Any framework for physics beyond the
Standard Model must conform with precision measurements of the electroweak parameters. Its consequences for physics at existing and future high-energy hadron colliders, and for the dark matter of the universe must also be explored.
Precision electroweak tests In 1990, the phenomenological
parameters , , and were introduced by Peskin and Takeuchi to quantify contributions to electroweak radiative corrections from physics beyond the Standard Model. They have a simple relation to the parameters of the electroweak chiral Lagrangian. The Peskin–Takeuchi analysis was based on the general formalism for weak radiative corrections developed by Kennedy, Lynn, Peskin and Stuart, and alternate formulations also exist. The , , and -parameters describe corrections to the electroweak gauge boson propagators from
physics beyond the Standard Model. They can be written in terms of polarization functions of electroweak currents and their spectral representation as follows: : \begin{align} (5)\qquad S &= 16\pi \frac{d}{d q^2} \left[\Pi_{33}^{\mathbf{new}} (q^2) - \Pi_{3Q}^{\mathbf{new}}(q^2)\right]_{q^2=0}\\ &= 4\pi \int\frac{dm^2}{m^4}\left[\sigma^3_V(m^2) - \sigma^3_A(m^2)\right]^{\mathbf{new}};\\ \\ (6)\qquad T &= \frac{16\pi}{M^2_Z \sin^2 2\theta_W}\; \left[\Pi_{11}^{\mathbf{new}}(0) - \Pi_{33}^{\mathbf{new}}(0) \right]\\ &= \frac{4\pi}{M^2_Z \sin^2 2\theta_W}\int_0^\infty\frac{dm^2}{m^2}\left[\sigma_V^1(m^2) + \sigma_A^1(m^2) - \sigma_V^3(m^2) - \sigma_A^3(m^2)\right]^{\mathbf{new}},\end{align} where only new, beyond-standard-model physics is included. The quantities are calculated relative to a minimal Standard Model with some chosen reference mass of the
Higgs boson, taken to range from the experimental lower bound of 117 GeV to 1000 GeV where its width becomes very large. For these parameters to describe the dominant corrections to the Standard Model, the mass scale of the new physics must be much greater than and , and the coupling of
quarks and
leptons to the new particles must be suppressed relative to their coupling to the gauge bosons. This is the case with technicolor, so long as the lightest technivector mesons, T and T, are heavier than 200–300 GeV. The -parameter is sensitive to all new physics at the TeV scale, while is a measure of weak-isospin breaking effects. The -parameter is generally not useful; most new-physics theories, including technicolor theories, give negligible contributions to it. The and -parameters are determined by global fit to experimental data including
Z-pole data from
LEP at
CERN, top quark and -mass measurements at Fermilab, and measured levels of atomic parity violation. The resultant bounds on these parameters are given in the Review of Particle Properties. It is unknown whether higher energy contributions to \sigma_\text{V,A}^3 are a tower of identifiable T and T states or a smooth continuum. It has been conjectured that T and T partners could be more nearly degenerate in walking theories (approximate parity doubling), reducing their contribution to .
Lattice calculations are underway or planned to test these ideas and obtain reliable estimates of in walking theories. The restriction on the -parameter poses a problem for the generation of the top-quark mass in the ETC framework. The enhancement from walking can allow the associated ETC scale to be as large as a few TeV, as well as the rate for the decay \mathrm{Z^0 \rightarrow \bar{b}b}, could be too large.
Hadron collider phenomenology Early studies generally assumed the existence of just one
electroweak doublet of technifermions, or of one techni-family including one doublet each of color-triplet techniquarks and color-singlet technileptons (four electroweak doublets in total). The number D of electroweak doublets determines the decay constant needed to produce the correct electroweak scale, as = = . In the minimal, one-doublet model, three
Goldstone bosons (technipions, T) have decay constant = EW = 246 GeV and are eaten by the electroweak gauge bosons. The most accessible collider signal is the production through \bar{q}q annihilation in a hadron collider of spin-one \mathrm \rho_\text{T}^{\pm,0}, and their subsequent decay into a pair of longitudinally polarized weak bosons, \mathrm W_\text{LP}^\pm \mathrm Z_\text{LP}^0 and \mathrm W_\text{LP}^+ \mathrm W_\text{LP}^-. At an expected mass of 1.5–2.0 TeV and width of 300–400 GeV, such T's would be difficult to discover at the LHC. A one-family model has a large number of physical technipions, with = = 123 GeV. There is a collection of correspondingly lower-mass color-singlet and octet technivectors decaying into technipion pairs. The T's are expected to decay to the heaviest possible quark and lepton pairs. Despite their lower masses, the T's are wider than in the minimal model and the backgrounds to the T decays are likely to be insurmountable at a hadron collider. This picture changed with the advent of walking technicolor. A walking gauge coupling occurs if SB lies just below the IR fixed point value IR, which requires either a large number of electroweak doublets in the
fundamental representation of the gauge group, e.g., or a few doublets in higher-dimensional TC representations. In the latter case, the constraints on ETC representations generally imply other technifermions in the fundamental representation as well. A second consequence of walking technicolor concerns the decays of the spin-one technihadrons. Since technipion masses M_{\pi_T}^2 \propto \langle\bar{T}T \bar{T}T\rangle_{M_{ETC}} (see Eq. (4)), walking enhances them much more than it does other technihadron masses. Thus, it is very likely that the lightest T < 2T and that the two and three-T decay channels of the light technivectors are closed. Thus, all their decay rates are suppressed by powers of \left[\frac{F}{F_{EW}}\right]^2 \ll 1 or the fine-structure constant, giving total widths of a few GeV (for T) to a few tenths of a GeV (for T and T). A more speculative consequence of walking technicolor is motivated by consideration of its contribution to the -parameter. As noted above, the usual assumptions made to estimate TC are invalid in a walking theory. In particular, the spectral integrals used to evaluate TC cannot be dominated by just the lowest-lying T and T and, if TC is to be small, the masses and weak-current couplings of the T and T could be more nearly equal than they are in QCD. Low-scale technicolor phenomenology, including the possibility of a more parity-doubled spectrum, has been developed into a set of rules and decay amplitudes. has been interpreted by Eichten, Lane and Martin as a possible signal of the technipion of low-scale technicolor. The general scheme of low-scale technicolor makes little sense if the limit on M_{\rho_{T}} is pushed past about 700 GeV. The LHC should be able to discover it or rule it out. Searches there involving decays to technipions and thence to heavy quark jets are hampered by backgrounds from \bar{t}t production; its rate is 100 times larger than that at the Tevatron. Consequently, the discovery of low-scale technicolor at the LHC relies on all-leptonic final-state channels with favorable signal-to-background ratios: \rho_{T}^{\pm} \rightarrow W_L^\pm Z_L^0, a_{T}^{\pm} \rightarrow \gamma W_L^\pm and \omega_{T} \rightarrow \gamma Z_L^0.
Dark matter Technicolor theories naturally contain
dark matter candidates. Almost certainly, models can be built in which the lowest-lying technibaryon, a technicolor-singlet bound state of technifermions, is stable enough to survive the evolution of the universe. If the technicolor theory is low-scale (F \ll F_{EW}), the baryon's mass should be no more than 1–2 TeV. If not, it could be much heavier. The technibaryon must be electrically neutral and satisfy constraints on its abundance. Given the limits on spin-independent dark-matter-nucleon cross sections from dark-matter search experiments (\lesssim 10^{-42}\,\mathrm{cm}^2 for the masses of interest), it may have to be electroweak neutral (weak isospin = 0) as well. These considerations suggest that the "old" technicolor dark matter candidates may be difficult to produce at the LHC. A different class of technicolor dark matter candidates light enough to be accessible at the LHC was introduced by
Francesco Sannino and his collaborators. These states are pseudo Goldstone bosons possessing a global charge that makes them stable against decay. == See also ==