Beyond the Standard Model
Beyond the Standard Model
The SM cannot explain dark matter, dark energy, gravity at quantum scales, or the matter-antimatter asymmetry. Extensions include supersymmetry, extra dimensions, grand unified theories, and string theory.
Definition
Grand Unified Theories (GUTs) embed \(SU(3)\times SU(2)\times U(1)\) in a single gauge group (e.g., \(SU(5)\)) at \(\sim10^{15}\) GeV. They predict proton decay with lifetime \(\tau_p > 10^{34}\) years — currently being tested at Super-Kamiokande.
Key Result
Supersymmetry pairs every boson with a fermion superpartner and vice versa. It elegantly solves the hierarchy problem by canceling quadratic divergences in the Higgs mass, but no superpartners have been found at the LHC.
Example 1
Dark matter: 27% of the universe's energy density, but its nature is unknown. WIMP candidates (\(m\sim 100\) GeV) arise naturally in SUSY. Axions (\(m\sim 10^{-5}\) eV) solve the strong CP problem. Direct detection experiments aim to observe nuclear recoils.
Example 2
String theory requires 10 or 11 dimensions, with extra dimensions compactified at the Planck scale (\(\ell_P \sim 10^{-35}\) m). It naturally includes gravity and produces the SM gauge group, but lacks experimental predictions at accessible energies.
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Practice
- What is the matter-antimatter asymmetry problem?
- How could the LHC have detected supersymmetric particles?
- What is the strong CP problem, and how does the Peccei-Quinn symmetry address it?
- Explain the cosmological constant problem.
Show Answer Key
1. The universe has far more matter than antimatter ($n_B/n_\gamma \sim 10^{-10}$), but the Big Bang should have produced equal amounts. Sakharov conditions for baryogenesis: (1) baryon number violation, (2) C and CP violation, (3) departure from thermal equilibrium. The SM has all three (weak interactions violate B+L, CP violation in CKM matrix, electroweak phase transition), but the SM CP violation is too small. BSM physics is needed.
2. SUSY predicts a superpartner for each SM particle (squarks, sleptons, gluinos, neutralinos, charginos) with masses possibly at the TeV scale. The LHC searches for SUSY via: (1) missing transverse energy (lightest SUSY particle is stable, invisible), (2) cascade decays producing multiple jets and leptons, (3) direct production of squarks/gluinos in $pp$ collisions. No SUSY particles found up to ~2 TeV so far (Run 2).
3. Strong CP problem: QCD allows a CP-violating term $\theta\frac{g^2}{32\pi^2}G\tilde{G}$ in the Lagrangian. Experiments (neutron EDM) constrain $|\theta| < 10^{-10}$, but there's no SM reason for it to be so small. Peccei-Quinn solution: introduce a global $U(1)_{PQ}$ symmetry that is spontaneously broken, producing the axion (a light pseudoscalar). The axion field dynamically relaxes $\theta \to 0$. Axions are also dark matter candidates.
4. The cosmological constant problem: quantum field theory predicts vacuum energy density $\rho_{\text{vac}} \sim M_P^4 \sim 10^{76}$ GeV$^4$. The observed dark energy density $\rho_\Lambda \sim 10^{-47}$ GeV$^4$ — a discrepancy of ~$10^{123}$, the worst prediction in physics. No known mechanism explains why the cosmological constant is so small but nonzero. Proposed approaches: supersymmetry (reduces but doesn't solve), string landscape + anthropics, modified gravity.