Technicolor (physics) - Extended Technicolor

Extended Technicolor

Elementary Higgs bosons perform another important task. In the Standard Model, quarks and leptons are necessarily massless because they transform under SU(2) ⊗ U(1) as left-handed doublets and right-handed singlets. The Higgs doublet couples to these fermions. When it develops its vacuum expectation value, it transmits this electroweak breaking to the quarks and leptons, giving them their observed masses. (In general, electroweak-eigenstate fermions are not mass eigenstates, so this process also induces the mixing matrices observed in charged-current weak interactions.)

In technicolor, something else must generate the quark and lepton masses. The only natural possibility, one avoiding the introduction of elementary scalars, is to enlarge G_TC to allow technifermions to couple to quarks and leptons. This coupling is induced by gauge bosons of the enlarged group. The picture, then, is that there is a large "extended technicolor" (ETC) gauge group G_ETC ⊃ G_TC in which technifermions, quarks, and leptons live in the same representations. At one or more high scales Λ_ETC, G_ETC is broken down to G_TC, and quarks and leptons emerge as the TC-singlet fermions. When α_TC(μ) becomes strong at scale Λ_TC ≅ F_EW, the fermionic condensate forms. (The condensate is the vacuum expectation value of the technifermion bilinear . The estimate here is based on naive dimensional analysis of the quark condensate in QCD, expected to be correct as an order of magnitude.) Then, the transitions can proceed through the technifermion's dynamical mass by the emission and reabsorption of ETC bosons whose masses M_ETC ≅ g_ETC Λ_ETC are much greater than Λ_TC. The quarks and leptons develop masses given approximately by

Here, is the technifermion condensate renormalized at the ETC boson mass scale,

where γ_m(μ) is the anomalous dimension of the technifermion bilinear at the scale μ. The second estimate in Eq. (2) depends on the assumption that, as happens in QCD, α_TC(μ) becomes weak not far above Λ_TC, so that the anomalous dimension γ_m of is small there. Extended technicolor was introduced in 1979 by Dimopoulos and Susskind, and by Eichten and Lane. For a quark of mass m_q ≅ 1 GeV, and with Λ_TC ≅ 250 GeV, one estimates Λ_ETC ≅ 15 TeV. Therefore, assuming that, M_ETC will be at least this large.

In addition to the ETC proposal for quark and lepton masses, Eichten and Lane observed that the size of the ETC representations required to generate all quark and lepton masses suggests that there will be more than one electroweak doublet of technifermions. If so, there will be more (spontaneously broken) chiral symmetries and therefore more Goldstone bosons than are eaten by the Higgs mechanism. These must acquire mass by virtue of the fact that the extra chiral symmetries are also explicitly broken, by the standard-model interactions and the ETC interactions. These "pseudo-Goldstone bosons" are called technipions, π_T. An application of Dashen's theorem gives for the ETC contribution to their mass

The second approximation in Eq. (4) assumes that . For F_EW ≅ Λ_TC ≅ 250 GeV and Λ_ETC ≅ 15 TeV, this contribution to M_πT is about 50 GeV. Since ETC interactions generate and the coupling of technipions to quark and lepton pairs, one expects the couplings to be Higgs-like; i.e., roughly proportional to the masses of the quarks and leptons. This means that technipions are expected to decay to the heaviest and pairs allowed.

Perhaps the most important restriction on the ETC framework for quark mass generation is that ETC interactions are likely to induce flavor-changing neutral current processes such as μ → e γ, K_L → μ e, and |Δ S| = 2 and |Δ B| = 2 interactions that induce and mixing. The reason is that the algebra of the ETC currents involved in generation imply and ETC currents which, when written in terms of fermion mass eigenstates, have no reason to conserve flavor. The strongest constraint comes from requiring that ETC interactions mediating mixing contribute less than the Standard Model. This implies an effective Λ_ETC greater than 1000 TeV. The actual Λ_ETC may be reduced somewhat if CKM-like mixing angle factors are present. If these interactions are CP-violating, as they well may be, the constraint from the ε-parameter is that the effective Λ_ETC > 104 TeV. Such huge ETC mass scales imply tiny quark and lepton masses and ETC contributions to M_πT of at most a few GeV, in conflict with LEP searches for π_T at the Z0.

Extended technicolor is a very ambitious proposal, requiring that quark and lepton masses and mixing angles arise from experimentally accessible interactions. If there exists a successful model, it would not only predict the masses and mixings of quarks and leptons (and technipions), it would explain why there are three families of each: they are the ones that fit into the ETC representations of q, and T. It should not be surprising that the construction of a successful model has proven to be very difficult.