SOFTLY BROKEN SUPERSYMMETRY AND SU(5)

SOFTLY BROKEN SUPERSYMMETRY AND SU(5)

Received 2 June 1981 | Savas DIMOPOULOS, Howard GEORGI
This paper presents a realistic grand unified theory (GUT) based on the SU(5) gauge group, where supersymmetry is softly broken at a scale of around 1 TeV. The authors construct a model that uses softly broken supersymmetry to protect the Higgs doublets from quadratic mass renormalization, ensuring their masslessness at low energies. This requires a precise adjustment of parameters, which they argue is necessary in any supersymmetric GUT where baryon number is not conserved. The model involves two Higgs doublet supermultiplets, one with average charge \(\frac{1}{2}\) and the other with \(-\frac{1}{2}\), to give mass to quarks and leptons, respectively. The soft breaking of supersymmetry is achieved by adding explicit mass terms to the Lagrangian, such as a positive mass squared term for matter bosons, a mass for Higgs fermions, and a negative mass squared term for the \(\Sigma\) supermultiplet. These terms ensure that the Higgs doublets remain massless while giving mass to their colored SU(5) partners. The phenomenological implications of the model are discussed, including the stability of the lightest supersymmetric partner and the suppression of flavor-changing effects through a super-GIM mechanism. The authors also address the issue of baryon number violation and the prediction of a specific b/τ mass ratio. The paper concludes by emphasizing the importance of using supersymmetry in GUTs and the naturalness of the required parameter adjustments. They suggest that the explicit breaking of supersymmetry through soft terms is a useful approach, even though it introduces a new scale (the SU(2) × U(1) breaking scale) that is distinct from the unification scale.This paper presents a realistic grand unified theory (GUT) based on the SU(5) gauge group, where supersymmetry is softly broken at a scale of around 1 TeV. The authors construct a model that uses softly broken supersymmetry to protect the Higgs doublets from quadratic mass renormalization, ensuring their masslessness at low energies. This requires a precise adjustment of parameters, which they argue is necessary in any supersymmetric GUT where baryon number is not conserved. The model involves two Higgs doublet supermultiplets, one with average charge \(\frac{1}{2}\) and the other with \(-\frac{1}{2}\), to give mass to quarks and leptons, respectively. The soft breaking of supersymmetry is achieved by adding explicit mass terms to the Lagrangian, such as a positive mass squared term for matter bosons, a mass for Higgs fermions, and a negative mass squared term for the \(\Sigma\) supermultiplet. These terms ensure that the Higgs doublets remain massless while giving mass to their colored SU(5) partners. The phenomenological implications of the model are discussed, including the stability of the lightest supersymmetric partner and the suppression of flavor-changing effects through a super-GIM mechanism. The authors also address the issue of baryon number violation and the prediction of a specific b/τ mass ratio. The paper concludes by emphasizing the importance of using supersymmetry in GUTs and the naturalness of the required parameter adjustments. They suggest that the explicit breaking of supersymmetry through soft terms is a useful approach, even though it introduces a new scale (the SU(2) × U(1) breaking scale) that is distinct from the unification scale.
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Understanding Softly Broken Supersymmetry and SU(5)