Supersymmetry proposes a new symmetry between particles, doubling the Standard Model's particle count. It aims to solve key issues like the hierarchy problem and offers a framework for unifying fundamental forces.

SUSY predicts superpartners for known particles and introduces the lightest supersymmetric particle (LSP). This could explain dark matter and help unify forces at high energies, potentially bridging quantum mechanics and gravity.

Supersymmetry: Extending the Standard Model

Theoretical Framework and Implications

• Supersymmetry (SUSY) proposes a symmetry between fermions and bosons predicting each known particle has a supersymmetric partner
• SUSY addresses the hierarchy problem concerning the large difference between the weak force and gravity
• Introduces a new quantum number called R-parity distinguishing between Standard Model particles and their supersymmetric partners
• Minimal supersymmetric extension of the Standard Model (MSSM) doubles the number of particles in the Standard Model
• Provides a framework for unification of fundamental forces at high energies potentially bridging the gap between quantum mechanics and general relativity
• Represents a significant paradigm shift in particle physics offering a more complete description of nature at the most fundamental level

Addressing Standard Model Limitations

• Tackles several limitations of the Standard Model
• Offers potential solutions to theoretical issues (hierarchy problem)
• Expands particle zoo with predicted superpartners
• Introduces new symmetry principles to particle physics
• Provides a framework for incorporating gravity into particle physics through supergravity theories
• Suggests mechanisms for resolving cosmological constant problem by potentially cancelling zero-point energies of bosons and fermions

Bosons vs Fermions in Supersymmetry

Superpartner Pairings

• Every known elementary particle paired with a superpartner differing in spin by 1/2 unit
• Fermions (spin-1/2 particles) paired with bosonic superpartners called sfermions
• Bosons (integer spin particles) paired with fermionic superpartners
• Superpartners of Standard Model fermions named by adding prefix "s-" (selectron, squark)
• Superpartners of bosons named by adding suffix "-ino" (gluino, wino)
• Supersymmetry transformations convert fermions into bosons and vice versa maintaining total number of degrees of freedom in the theory

Theoretical Implications

• Relationship between bosons and fermions in SUSY theories leads to cancellation of quantum corrections to particle masses
• Potentially solves the hierarchy problem through superpartner interactions
• In unbroken supersymmetry superpartners would have identical masses to their Standard Model counterparts
• Symmetry must be broken in nature to explain why superpartners have not been observed
• Breaking mechanisms introduce mass differences between particles and their superpartners
• Precise nature of SUSY breaking remains an active area of theoretical research

Supersymmetry Predictions: Superpartners and LSP

Superpartner Predictions

• Predicts existence of complete set of superpartners for all known elementary particles
• Effectively doubles the particle content of the Standard Model
• Predicts Higgs boson mass below about 135 GeV consistent with observed mass of 125 GeV
• Forecasts existence of multiple Higgs bosons two charged Higgs bosons one CP-odd neutral Higgs boson and two CP-even neutral Higgs bosons
• Precise masses and properties of superpartners depend on specific SUSY breaking mechanism
• Various phenomenological models with distinct experimental signatures arise from different breaking scenarios

Lightest Supersymmetric Particle (LSP)

• LSP crucial prediction of many SUSY models often assumed stable due to R-parity conservation
• In many SUSY scenarios LSP predicted to be the neutralino
• Neutralino mixture of superpartners of photon Z boson and neutral Higgs bosons
• LSP characteristics depend on specific SUSY model parameters
• Stability of LSP makes it a candidate for dark matter
• Experimental searches for LSP focus on missing energy signatures in particle colliders

Supersymmetry Implications: Dark Matter and Force Unification

Dark Matter Connections

• LSP if stable and weakly interacting serves as leading candidate for dark matter
• Potentially explains observed dark matter abundance in the universe
• LSP production in collider experiments could lead to distinctive missing energy signatures
• Indirect evidence for dark matter might be obtained through these collider observations
• SUSY models provide framework for calculating dark matter relic abundance
• Constraints from dark matter observations help narrow down viable SUSY parameter space

Force Unification and High-Energy Physics

• Naturally provides mechanism for gauge coupling unification
• Strengths of electromagnetic weak and strong forces converge at high energies in SUSY models
• Unification typically occurs at energy scale of about $10^{16}$ GeV
• Consistent with constraints from proton decay experiments
• Offers framework for incorporating gravity into particle physics through supergravity theories
• Could lead to quantum theory of gravity bridging quantum mechanics and general relativity
• Absence of observed superpartners at current collider energies necessitates more complex breaking mechanisms or higher mass scales for superpartners