Yukawa couplings listed in Table I of [14], only 15 survive. We may run the renormalization group (RG) equations with these nonets and Yukawa couplings and it can be expected that the gauge symmetry breaking will take place at a scale, say, greater than 1.OX 1016 GeV.…”

“…It is found there that the model does admit a very large intermediate breaking scale MI 2 1016. One lesson we have learned in [14] is that the mixing in the generation space can produce, through loops, some new Yukawa couplings which are zero valued at the tree level. These new Yukawa couplings are generally very small compared to the ones with nonvanishing tree level values and hence provide a possible new mechanism to solve the quark-lepton mass hierarchy problem.…”

“…Of two possible flux-breaking patterns [12], we are interested in the one which produces nine lepton, six mirror-lepton, three quark, three antiquark and no mirror-quark or mirror antiquark generations [7,11,13]. These massless fields can be represented by their SU (3),_X SU(3)L X SU (3) (3), X SU(2), X U(1), signaled by the scalar ( m a d 2 turning negative, via the renormalization group equations [14]. It is found there that the model does admit a very large intermediate breaking scale MI 2 1016.…”

“…This process cannot go on forever, because the index theorem guaran-493 1 @ 1994 The American Physical Society tees three light generations. This motivated us to suggest a scenario in [14] in which the gauge singlets grow VEV's in the following order: (i) 4s8 grows a VEV, then L, and L4 p ! i r up and decouple, (ii) $J~, grows a VEV, then L, and L , pair up and decouple, (iii) 4, grows a VEV, then L 4 and r6 ptir up and decouple, (iv) $61 grows a VEV, then L 5 and L 5 pair up and decouple, where the notation for the gauge singlets follows that of Ref.…”