SOFTLY BROKEN SUPERSYMMETRY AND SU(5)

SOFTLY BROKEN SUPERSYMMETRY AND SU(5)

1981 | Savas DIMOPOULOS, Howard GEORGI
This paper presents an SU(5) grand unified theory with softly broken supersymmetry, designed to protect Higgs doublets from quadratic mass renormalization. The model requires a single, natural parameter adjustment to ensure the Higgs doublets remain massless while their supersymmetric partners acquire large masses. The authors argue that such an adjustment is necessary in any supersymmetric GUT where baryon number is not conserved. The model is built using two Higgs doublet supermultiplets, which are essential for giving mass to quarks and leptons through Yukawa couplings. The soft breaking of supersymmetry allows for a straightforward model where all particle masses and their supersymmetric partners can be reliably calculated in the tree approximation. The SU(5) symmetry is broken down to SU(3)×SU(2)×U(1) while preserving supersymmetry, requiring a careful parameter choice to maintain the masslessness of the Higgs doublets. The paper discusses the implications of supersymmetry breaking, showing that spontaneous breaking leads to a light color triplet boson, which is not acceptable in tree approximation. Instead, the authors propose soft supersymmetry breaking, which allows for a TeV-scale mass splitting without inducing large quadratic renormalizations of the Higgs mass. This results in two distinct mass scales: one for the unification scale and one for the SU(2)×U(1) breaking scale. The phenomenology of the model is sparse, with all supersymmetric partners of the usual fields being heavy. The lightest supersymmetric partner is stable, and flavor-changing effects from loops involving supersymmetric partners are suppressed by a super-GIM mechanism. The model also addresses the issue of lepton-quark mass relations, requiring a more complex Higgs structure while maintaining the qualitative structure. The authors conclude that supersymmetry can be incorporated into a unified theory in a way that makes use of the special renormalization properties of supersymmetric theories. While the masslessness of the Higgs doublets is not automatic, it requires an exact but natural parameter adjustment. The model is shown to be consistent with the requirement of baryon number conservation and provides a framework for understanding supersymmetry breaking in a realistic unified model.This paper presents an SU(5) grand unified theory with softly broken supersymmetry, designed to protect Higgs doublets from quadratic mass renormalization. The model requires a single, natural parameter adjustment to ensure the Higgs doublets remain massless while their supersymmetric partners acquire large masses. The authors argue that such an adjustment is necessary in any supersymmetric GUT where baryon number is not conserved. The model is built using two Higgs doublet supermultiplets, which are essential for giving mass to quarks and leptons through Yukawa couplings. The soft breaking of supersymmetry allows for a straightforward model where all particle masses and their supersymmetric partners can be reliably calculated in the tree approximation. The SU(5) symmetry is broken down to SU(3)×SU(2)×U(1) while preserving supersymmetry, requiring a careful parameter choice to maintain the masslessness of the Higgs doublets. The paper discusses the implications of supersymmetry breaking, showing that spontaneous breaking leads to a light color triplet boson, which is not acceptable in tree approximation. Instead, the authors propose soft supersymmetry breaking, which allows for a TeV-scale mass splitting without inducing large quadratic renormalizations of the Higgs mass. This results in two distinct mass scales: one for the unification scale and one for the SU(2)×U(1) breaking scale. The phenomenology of the model is sparse, with all supersymmetric partners of the usual fields being heavy. The lightest supersymmetric partner is stable, and flavor-changing effects from loops involving supersymmetric partners are suppressed by a super-GIM mechanism. The model also addresses the issue of lepton-quark mass relations, requiring a more complex Higgs structure while maintaining the qualitative structure. The authors conclude that supersymmetry can be incorporated into a unified theory in a way that makes use of the special renormalization properties of supersymmetric theories. While the masslessness of the Higgs doublets is not automatic, it requires an exact but natural parameter adjustment. The model is shown to be consistent with the requirement of baryon number conservation and provides a framework for understanding supersymmetry breaking in a realistic unified model.
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