Beyond the Standard Model

Despite the success of the standard model in describing a wide range of data, there are reasons to believe that additional phenomena exist, which would point to new theoretical structures. Some of these phenomena may be discovered in particle physics experiments in the near future. These lectures overview hypothetical particles, solutions to the hierarchy problem, theories of dark matter, and new strong interactions. 1 What is the standard model? The Standard Model of particle physics is an SU(3)c × SU(2)W × U(1)Y gauge theory with quarks transforming in the qi L ∼ (3, 2, 1/6), uR ∼ (3, 1, 2/3) and dR ∼ (3, 1,−1/3) representations of the gauge group, and leptons transforming as LL ∼ (1, 2,−1/2) and eR ∼ (1, 1,−1). The index i = 1, 2, 3 labels the generations of fermions. The Standard Model also includes a single Higgs doublet [1] transforming asH ∼ (1, 2, 1/2). The vacuum expectation value (VEV) of the Higgs doublet, 〈H〉 = (vH , 0), breaks the electroweak SU(2)W ×U(1)Y symmetry down to the gauge symmetry of electromagnetism, U(1)em. With these fields of spin 1 (gauge bosons), 1/2 (quarks and leptons) and 0 (Higgs doublet), the Standard Model is remarkably successful at describing a tremendous amount of data [2] in terms of a single mass parameter (the electroweak scale vH ≈ 174GeV) and 18 dimensionless parameters [3]. If one requires that the Lagrangian contains only renormalizable interactions, then the Standard Model cannot accommodate gravity or neutrino masses. However, the requirement of renormalizability goes beyond the sound comparison of theory and experiment, by imposing theoretical constraints at energy scales well above those accessible in current experiments. Gravity is nicely imbedded in an extension of the Standard Model through the inclusion of a graviton (massless spin-2 particle) with dimension-5 couplings to the stress-energy tensor [4] suppressed by the Planck scale MP = 2 × 1019 GeV. Graviton exchange reproduces (up to order 1/MP effects) general relativity, so this theory describes gravitational interactions with sufficient accuracy for practical purposes (issues related to quantum gravity are not experimentally accessible in the foreseeable future).1 Neutrino masses can be included in a couple of ways which may be differentiated in principle through future experiments [5]. An important dichotomy is whether the neutrino masses are of Majorana or Dirac type. Majorana masses may be obtained from dimension-5 operators of the type cij MN HH ( Lc i LL j L ) . (1) The dimensionless coefficients cij then determine the elements of the neutrino mass matrix through m ν = cijv /MN . Imposing cij < O(1), the measured atmospheric neutrino mass-squared difference |∆matm| ≈ (0.05 eV)2 requires the mass scale where the description in terms of dimension-5 operators breaks down to satisfy MN . 1014 GeV. The nonrenormalizable operators (1) may be generated by the tree-level exchange of gauge-singlet fermions (commonly called "right-handed neutrinos"2 and labelled by νR) or SU(2)W -triplet particles, or by loops involving various new particles. General relativity includes an additional mass scale, the cosmological constant, which given current knowledge appears to be independent of the Planck scale. The accelerated expansion of the Universe indicates that the cosmological constant minus the vacuum energy density is tiny (but nonzero). Ignoring issues about fine-tuning (discussed in Section 2), this may be a Standard Model effect because all existing particles contribute to the vacuum energy density. "Right-handed neutrino" is a potentially confusing name given that leftand right-handed fermions may be interchanged by a charge conjugation operation.