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Tests of a Family Gauge Symmetry Model at 103 Tev Scale Physics Letters B 695 (2011) 279–284 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Tests of a family gauge symmetry model at 103 TeV scale ∗ Yoshio Koide a, , Yukinari Sumino b, Masato Yamanaka c a Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan b Department of Physics, Tohoku University, Sendai 980-8578, Japan c MISC, Kyoto Sangyo University, Kyoto 603-8555, Japan article info abstract Article history: Based on a specific model with U(3) family gauge symmetry at 103 TeV scale, we show its experimental Received 5 October 2010 signatures to search for. Since the gauge symmetry is introduced with a special purpose, its gauge Received in revised form 16 November 2010 coupling constant and gauge boson mass spectrum are not free. The current structure in this model Accepted 20 November 2010 leads to family number violations via exchange of extra gauge bosons. We investigate present constraints Available online 24 November 2010 from flavor changing processes and discuss visible signatures at LHC and lepton colliders. Editor: T. Yanagida © 2010 Elsevier B.V. All rights reserved. Keywords: Family gauge symmetry Family number violations LHC extra gauge boson search 1. Introduction First,letusgiveashortreview:“Whydoweneedafamily gauge symmetry?” In the charged lepton sector, we know that an empirical relation [4] In the current flavor physics, it is a big concern whether fla- vors can be described by concept of “symmetry” or not. If the flavors are described by a symmetry (family symmetry), it is also me + mμ + mτ 2 K ≡ √ √ √ = (1) interesting to consider that the symmetry is gauged. (For an ear- 2 ( me + mμ + mτ ) 3 lier work of gauge SU(3) symmetry, for example, see Ref. [1].) Most models with a family gauge symmetry have been introduced −5 for the purpose of understanding mass spectra and mixings of is satisfied with the order of 10 with the pole masses, i.e. pole = × ± quarks and leptons. However, it is difficult to exclude such mod- K (2/3) (0.999989 0.000014) [5], while it is only valid −3 = els by the present and near future experiments, because in most with the order of 10 with the running masses, i.e. K (μ) (2/3) × (1.00189 ± 0.00002) at μ = mZ . In conventional mass ma- models the gauge coupling constant g f and gauge boson masses are free parameters. In the present Letter, we pay attention to trix models, “mass” means not “pole mass” but “running mass”. a specific model with a U(3) family gauge symmetry which was Why is the mass formula (1) so remarkably satisfied with the pole proposed by one of the authors (Y.S.) [2,3]. In contrast to the con- masses? This has been a mysterious problem as to the relation (1) ventional U(3) family gauge model, the present model has been for long years. Recently, a possible solution to this problem has introduced to explain the charged lepton spectrum with high pre- been proposed by one of the authors (Y.S.) [2,3]: The deviation of pole K (μ) from K is caused by a logarithmic term mei log(μ/mei) cision. Therefore, the gauge coupling constant g f is fixed with respect to the standard electroweak gauge coupling constants as in the running mass. It was advocated that a family symmetry is gauged, and that the logarithmic term in the radiative correction g f /2 = e = g2 sin θW , and the mass spectrum of the gauge bosons is also fixed (see Eq. (8) below). As a result, we can give definite to K (μ) due to photon is canceled by that due to family gauge = pole predictions, which may allow these gauge bosons to be clearly de- bosons. (This does not mean mei(μ) mei .) In order that can- tected or excluded in forthcoming experiments. cellation works correctly, the left-handed lepton field ψL and its ∗ right-handed partner ψR should be assigned to 3 and 3 of U(3) [6], respectively, differently from the conventional assignment [1] (ψL ,ψR ) = (3, 3). Corresponding author. ∗ * The assignment (ψL ,ψR ) = (3, 3 ) can induce interesting ob- E-mail addresses: [email protected] (Y. Koide), [email protected] (Y. Sumino), [email protected] servable effects. In the conventional assignment, a family gauge i j = ¯ j + (M. Yamanaka). boson A j couples to a current component ( Jμ)i ψL γμψLi 0370-2693/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2010.11.048 280 Y. Koide et al. / Physics Letters B 695 (2011) 279–284 j ψ¯ , while in the present model, the gauge boson Ai cou- The mass spectrum (8) is essential in this model. For example, if R γμψRi j ples to eff j ∝ k j we assume (Ye )i k (Φe)i (Φe)k , we cannot obtain the rela- tion (8). It is assumed that other scalar VEV’s with non-zero family j = ¯ j − ¯ j ( Jμ)i ψL γμψLi ψRiγμψR . (2) charge, if they exist, have much smaller magnitudes than Φe , such that they do not affect the family gauge boson spectrum. This In general, the currents (2) cause the violation of individual family is crucial to protect the cancellation mechanism within the present | |= number N f by N f 2. The influence of the family number vio- scenario. lation is determined by the family gauge coupling constant g f and The purpose of the present Letter is to discuss how to test ≡ j each family gauge boson mass m fij m(Ai ). Here, for simplicity, this family gauge symmetry within the above model. We note that the family current structure has been presented by a field ψ as a this model is incomplete, e.g. the quark and neutrino sectors are representative of quarks u and d and leptons e and ν.Forexample, not included, anomaly of the family gauge symmetry is not can- 2 1 the charged lepton current component ( Jρ)1 is given by celed. We focus only on the family gauge interactions, which are fairly independent of the details of the model. We examine the in- 2 = ¯ − ¯ | |= 1 ( Jρ)1 μL γρeL eR γρμR . (3) teractions with N f 2viathegaugebosonA2. In the next − section, we estimate a lower bound of its mass m f 12 from the This causes an e (or μ) lepton-number-violating process e + − − − experimental limit on the branching ratio of a rare kaon decay e → + through the effective current–current interaction + + − + μ μ K → π μ e , assuming that the quarks are assigned to mul- × G tiplets of the U (3) O (3) family gauge group in the same way eff f 12 ρ 2 0 ¯ 0 L = √ μγ¯ ρ(1 − γ5)e μγ¯ (1 + γ5)e + h.c., (4) as the charged leptons. We also discuss K –K mixing and muo- 2 nium into antimuonium conversion. (For a review of searches for √ 2 2 1 signatures with |N f |=2, see, for example, Ref. [8].) In Section 3, where G f 12/ 2 = g /8(m f 12) (m f 12 = m(A )). f 2 we investigate possible signatures in collider experiments, such as In order to realize the cancellation mechanism between pho- − − − − e + e → μ + μ production. Since the mass of the lightest ton and family gauge bosons, g should be related to the electric f gauge boson A1 may take a value within 1–10 TeV range, we may charge e as 1 + → 1 + → + − + expect a production p p A1 X (e e ) X at LHC. We 1 2 2 2 2 estimate the production cross section and decay rate. Finally, Sec- g = e ≡ g sin θW , (5) 4 f 2 tion 4 is devoted to a summary. where g is the gauge coupling constant of SU(2) .In[2,3] aspec- 2 L 2. Lower bounds for the gauge boson masses ulation is given that the relation (5) may originate from unification 2 3 of SU(2)L and family U(3) gauge symmetries at 10 –10 TeV scale; the level of tuning of the unification scale required in this scenario First, in order to see more details of the characteristic current is estimated to be a factor of 3 to match the present experimental structure (2), we discuss the flavor changing neutral currents rel- 2 accuracy of Eq. (1). This model of charged lepton sector has been evant for μ and e. According to Eq. (2),thecurrent( Jρ)1 can be constructed in the context of an effective field theory with a cut- written as off scale Λ ∼ 103–104 TeV, assuming this unification scenario and j 2 = ¯ − ¯ = − ( Jρ)1 μL γρeL eR γρμR ( J V )ρ ( J A )ρ, (9) incorporating the family U(3) gauge symmetry. The masses of Ai are predicted to be in the 1–1000 TeV range. ¯ where ( J V )ρ = (1/2)(μγ¯ ρe − eγρμ) and ( J A )ρ = (1/2)(μγ¯ ργ5e + Thus, the ratio of the coefficients of the four-Fermi contact in- ρ ρ e¯γ γ μ). The vector current J and axial current J have CP = teractions is given by ρ 5 V A −1 and CP =+1, respectively. However, this does not mean that − G m 2 5 98 × 10 3 the effective current–current interactions cause CP-violating inter- fij 2 W . 1 ρ 1 ¯ ρ = 4sin θ = . (6) actions. In fact, the current ( Jρ) is written as ( J ) = eL γ μL − W [ ] 2 2 2 G F m fij (m fij TeV ) μ¯ γ ρe =−( J )ρ − ( J )ρ , so that the effective current–current √ √ R R V A = 2 2 = 2 2 interaction is CP conserving: Here G fij/ 2 g f /8m fij and G F / 2 g2/8mW .Inthismodel, eff G Yukawa coupling constants Ye of the charged leptons are effec- Leff = √f 12 2 ρ 1 4 ( Jρ)1 J tively given by 2 2 3 G f 12 1 =−4 √ ( J ) ( J )ρ − ( J ) ( J )ρ .
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