The Standard Model, while incredibly successful, has some glaring gaps. It can't explain gravity, dark matter, or why there's more matter than antimatter in the universe. These limitations point to the need for new physics beyond what we currently know.

Scientists are working on theories to fill these gaps, like grand unification and supersymmetry. These ideas aim to create a more complete picture of the universe, addressing issues like the hierarchy problem and the quest for a quantum theory of gravity.

Limitations of the Standard Model

Fundamental Forces and Particle Composition

• Standard Model fails to incorporate gravity leaves it incomplete as a unified theory of fundamental forces
  • Gravity remains separate from electromagnetic, strong, and weak nuclear forces
  • Unification of all four forces a major goal in theoretical physics
• Dark matter constitutes ~85% of universe's matter not accounted for within Standard Model
  • Observed through gravitational effects on visible matter (galaxy rotation curves)
  • Candidates include weakly interacting massive particles (WIMPs) and axions
• Neutrino masses experimentally observed not naturally accommodated within Standard Model framework
  • Requires addition of right-handed neutrinos or other mechanisms
  • Neutrino oscillations indicate non-zero masses (Super-Kamiokande experiment)

Symmetry and Generation Problems

• Strong CP problem questions why quantum chromodynamics does not seem to break CP-symmetry remains unresolved
  • CP violation observed in weak interactions but not in strong interactions
  • Proposed solutions include axions and spontaneous CP violation
• Standard Model does not explain existence of exactly three generations of fermions
  • Electron, muon, and tau leptons
  • Up, charm, and top quarks
  • Down, strange, and bottom quarks
• Model fails to predict or explain cosmological constant and nature of dark energy
  • Dark energy comprises ~68% of universe's energy content
  • Drives accelerating expansion of universe (observed through Type Ia supernovae)

The Hierarchy Problem

Scale Discrepancies

• Hierarchy problem refers to large discrepancy between weak force and gravity with gravity ~10^32 times weaker than weak force
• Manifests in huge difference between Planck scale (10^19 GeV) and electroweak scale (10^2 GeV)
  • Planck scale energy where quantum gravity effects become significant
  • Electroweak scale energy of weak force carrier particles (W and Z bosons)
• Higgs boson mass observed much smaller than theoretical predictions suggests fine-tuning problem in Standard Model
  • Observed mass ~125 GeV
  • Natural expectation closer to Planck scale

Quantum Corrections and Implications

• Quantum corrections to Higgs mass should make it comparable to Planck mass but observations show it much lighter
  • Radiative corrections from virtual particle loops
  • Requires extreme fine-tuning of parameters to cancel out large corrections
• Hierarchy problem implies new physics beyond Standard Model to explain discrepancy
  • Proposed solutions include supersymmetry, extra dimensions, and technicolor theories
• Resolution crucial for understanding stability of electroweak scale and naturalness of Standard Model
  • Naturalness principle suggests fundamental parameters should not require fine-tuning
  • Addresses question of why electroweak scale is so much smaller than Planck scale

Quantum Gravity and Particle Physics

Theoretical Challenges

• Gravity only fundamental force not described by quantum field theory within Standard Model
  • Electromagnetic, strong, and weak forces have quantum field theories
  • General relativity describes gravity classically
• Incompatibility between general relativity and quantum mechanics creates theoretical inconsistencies at extremely high energies or small distances
  • Planck scale (10^-35 meters) where both quantum and gravitational effects significant
• Attempts to quantize gravity lead to non-renormalizable infinities make traditional quantum field theory approaches problematic
  • Perturbative quantum gravity breaks down at high energies
  • Difficulty in removing infinities through renormalization techniques

Implications and Proposed Solutions

• Lack of quantum theory of gravity prevents complete understanding of phenomena at Planck scale where quantum gravity effects become significant
  • Early universe physics
  • Black hole information paradox
• Absence hinders development of unified theory of all fundamental forces long-standing goal in theoretical physics
  • Theory of Everything (TOE) would combine all forces and particles
• Proposed theories of quantum gravity such as string theory and loop quantum gravity have profound implications for particle physics but lack experimental verification
  • String theory suggests extra dimensions and supersymmetry
  • Loop quantum gravity proposes quantized spacetime
• Reconciliation of gravity with quantum mechanics essential for understanding early universe, black holes, and nature of spacetime itself
  • Quantum gravity effects crucial in singularities (Big Bang, black holes)
  • May resolve issues like the information paradox in black holes

Matter-Antimatter Asymmetry

Observational Evidence and Standard Model Predictions

• Universe contains significantly more matter than antimatter contradicts expectation of equal amounts produced in Big Bang
  • Observed through cosmic microwave background and large-scale structure
• Standard Model predicts only tiny imbalance between matter and antimatter insufficient to explain observed asymmetry
  • Predicted asymmetry from Standard Model CP violation ~10^-18
  • Observed asymmetry ~10^-10

Theoretical Framework and Proposed Mechanisms

• Sakharov conditions outline necessary requirements for baryogenesis including baryon number violation and CP violation
  • Baryon number violation
  • C and CP violation
  • Departure from thermal equilibrium
• Degree of CP violation observed in weak interactions within Standard Model too small to account for matter-antimatter asymmetry
  • CP violation in quark sector (CKM matrix)
  • Jarlskog invariant measures CP violation ~10^-5
• Leptogenesis and electroweak baryogenesis proposed mechanisms to explain asymmetry but require physics beyond Standard Model
  • Leptogenesis involves heavy right-handed neutrinos
  • Electroweak baryogenesis requires modified Higgs sector
• Search for additional sources of CP violation particularly in neutrino oscillations ongoing and may provide insights into this problem
  • Long-baseline neutrino experiments (DUNE, T2K)
  • Neutrinoless double beta decay searches