# Supersymmetric grand unified theories: Two-loop evolution of gauge and Yukawa couplings

## Abstract

We make a numerical study of guage and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass [ital Ansa]$[ital iuml]---[ital tze] at the grand unified scale. Integrating the renormalization group equations with [alpha][sub 1]([ital M][sub [ital Z]]) and [alpha][sub 2]([ital M][sub [ital Z]]) as inputs, we find [alpha][sub 3]([ital M][sub [ital Z]])[congruent]0.111(0.122) for [ital M][sub SUSY]=[ital m][sub [ital t]] and [alpha][sub 3]([ital M][sub [ital Z]])[congruent]0.106(0.116) for [ital M][sub SUSY]=1 TeV at one-loop (two-loop) order. Including [ital b] and [tau] Yukawa couplings in the evolution, we find an upper limit of [ital m][sub [ital t]][approx lt]200 GeV from Yukawa unification. For given [ital m][sub [ital t]][approx lt]175 GeV, there are two solutions for [beta]: one with tan[beta][gt][ital m][sub [ital t]]/[ital m][sub [ital b]], and one with sin[beta][congruent]0.78([ital m][sub [ital t]]/150 GeV). Taking a popular [ital Ansatz] for the mass matrices at the unified scale, we obtain a lower limit on the top-quark mass of [ital m][sub [ital t]][approx gt]150(115) GeV for [alpha][sub 3]([ital M][sub [ital Z]])=0.11(0.12) and an upper limit on the supersymmetry parameter tan[beta][approx lt]50 if [alpha][sub 3]([ital M][sub [ital Z]])=0.11. The evolution of the quark mixing elements is also evaluated.

- Authors:

- (Physics Department, University of Wisconsin, Madison, Wisconsin 53706 (United States))

- Publication Date:

- OSTI Identifier:
- 6819098

- Alternate Identifier(s):
- OSTI ID: 6819098

- DOE Contract Number:
- AC02-76ER00881

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D (Particles Fields); (United States)

- Additional Journal Information:
- Journal Volume: 47:3; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Pa; GRAND UNIFIED THEORY; SUPERSYMMETRY; COUPLING; FERMIONS; GAUGE INVARIANCE; MASS; MATRIX ELEMENTS; QUARKS; RENORMALIZATION; STANDARD MODEL; TOP PARTICLES; YUKAWA POTENTIAL; ELEMENTARY PARTICLES; FIELD THEORIES; INVARIANCE PRINCIPLES; MATHEMATICAL MODELS; NUCLEAR POTENTIAL; PARTICLE MODELS; POSTULATED PARTICLES; POTENTIALS; SYMMETRY; UNIFIED GAUGE MODELS; UNIFIED-FIELD THEORIES 662210* -- Specific Theories & Interaction Models; Particle Systematics-- Unified Theories & Models-- (1992-); 662120 -- General Theory of Particles & Fields-- Symmetry, Conservation Laws, Currents & Their Properties-- (1992-)

### Citation Formats

```
Barger, V., Berger, M.S., and Ohmann, P.
```*Supersymmetric grand unified theories: Two-loop evolution of gauge and Yukawa couplings*. United States: N. p., 1993.
Web. doi:10.1103/PhysRevD.47.1093.

```
Barger, V., Berger, M.S., & Ohmann, P.
```*Supersymmetric grand unified theories: Two-loop evolution of gauge and Yukawa couplings*. United States. doi:10.1103/PhysRevD.47.1093.

```
Barger, V., Berger, M.S., and Ohmann, P. Mon .
"Supersymmetric grand unified theories: Two-loop evolution of gauge and Yukawa couplings". United States. doi:10.1103/PhysRevD.47.1093.
```

```
@article{osti_6819098,
```

title = {Supersymmetric grand unified theories: Two-loop evolution of gauge and Yukawa couplings},

author = {Barger, V. and Berger, M.S. and Ohmann, P.},

abstractNote = {We make a numerical study of guage and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass [ital Ansa]$[ital iuml]---[ital tze] at the grand unified scale. Integrating the renormalization group equations with [alpha][sub 1]([ital M][sub [ital Z]]) and [alpha][sub 2]([ital M][sub [ital Z]]) as inputs, we find [alpha][sub 3]([ital M][sub [ital Z]])[congruent]0.111(0.122) for [ital M][sub SUSY]=[ital m][sub [ital t]] and [alpha][sub 3]([ital M][sub [ital Z]])[congruent]0.106(0.116) for [ital M][sub SUSY]=1 TeV at one-loop (two-loop) order. Including [ital b] and [tau] Yukawa couplings in the evolution, we find an upper limit of [ital m][sub [ital t]][approx lt]200 GeV from Yukawa unification. For given [ital m][sub [ital t]][approx lt]175 GeV, there are two solutions for [beta]: one with tan[beta][gt][ital m][sub [ital t]]/[ital m][sub [ital b]], and one with sin[beta][congruent]0.78([ital m][sub [ital t]]/150 GeV). Taking a popular [ital Ansatz] for the mass matrices at the unified scale, we obtain a lower limit on the top-quark mass of [ital m][sub [ital t]][approx gt]150(115) GeV for [alpha][sub 3]([ital M][sub [ital Z]])=0.11(0.12) and an upper limit on the supersymmetry parameter tan[beta][approx lt]50 if [alpha][sub 3]([ital M][sub [ital Z]])=0.11. The evolution of the quark mixing elements is also evaluated.},

doi = {10.1103/PhysRevD.47.1093},

journal = {Physical Review, D (Particles Fields); (United States)},

issn = {0556-2821},

number = ,

volume = 47:3,

place = {United States},

year = {1993},

month = {2}

}