Abstract
Consistency of trans-unification renormalization group (RG) evolution is used to discuss the domain of definition of the New Minimal Supersymmetric SO(10)GUT (NMSGUT). We define the 1-loop RGE $\ensuremath{\beta}$ functions, simplifying generic formulae using constraints of gauge invariance and superpotential structure. We also calculate the 2 loop contributions to the gauge coupling and gaugino mass and indicate how to get full 2 loop results for all couplings. Our method overcomes combinatorial barriers that frustrate computer algebra based attempts to calculate SO(10) $\ensuremath{\beta}$ functions involving large irreps. Use of the RGEs identifies a perturbative domain $Q<{M}_{E}$, where ${M}_{E}<{M}_{\text{Planck}}$ is the scale of emergence where the NMSGUT, with GUT compatible soft supersymmetry breaking terms emerges from the strong UV dynamics associated with the Landau poles in gauge and Yukawa couplings. Due to the strength of the RG flows the Landau poles for gauge and Yukawa couplings lie near a cutoff scale ${\mathrm{\ensuremath{\Lambda}}}_{E}$ for the perturbative dynamics of the NMSGUT which just above ${M}_{E}$. SO(10) RG flows into the IR are shown to facilitate small gaugino masses and generation of negative Non Universal Higgs masses squared needed by realistic NMSGUT fits of low energy data. Running the simple canonical theory emergent at ${M}_{E}$ through ${M}_{X}$ down to the electroweak scale enables tests of candidate scenarios such as supergravity based NMSGUT with canonical kinetic terms and NMSGUT based dynamical Yukawa unification.
Highlights
Renormalization group equations (RGE) are an important mathematical tool to study the evolution of the parameters of a quantum field theory with energy scale
Use of the RGEs identifies a perturbative domain Q < ME, where ME < MPlanck is the scale of emergence where the New Minimal Supersymmetric SO(10)GUT (NMSGUT), with GUT compatible soft supersymmetry breaking terms emerges from the strong UV dynamics associated with the Landau poles in gauge and Yukawa couplings
We have proposed a framework for a consistent interpretation of asymptotically strong GUTs by considering renormalization group (RG) flows of GUT parameters from an emergence scale ME of a weakly coupled GUT down to the scale MX where the GUT is matched to its low energy effective theory
Summary
Renormalization group equations (RGE) are an important mathematical tool to study the evolution of the parameters (couplings and masses) of a quantum field theory with energy scale. The IR flows of these theories very rapidly drive the coupling from arbitrarily strong coupling to the typical values found via RGpanffiffialyses near the supersymmetric unification scale g10 ∼ g5= 2 ∼ 0.5 (subscripts 5 and 10 refer to SUð5Þ and SOð10Þ normalizations for the running gauge coupling constant) From this point of view the transunification flows of the GUT gauge and Yukawa couplings that presumably underwrite the convergence of MSSM couplings(and third generation Yukawa couplings [18]) at or near M0X ∼ 1016.3 GeV require the existence of a regime Q < ME where a perturbative unified theory operates as the proper renormalizable effective theory describing all particle phenomena except gravity. In the Appendix we collect the explicit form of the 1-loop RG β functions of the NMSGUT for soft and hard parameters
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