Charged Scalar Particles and Τ Leptonic Decay

Charged scalar particles introduced in some extensions of the standard model can induce τ leptonic decay at tree level. We find that with some charged SU(2)-singlet scalar particles, like ones introduced in Zee-type models, τ leptonic decay width is always smaller than what is predicted by the standard model, therefore they may offer a natural solution to τ decay puzzle. To be more specific, we examine some Zee-type models in detail to see if at the same time they are acceptable in particle physics, cosmology and astrophysics. It is shown that τ decay data do put some constrains on these models. PACS numbers: 13.35.+s, 13.10.+q, 12.15.Ff τ lepton is an interesting system to test the standard model (SM) and search for new physics, since τ is the heaviest lepton yet known. There is a long-standing puzzle in τ lepton decays, which has received attention for some years. The puzzle is that the measured τ lifetime may be longer than one expected in the SM with three families [1, 2]. From Particle Data Group (PDG) [3], the measured τ lifetime is τ exp = (3.05 ± 0.06) × 10s, while the SM’s expectation is τ th = (2.87± 0.07)× 10s, where mτ = 1784.1 +2.7 −3.6 MeV is used. So one sees that the measured τ lifetime is about 2.3σ higher than SM expectation value [2]. The latest measurement of τ mass at BES [4] mτ = 1776.9± 0.5 MeV somehow relaxes the τ lifetime problem. But this downward shift of mτ is not enough. τ exp is still about 1.9σ higher than τ (= 2.92± 0.04× 10) . Of course it is very possible that this τ decay puzzle will disappear when new measurements of leptonic decays become available, as the expected value does not deviate too much from the measured one (In fact, it is noticed that there are some new measurements after PDG [3] on τ lifetime and leptonic decay branching ratios. We will comment on that at the end of the paper). However, we feel that there are some theoretical motivations for taking this puzzle seriously, such as the existence of a fourth generation or charged scalar particles (the latter case will be discussed in detail later). One simple solution to τ decay puzzle is to introduce a fourth generation [2, 5]. If the mixing between τ neutrino ντ and the fourth heavy neutrino (it must be heavier than 45.3 GeV from LEP Z-width constraints [6]) is around sin2θmix ≃ 0.05, the central value of τ exp is in consistency with the corresponding theoretical expectation value in this model. We denote ge, gμ and gτ as weak couplings of e, μ and τ leptons respectively, universality of weak interaction means ge = gμ = gτ . Any deviation from this relation (for example ge = gμ 6= gτ ) implies a violation of the universality (of τ). In the four generation model, τ universality in the charged and neutral current sector is obviously violated by a small amount [7]. Nevertheless, this is not favored by the neutral-current data from Z decay which agrees with the universality of the weak interaction of e, μ and τ leptons at the