Beyond the Standard Model
Open questions and the search for new physics
Why Go Beyond?
Despite its extraordinary success, the Standard Model cannot be the final theory. There are compelling theoretical problems and experimental observations it doesn't explain:
1. Dark Matter Problem
Evidence:
- • Galaxy rotation curves: v(r) ~ constant, not ∝ 1/√r (Rubin 1970s)
- • Gravitational lensing: Bullet Cluster shows mass ≠ light
- • CMB: ΩDMh² = 0.120 ± 0.001 (Planck 2018)
- • Structure formation: N-body simulations require cold DM
Abundance: ρDM/ρcritical ≈ 0.27, about 5× more than baryons!
BSM Candidates:
WIMPs (Weakly Interacting Massive Particles):
Mass ~ 10-1000 GeV, weak-scale interactions. Examples:
- • Neutralino (χ̃⁰): Lightest SUSY particle (LSP)
- • KK photon: From extra dimensions
- • Thermal relic: Σv ~ 3 × 10-26 cm³/s ("WIMP miracle")
Direct detection: XENON, LUX, PandaX (no signal yet). Indirect: Fermi, AMS-02 (ambiguous).
Axions:
Ultra-light pseudoscalar (10-6 - 10-3 eV), solves strong CP problem
- • Peccei-Quinn symmetry breaking: fa ~ 109-12 GeV
- • Searches: ADMX, CAST, IAXO (axion-photon coupling)
- • Could be fuzzy dark matter (wave-like on galactic scales)
Sterile Neutrinos:
Right-handed neutrinos νR with keV-GeV mass. Warm DM candidate. X-ray searches ongoing.
Primordial Black Holes:
Non-particle DM. Mass windows constrained by LIGO, microlensing, CMB. Fraction of DM unclear.
2. Hierarchy Problem
The Problem:
Quantum corrections to Higgs mass-squared are quadratically divergent:
δmH² ~ -yt² Λ² / (4π²) + (gauge loops)If Λ ~ MPlanck = 10¹⁹ GeV, then δmH² ~ 10³⁴ GeV², but mH² ~ (100 GeV)²!
Requires fine-tuning to 1 part in 10³² to cancel. This is "unnatural."
Proposed Solutions:
Supersymmetry (SUSY):
Symmetry between fermions ↔ bosons. Each SM particle gets superpartner:
- • Quarks → squarks (q̃), leptons → sleptons (ℓ̃)
- • Gauge bosons → gauginos (g̃, W̃, B̃)
- • Higgs → higgsinos (H̃)
Top loop: Δm² ~ +yt²Λ². Stop loop: Δm² ~ -yt²Λ². Cancellation!
Problem: No SUSY particles found at LHC yet. If mSUSY > 1 TeV, little hierarchy returns.
Extra Dimensions:
Lower fundamental scale M* << MPlanck via large/warped extra dimensions
- • ADD model: n large flat dimensions, M* ~ TeV, gravity diluted
- • Randall-Sundrum: Warped 5D, Higgs on TeV brane, gravity on Planck brane
- • Predicts KK resonances, missing energy signatures at LHC
Composite Higgs:
Higgs is not elementary but a bound state (like pions in QCD). Cutoff Λ ~ 4πv ~ 3 TeV. Predicts new strong dynamics, resonances.
Anthropic Multiverse:
Accept fine-tuning. String theory landscape has ~10⁵⁰⁰ vacua. We live in one where mH ~ 100 GeV because larger values don't form galaxies/stars (anthropic selection). Controversial!
3. Grand Unified Theories (GUTs)
Motivation:
The three SM gauge couplings almost unify at MGUT ~ 10¹⁶ GeV:
α1-1(MZ) ≈ 59, α2-1(MZ) ≈ 30, α3-1(MZ) ≈ 8.5With MSSM (minimal SUSY), they unify perfectly! Suggests SU(3)×SU(2)×U(1) ⊂ larger group.
GUT Models:
SU(5) (Georgi-Glashow 1974):
- • Simplest GUT: SU(5) ⊃ SU(3)×SU(2)×U(1)
- • One generation: 5̄ ⊕ 10 representations
- • Predicts proton decay: p → e+π⁰ via X, Y bosons (MX ~ 10¹⁶ GeV)
- • τp ~ 10²⁹ years (predicted) vs τp > 10³⁴ years (Super-K limit) ✗
- • Minimal SU(5) ruled out!
SO(10):
- • SO(10) ⊃ SU(5) ⊃ SU(3)×SU(2)×U(1)
- • One generation fits in single 16-dimensional spinor (includes νR!)
- • Natural place for right-handed neutrinos → seesaw mechanism
- • More parameters, harder to test. τp can be made consistent.
E6, SU(5) SUSY, etc:
Various extensions with additional matter, gauge groups. Generally predict:
- • Proton decay (dominant constraint)
- • Magnetic monopoles (cosmological problem if too abundant)
- • Leptogenesis (generate baryon asymmetry via νR decay)
4. Neutrino Masses & Leptogenesis
Type-I Seesaw: Add heavy Majorana νR with mass MR ~ 10¹⁰-10¹⁵ GeV:
mν ≈ mD² / MR ~ (100 GeV)² / 10¹⁴ GeV ~ 0.1 eV ✓Explains tiny neutrino masses via high-scale physics!
Leptogenesis:
Heavy νR decay produces lepton asymmetry L via CP violation in Yukawas:
- • νR → ℓ + H vs νR → ℓ̄ + H* (different rates if CP ≠ 0)
- • Sphaleron processes convert L → B (baryon asymmetry)
- • Requires MR ~ 10⁹-10¹⁵ GeV, δCPPMNS ≠ 0
- • Can explain ηB = (nB - nB̄)/nγ ~ 6 × 10-10
Links neutrino physics to matter-antimatter asymmetry!
5. String Theory & Quantum Gravity
The Goal:
Unify all forces including gravity in a consistent quantum theory. Strings replace point particles with 1D objects oscillating at Planck scale ℓP ~ 10-35 m.
Key Features:
- • Requires 10 or 11 spacetime dimensions (6-7 compactified)
- • Naturally includes spin-2 graviton
- • No free parameters in principle (all from geometry)
- • 5 consistent superstring theories unified in M-theory
Challenges:
- • Landscape problem: ~10⁵⁰⁰ vacua (which one is our universe?)
- • No experimental predictions at accessible energies (yet)
- • Moduli stabilization unclear
- • How to get 3 generations, CKM mixing, etc. from geometry?
Connections to SM:
- • Intersecting D-branes can give chiral fermions, gauge groups
- • F-theory compactifications produce SU(5), SO(10) GUTs
- • Moduli/dilaton could be dark energy candidates
- • Black hole information paradox, holography (AdS/CFT)
6. Experimental Frontiers
Summary
The Standard Model is an extraordinary achievement, but we know it's incomplete:
- ✓ Dark matter: WIMPs, axions, sterile ν? Searches ongoing across mass scales
- ✓ Hierarchy problem: SUSY, extra dimensions, composite Higgs, or anthropics?
- ✓ Neutrino masses: Seesaw mechanism at 10¹⁴ GeV? Majorana or Dirac?
- ✓ GUTs: SU(5), SO(10), E6 unify forces at MGUT ~ 10¹⁶ GeV
- ✓ Baryon asymmetry: Leptogenesis via heavy νR most promising
- ✓ Quantum gravity: String theory, loop quantum gravity—no experimental test yet
- ✓ Next steps: HL-LHC, future colliders, precision measurements, dark matter searches
The journey from classical fields to the Standard Model and beyond represents one of humanity's greatest intellectual achievements. What lies beyond is the most exciting question in physics today!
Further Resources
- • Peskin - Concepts of Elementary Particle Physics (Oxford, 2019)
- • Quigg - Gauge Theories of the Strong, Weak, and Electromagnetic Interactions
- • Kane - Modern Elementary Particle Physics (2nd ed.)
- • Langacker - The Standard Model and Beyond (2nd ed., 2017)
- • Weinberg - Vol III: Supersymmetry
- • Polchinski - String Theory (2 volumes, Cambridge)
- • arXiv - hep-ph, hep-ex daily for latest developments