Physics Letters B 564 (2003) 55–59 www.elsevier.com/locate/npe

Lepton flavor violating processes li → lj νlν¯l in -assisted technicolor models

Chongxing Yue a, Lanjun Liu b

a Department of Physics, Liaoning Normal University, Dalian 116029, PR China b College of Physics and Information Engineering, Henan Normal University, Xinxiang 453002, PR China Received 25 March 2003; accepted 6 May 2003 Editor: M. Cveticˇ

Abstract

We study the flavor violating (LFV) processes li → lj νl ν¯l in the context of the topcolor-assisted technicolor (TC2) models. We find that the branching ratios Br (τ → lj ντ ν¯τ ) are larger than the branching ratios Br (τ → lj νlν¯l) in all of the −6 −9 parameter space. Over a wide range of parameter space, we have Br (τ → lj ντ ν¯τ ) ∼ 10 and Br (τ → lj νlν¯l) ∼ 10 (l = µ − or e). Taking into account the bounds given by the experimental upper limit Brexp(µ → 3e)  1 × 10 12 on the free parameters of TC2 models, we further give the upper limits of the LFV processes li → lj νlν¯l . We hope that the results may be useful to partly explain the data of the neutrino oscillations and the future neutrino experimental data might be used to test TC2 models.  2003 Published by Elsevier Science B.V.

It is well known that the individual lepton numbers of these LFV processes would be a clear signature of Le, Lµ and Lτ are automatically conserved and the new physics beyond the SM, which has been widely tree-level lepton flavor violating (LFV) processes are studied in different scenarios such as Two Higgs Dou- absent in the (SM). However, the so- blet Models, , Grand Unification [4,5] lar neutrino experiments [1], the data on atmospheric and topcolor models [6]. neutrinos obtained by the Super-Kamiokande Collab- On the other hand, neutrino oscillations imply that oration [2], and the results from the KamLAND re- there are solar νe → νµ,ντ transitions and there are actor antineutrino experiments [3] provide very strong atmospheric νµ → ντ transitions. The standard tau de- evidence for mixing and oscillation of the flavor neu- cays τ → µνµν¯τ , eνeν¯τ and the standard muon de- trinos, which imply that the separated lepton number cay µ → eνeν¯µ cannot explain the experimental fact. are not conserved. Thus, the SM requires some mod- However, the LFV processes li → lj νl ν¯l,whereli = τ ification to account for the pattern of neutrino mix- or µ, lj = µ or e and l = τ,µ or e, might explain ing suggested by the data and the LFV processes like the data. With these motivations li → lj γ and li → lj lkll are allowed. The observation in mind, we study the LFV processes li → lj νlν¯l in the context of topcolor-assisted technicolor (TC2) models [7]. These models predict the existence of  E-mail address: [email protected] (C. Yue). the extra U(1) Z , which can induce

0370-2693/03/$ – see front matter  2003 Published by Elsevier Science B.V. doi:10.1016/S0370-2693(03)00677-4 56 C. Yue, L. Liu / Physics Letters B 564 (2003) 55–59

 the tree-level FC coupling vertices Z li lj . The effects  of the gauge boson Z on the LFV processes li → lj γ , li → lj lkll and Z → li lj have been studied in Refs. [6,8]. They have shown that the contributions of Z to these processes are significantly large, which may be detected in the future experiments. In this Let- ter, we shown that the Z can generate large contri- butions to the LFV processes τ → µντ ν¯τ , eντ ν¯τ and µ → eντ ν¯τ , which may be used to partly explain the data of the neutrino oscillations. Furthermore, consid- ering the constraints of the present experimental bound → Fig. 1. for the LFV processes li → lj νlν¯l induced on the LFV process µ 3e on the free parameters of  TC2 models, we give the upper bounds on the branch- by Z exchange.  ing ratios Br(li → lj νlν¯l), which arise from Z ex- change. generations of mix with a universal constant k, For TC2 models, the underlying interactions, top- i.e., kτµ = kτe = kµe = k in this Letter.  color interaction, are non-universal. This is an essen- li → lj νlν¯l can be generated via gauge boson Z tial feature of TC2 models, due to the need to sin- exchange at tree-level. The relevant Feynman dia- gle out the top for condensate. Therefore, TC2 grams are depicted in Fig. 1. The partial widths can models predict the existence of the non-universal U(1) be written as: gauge boson Z. The new particle treats the third gen- = → ¯ eration differently from those in the first and Γ1 Γ(τ µντ ντ ) 5 second generations and can lead to the tree-level FC 5k1αe m  = → ¯ = τ 2 Γ(τ eντ ντ ) 2 4 k , couplings. The flavor-diagonal couplings of Z to lep- 384πC M  tons can be written as [7,9]: W Z Γ2 = Γ(τ → µνµν¯µ) = Γ(τ→ µνeν¯e) LFD =−1   Z g1 cotθ Zµ = Γ(τ → eνµν¯µ) = Γ(τ→ eνeν¯e) 2  × ¯ µ + ¯ µ −¯ µ 3 5 τLγ τL 2τRγ τR ντLγ ντL = 5αe mτ 2 6 4 k ,  384πk C M  − 1   ¯ µ + ¯ µ 1 W Z g1 tan θ Zµ µLγ µL 2µRγ µR 2 5α3 m5 µ µ = → ¯ = e µ 2 +¯νµLγ νµL +¯eLγ eL Γ3 Γ(µ eντ ντ ) 6 4 k ,  384πk1C M  µ µ W Z + 2e¯Rγ eR +¯νeLγ νeL , Γ4 = Γ(µ→ eνµν¯µ) (1) 5 5 5α mµ where g1 is the ordinary hypercharge gauge cou- = Γ(µ→ eν ν¯ ) = e k2,   e e 3 10 4 pling√ constant, θ is the mixing angle with tan θ = 384πk1CW MZ  g1/ 4πk1. The flavor changing couplings of Z to where C2 = cos2 θ , θ is the Weinberg angle, M  leptons can be written as: W W W Z is the mass of the non-universal U(1) gauge boson  LFC =−1  Z predicted by TC2 models. In above equations, Z g1Zµ 2   we have assumed mµ ≈ 0, me ≈ 0 for the processes µ µ × kτµ τ¯Lγ µL + 2τ¯Rγ µR τ → lj νlν¯l and me ≈ 0 for the processes µ → eνlν¯l.   → ¯ + k τ¯ γ µe + 2τ¯ γ µe The widths of the processes li lj νµνµ are equal to τe L L R R  → ¯  those of the processes li lj νeνe. This is because + 2 ¯ µ + ¯ µ  kµe tan θ µLγ eL 2µRγ eR , the gauge boson Z only treats the fermions in the (2) third generation differently from those in the first and where kij are the flavor mixing factors. For the sake second generations and treats the fermions in the first of simplicity, we consider the case where all three generation same as those in the second generation. C. Yue, L. Liu / Physics Letters B 564 (2003) 55–59 57

The corresponding branching ratios can be written as:

exp Γ1 Br1 = Br (τ → eνeν¯τ ) , Γ(τ→ eνeν¯τ ) exp Γ2 Br2 = Br (τ → eνeν¯τ ) , Γ(τ→ eνeν¯τ ) Γ3 Br3 = , Γ(µ→ eνeν¯µ) Γ4 Br4 = , Γ(µ→ eνeν¯µ) with 5 2 mτ GF Γ(τ→ eνeν¯τ ) = , 192π3  Fig. 2. Branching ratio Br1 as a function of the Z mass MZ for the 5 2 flavor mixing factor k = 0.22 and k = 0.2 (solid line), 0.5 (dotted mµGF 1 Γ(µ→ eνeν¯µ) = . line), 0.8 (dashed line). 192π3

Here the Fermi GF = 1.16639 × 10−5 GeV−2 and the branching ratio Brexp(τ → eνeν¯τ ) = (17.83 ± 0.06)% [10]. To obtain numerical results, we take the SM para- 2 = = 1 = meters as CW 0.7685, αe 128.8 , mτ 1.78 GeV, mµ = 0.106 GeV [10]. It has been shown that vac- uum tilting and the constraints from Z-pole physics and U(1) triviality require k1  1 [11]. The limits on  the Z mass MZ can be obtained via studying its ef- fects on various experimental observables [9]. For ex- ample, Ref. [12] has been shown that to fit the elec-  troweak measurement data, the Z mass MZ must be larger than 1 TeV. As numerical estimation, we take the MZ and k1 as free parameters. The branching ratios Br1 and Br2 are ploted in  = = Figs. 2 and 3 as functions of MZ for k λ Fig. 3. Same as Fig. 2 but for Br2. 0.22 (λ is the Wolfenstein parameter [13]) and three values of the parameter k1: k1 = 0.2 (solid line), maximum values√ of the parameters, i.e., (k1)max = 1 0.5 (dotted line), 0.8 (dashed line). One can see that −4 and (k)max = 1/ 2, we have Br1 = 1.63 × 10 , the value of Br1 is larger than that of Br2 in all −8 −5 Br2 = 1.67 × 10 and Br1 = 1.02 × 10 ,Br2 = of the parameter space of TC2 models. This is because −9  1.04 × 10 for MZ = 1 TeV and 2 TeV, respectively. U( ) Z  the extra 1 gauge boson couple preferentially The extra U(1) gauge boson Z can also contribute to the third generation fermions. The value of the → −8 to the LFV process µ 3e. The relevant decay width branching ratio Br1 increases from 3.09 × 10 to  −6 arisen from the Z exchange can be written as: 7.91 × 10 as MZ decreasing from 4 to 1 TeV for = 5 5 k1 0.5 and the value of branching ratio Br2 increases 25α mµ −11 −9 → = e 2 from 1.26 × 10 to 3.23 × 10 .Fork1 = 1, MZ = Γ(µ 3e) 3 10 4 k . −5 384πk1CW MZ 1 TeV, the branching ratio Br1 can reach 1.6 × 10 . Certainly, the numerical results are changed by the The current experimental upper limit is Brexp(µ → value of the flavor mixing parameter k.Ifwetakethe 3e)  1 × 10−12 [14]. Therefore, the present experi- 58 C. Yue, L. Liu / Physics Letters B 564 (2003) 55–59 mental bound on the LFV process µ → 3e can give trino oscillations. The future neutrino experiment data severe constraints on the free parameters of TC2 mod- might be used to test TC2 models. els. Then the branching ratios Br1,Br2,Br3 and Br4 can be written as: Acknowledgements k4C8  1 W exp → ¯ exp → Br1 4 Br (τ eνeντ ) Br (µ 3e), 5αe Chongxing Yue thanks Professor J.M. Yang for use- k2C4 ful discussions. This work was supported by the Na-  1 W exp → ¯ exp → tional Natural Science Foundation of China Br2 2 Br (τ eνeντ ) Br (µ 3e), 5αe (90203005). k2C4  1 W exp → Br3 2 Br (µ 3e), 5αe References 1 exp Br4  Br (µ → 3e). 5 [1] Super-Kamiokande Collaboration, Y. Fukuda, et al., Phys. Rev. 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