A Supersymmetry Primer

TL;DR

A Supersymmetry Primer provides a concise, pedagogical introduction to SUSY for readers familiar with the Standard Model and quantum field theory. It develops both component and superspace formalisms, showing how chiral and gauge multiplets assemble into softly broken, renormalizable theories and how the MSSM arises from holomorphic superpotentials and gauge invariance. The text highlights the mechanisms by which SUSY cancels quadratic divergences, details the structure of F- and D-terms, and explains how soft SUSY breaking is introduced without reintroducing large radiative sensitivities. It concludes with the MSSM phenomenology, possible SUSY-breaking origins, and extensions, emphasizing the experimental and theoretical implications of SUSY in particle physics.

Abstract

I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework.

Figures (5)

• Figure 1.1: One-loop quantum corrections to the Higgs squared mass parameter $m_H^2$, due to (a) a Dirac fermion $f$, and (b) a scalar $S$.
• Figure 1.2: Two-loop corrections to the Higgs squared mass parameter involving a heavy fermion $F$ that couples only indirectly to the Standard Model Higgs through gauge interactions.
• Figure 3.1: The dimensionless non-gauge interaction vertices in a supersymmetric theory: (a) scalar-fermion-fermion Yukawa interaction $y^{ijk}$, (b) the complex conjugate interaction $y_{ijk}$, and (c) quartic scalar interaction $y^{ijn}y^*_{kln}$.
• Figure 3.2: Supersymmetric dimensionful couplings: (a) (scalar)$^3$ interaction vertex $M^*_{in} y^{jkn}$ and (b) the conjugate interaction $M^{in} y^*_{jkn}$, (c) fermion mass term $M^{ij}$ and (d) conjugate fermion mass term $M^*_{ij}$, and (e) scalar squared-mass term $M^*_{ik}M^{kj}$.
• Figure 3.3: Supersymmetric gauge interaction vertices.