Pinning down the new minimal supersymmetric GUT

Charanjit S Aulakh

doi:10.1016/j.physletb.2008.01.053

Abstract

We show that generic 10⊕120⊕126¯ fits of fermion masses and mixings, using real superpotential couplings but with complex ‘Higgs fractions’ leading to complex Yukawa couplings in the effective MSSM, overdetermine (by one extra constraint) the superpotential parameters of the new minimal supersymmetric SO(10) GUT(NMSGUT) [C.S. Aulakh, S.K. Garg, hep-ph/0612021]. Therefore fits should properly be done by generating the 24 generic fit parameters from the 23 parameters of the NMSGUT superpotential, given tanβ as input. Each numerical fit then fully specifies the parameters of the NMSGUT. Thus the NMSGUT offers the possibility of a mutual confrontation between gauge unification, the fit to fermion masses and proton decay calculations due to their extractable common dependence on the NMSGUT parameters. If and when ‘smoking gun’ discoveries of supersymmetry and proton decay occur they will find the NMSGUT vulnerable to falsification.

Highlights

In this letter we pointed out the correct procedure for fitting the only data currently available for constraining any GUT beyond the basic requirements of gauge unification : the low energy fermion masses and mixing
The NMSGUT has 23 superpotential parameters(after the fine tuning to keep a Higgs pair light) all of which enter the fermion mass formulae, the number of data values is smaller in number
The only practicable way of doing this is through a numerical fitting procedure such as the downhill simplex algorithm[7, 8] or possibly using some hybrid procedure of an ansatz regarding the hierarchy structure combined with numerical fitting[4, 5]

Summary

Introduction

A series of papers over the last few years[2, 3, 4, 5, 7, 1, 8] have developed the renormalizable Supersymmetric SO(10) GUT based on the Higgs set 210 ⊕ 10 ⊕ 120 ⊕ 126 ⊕ 126 (the so called New Minimal Supersymmetric GUT(NMSGUT)) into a theory capable of encompassing the entire gamut of fermion mass-mixing data in a most parameter economical way, while preserving the traditional advantages and attractions of renormalizable Supersymmetric SO(10)GUTs[9, 10, 11, 12, 13, 14, 15]. This is one less parameter than the original MSGUT[9, 10, 12] in spite of the introduction of the 120 representation to save the feasibility of the fermion fit [2, 3, 4, 5, 1, 6] It has a very characteristic pattern of fermion yukawas where the 10, 120 couplings to 16 · 16 must necessarily dominate[3, 4, 5, 7, 8, 1, 6] those of the 126 to permit a (Type I) seesaw mechanism to generate the observed neutrino masses. Even before supersymmetry or proton decay are observed we may obtain significant insights into the entire structure of the NMSGUT ! In this letter we give only the analytic details of the above arguments and leave the very involved numerical implementation to succeeding works[19]

Basics of NMSGUT

NMSGUT Constraints on the Grimus Kuhbock generic parametrization

Discussion