Possible reason why leptons are lighter than quarks.

The minimal model of spontaneously broken leptonic colour and discrete quarklepton symmetry predicts that charged leptons have the same masses as their partner charge +2/3 quarks up to small radiative corrections. By invoking a different pattern of symmetry breaking, a similar model can be constructed with the structural feature that charged leptons have to be lighter than their partner quarks because of mixing between leptonic colours, provided mixing between generations is not too strong. As well as furnishing a new model-building tool, this is phenomenologically interesting because some of the new physics responsible for the quark-lepton mass hierarchy could exist on scales as low as several hundred GeV. [email protected] The patterns evident in the mass and mixing angle spectrum of quarks and leptons continue to challenge us to provide an explanation. One may broadly categorise these patterns as hierarchies between generations, between weak-doublet partners and between quarks and leptons. We do not know if these three sub-problems can be solved separately, or if an all-encompassing explanation is necessary. In this paper I will introduce a novel suggestion for why the charged lepton is less massive than the charge +2/3 quark for a given generation. An analysis of its explanatory success will lead us to discuss how the quark-lepton hierarchy problem might be connected with other hierarchy problems. The obvious place to look for a reason for quarks to be heavier than leptons is in the dynamics of colour. Is there any reason why coloured fermions in a generation should be more massive than colourless fermions? There is a well-known answer to this question in the context of ultra-high–scale unification theories: If quarks and leptons have similar or equal running masses in the 10 GeV to Planck mass regime, then gluonic interactions affect the running to lower energies so as to raise quark masses by roughly the correct amount relative to lepton masses [1]. However, evolution through thirteen orders of magnitude or more in energy is required since the masses run only logarithmically. Although this is an interesting observation, it has the observational disadvantage that the new physics of mass generation would be difficult to test properly. Is there a way to understand the quark-lepton mass hierarchy through new colour physics at much lower energy scales? One likely avenue is through a spontaneously broken colour group for leptons and discrete quark-lepton (q-l) symmetry [2]. These ideas have been pursued for the last few years [3]. The original motivation for them was to connect the quantum numbers of quarks and leptons by new symmetries that could be spontaneously broken at a relatively low scale such as 1 TeV. However, increasing symmetry beyond the SU(3)⊗SU(2)⊗U(1) of the Standard Model (SM) can also relate parameters such as coupling constants that were previously unrelated. Indeed, it was immediately noticed that in the minimal model discrete q-l symmetry enforced the tree-level mass relations me,μ,τ = mu,c,t and m Dirac νe,νμ,ντ = md,s,b. (1) The most constructive way to view the phenomenologically unacceptable chargedlepton–up-quark equality is as a spring-board for further pondering. Although it is unacceptable per se, we after all ultimately do want a theory that will relate quark and lepton masses. I will show how this equality can be transformed into an explanation for why charged leptons are less massive than their up quark partners. (The m ν = md equality is perfectly acceptable if one uses the see-saw mechanism [4] to explain why the standard neutrinos have such tiny masses.)