Part VIII: Beyond the Standard Model
Introduction
Despite its remarkable success, the Standard Model is incomplete. It doesn't explain dark matter, dark energy, neutrino masses, matter-antimatter asymmetry, or gravity. Beyond Standard Model (BSM) theories attempt to address these shortcomings.
Featured Lecture
Physics Beyond the Standard Model at the Large Hadron Collider
An overview of BSM searches at the LHC including supersymmetry, extra dimensions, and exotic particles.
Supersymmetry (SUSY)
Concept
Supersymmetry relates fermions and bosons through a new symmetry. Every SM particle has a superpartner:
Fermions → Sfermions:
- Quarks → Squarks ($\tilde{q}$)
- Leptons → Sleptons ($\tilde{\ell}$)
- Spin-1/2 → Spin-0
Bosons → Fermions:
- Gluons → Gluinos ($\tilde{g}$)
- W, Z, γ → Winos, Zinos, Photino
- Spin-1 → Spin-1/2
SUSY solves hierarchy problem by canceling quadratic divergences in Higgs mass.
Experimental Status
No SUSY particles discovered yet. LHC searches exclude:
- Gluinos: $m_{\tilde{g}} > 2.3$ TeV
- Squarks: $m_{\tilde{q}} > 1.8$ TeV (first generation)
- Stops: $m_{\tilde{t}} > 1.2$ TeV (depending on decay mode)
- Neutralinos: $m_{\tilde{\chi}_1^0} > 100$ GeV (model-dependent)
Limits push SUSY to "unnatural" parameter space
Dark Matter Candidates
WIMPs
Weakly Interacting Massive Particles ($m \sim 10$ GeV - 1 TeV):
- Neutralino (lightest SUSY particle in many models)
- Thermal freeze-out: $\Omega h^2 \sim 0.12$
- Direct detection: XENON, LUX, SuperCDMS
- Indirect detection: Fermi-LAT, IceCube
- Current limits: $\sigma_{\text{SI}} < 10^{-46}$ cm$^2$ (1 TeV WIMP)
Other Candidates
Axions:
$m \sim \mu$eV - meV
Solves strong CP problem
ADMX experiment
Sterile Neutrinos:
$m \sim$ keV
Right-handed neutrinos
X-ray searches
Primordial Black Holes:
Non-particle dark matter
Microlensing constraints
Dark Photons:
Hidden sector $U(1)'$
Mixing with photon
Grand Unification (GUTs)
Unification of Forces
GUTs unify strong, weak, and electromagnetic forces at high energy ($M_{\text{GUT}} \sim 10^{16}$ GeV):
Common GUT Groups:
- $SU(5)$: Simplest GUT (Georgi-Glashow)
- $SO(10)$: Includes right-handed neutrinos naturally
- $E_6$: Exceptional group
Predictions & Tests:
- Proton decay: $p \to e^+ \pi^0$
- Super-K limit: $\tau_p > 10^{34}$ years
- Excludes minimal $SU(5)$ but not SUSY GUTs
- Gauge coupling unification (works with SUSY)
Extra Dimensions
Theories
Kaluza-Klein (KK):
Compactified extra dimensions
KK excitations of SM particles
TeV-scale KK gravitons
Randall-Sundrum:
Warped extra dimension
Solves hierarchy problem
Radion and KK graviton searches
ADD Model:
Large extra dimensions
Gravity diluted in bulk
Missing energy signatures
Universal Extra Dimensions:
All SM fields in bulk
KP conserved (like R-parity)
Dark matter candidate: LKP
No evidence yet; LHC searches constrain extra dimension scales to $> 5-10$ TeV.
Other BSM Ideas
Diverse Approaches
Composite Higgs:
Higgs as bound state
Technicolor variants
Searches for resonances
Leptoquarks:
Connect quarks and leptons
Could explain flavor anomalies
$m_{LQ} > 1$ TeV (LHC)
Heavy Neutrinos:
Seesaw mechanism
Explains tiny $\nu$ masses
Leptogenesis
Z' Bosons:
Additional $U(1)'$ symmetry
Dilepton resonances
$m_{Z'} > 5$ TeV (LHC)
Key Takeaways
- •Standard Model incomplete: doesn't explain dark matter, neutrino masses, hierarchy problem
- •SUSY: elegant but increasingly constrained by null results at LHC
- •Dark matter: WIMPs, axions, sterile neutrinos - multiple candidates, no detection yet
- •GUTs: predict proton decay, gauge unification (works with SUSY)
- •Extra dimensions, composite Higgs, leptoquarks: diverse theoretical ideas
- •Challenge: no clear BSM signals despite decades of searching