PHENOMENOLOGY OF A THREE-FAMILY MODEL WITH GAUGE SYMMETRY Villada Gil, Stiven Sánchez Duque, Luis Alberto Theoretical Physics Group, School of Physics, National University of Colombia FERMION CONTENT An extension of the Standard Model to the gauge group SU(3) C ⊗ SU(4) L ⊗ U(1) X as a three-family model is presented. The model does not contain exotic electric charges and anomaly cancellation is achieved with a family of quarks transforming differently from the other two, thus leading to FCNC. By introducing a discrete Z 2 symmetry we obtain a consistent fermion mass spectrum, and avoid unitarity violation of the CKM mixing matrix arising from the mixing of ordinary and exotic quarks. The neutral currents coupled to all neutral vector bosons are studied, and by using CERN LEP and SLAC Linear Collider data at Z-pole and APV data, we bound the relevant parameters of the model. These parameters are further constrained by using experimental input from neutral meson mixing in the analysis of sources of FCNC present in the model. INTRODUCTION One intriguing puzzle completely unanswered in modern particle physics concerns the number of fermion families in nature. The SU(3) C ⊗ SU(4) L ⊗ U(1) X extension (3-4-1 for short) of the gauge symmetry SU(3) C ⊗ SU(2) L ⊗ U(1) Y of the standard model (SM) provides an interesting attempt to answer the question of family replication, in the sense that anomaly cancellation is achieved when N f = N c = 3, N c being the number of colors of SU(3) c. A systematic study of possible extensions for three-family anomaly free models, based on the gauge group 3-4-1, was carried out by our group in reference [1], leading to different models. Three of them have been studied in reference [2] and the other one has not been yet analyzed in the literature and will be presented in a paper, which is the base for this poster. SCALARS To avoid unnecessary mixing in the electroweak gauge boson sector and to give masses for all the fermion fields (except for the neutral leptons), we introduce the following four Higgs scalars and its vacuum expectation values (VEV): This set of scalars break the symmetry in three steps: FERMION SPECTRUM GAUGE BOSONS When the symmetry is broken to the SM, we get the gauge matching conditions: and where g and g’ are the gauge coupling constants of the SU(2) L and U(1) Y gauge groups of the SM respectively, and g 4 and g X are associated with the groups SU(4) L and U(1) X respectively. For our purposes, we will be mainly interested in the neutral gauge boson sector which consists of four physical fields: the massless photon and the massive gauge bosons and. In terms of the electroweak basis, they are given by: where: is the field to be identified as the Y hypercharge associated with the SM abelian gauge boson. For convenience we choose V = V’ and v = v’, for which the current decouples from the other two and acquires a squared mass. The remaining mixing between and is parametrized by the mixing angle θ as: where and are the mass eigenstates and NEUTRAL CURRENTS The neutral currents are given by: where the left-handed currents are: where is the third component of the weak isospin, and are convenient 4x4 diagonal matrices, acting both of them on the representation 4 of SU(4) L. The current is clearly recognized as the generalization of the neutral current of the SM. This allows us identify as the neutral gauge boson of the SM. The couplings between the flavor diagonal mass eigenstates.. and, and the fermion fields are obtained from The expresions for g iV and g iA with i = 1,2 are listed in Tables 2 and 3, where: Note that in the limit the couplings of to the ordinary quarks and leptons are the same in the SM. This allows us to test the new physics beyond the SM predicted by this particular model. Mixing between ordinary and exotic fermions and violation of unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix is avoided by introducing a discrete Z 2 symmetry with assignments of Z 2 charge q z given by: After the symmetry breaking, the Yukawa couplings allowed by the gauge invariance and the Z 2 symmetry produces for up- and down-type quarks, in the basis (u 1,u 2,u 3,U 1,U 2,U 3 ) and (d 1,d 2,d 3, D 1,D 2,D 3 ) respectively, block diagonal mass matrices of the form Similary for the charged leptons, in the basis (e 1,e 2,e 3,E 1, E 2,E 3 ), we find the following block diagonal mass matrix Bounds on M Z 2 and θ from Z-pole observables and APV data To get bounds on the parameter space (θ-M Z 2 ) we use experimental parameters measured at the Z-pole from CERN e + e - collider (LEP), SLAC Linear Collider (SLC), and atomic parity violation data which are given in Table 4. Bounds on M Z 3 from FCNC processes These three mass matrices show that all the charged fermions in the model acquire masses at the three level. The partial decay width for is given by [4,5] where f is an ordinary SM fermion, is the physical gauge boson observed at LEP. The prediction of the SM for the value of the nuclear weak charge Q W in Cesium atom is given by [6] ΔQ W, which includes the contribution of new physics, can be written as [7]: The term is model dependent. In particular, is a function of the couplings g(q) 2V and g(q) 2A (q=u,d) of the first family of quarks to the new neutral gauge boson Z 2. So, the new physics in depends on which family of quarks transform dierently under the gauge group. Taking the third generation being diferent the value we obtain is The diference between the experimental value and that predicted by the SM for ΔQ W is given by [6]: which is 1.1σ away from the SM predictions. REFERENCES [1] W.A. Ponce and L.A. Sánchez, Mod. Phys. Lett. A22, 435 (2007). [2] L.A. Sánchez,, F. A. Pérez and W.A. Ponce, Eur. Phys. J. C35, 259 (2004); W.A. Ponce, D.A. Gutiérrez and L.A. Sánchez, Phys. Rev. D69, (2004); L.A. Sánchez, L.A. Wills-Toro and Jorge I. Zuluaga, Phys. Rev. D77, (2008). [3] L.E. Ibañez and G.G. Ross, Phys. Lett. B260, (1991) 291. [4] Particle Data Group, C. Amsler et al., Phys. Lett. B667, 1 (2008); [5] J. Bernabeu, A. Pich and A. Santamaria, Nucl. Phys. B363, 326 (1991). [6] J.S.M. Ginges, V.V. Flambaum, Phys. Rep. 397, 63 (2004). [7] G. Altarelli, R. Casalbuoni, S. De Curtis, N. Di Bartolomeo, F. Feruglio and R. Gatto, Phys. Lett. B261, 146 (1991). [8] F. Abe et al., Phys. Rev. Lett. 79, 2192 (1997). [9] J. Urban, F. Krauss, U. Jentschura and G. So, Nucl. Phys. B 523, 40 (1998). [10] J.T. Liu, Phys. Rev. D 50, 542 (1994). [11] H. Fritzsch, Phys. Lett. B 73, 317 (1978). Introducing the expressions for Z-pole observables in the partial decay width for, with ΔQ W in terms of new physics and using experimental data from Table 4, we do fit and find the best allowed region in the (θ-M Z 2 ) plane at 95% condence level. In Fig. 1 we display this region which gives us the constraints From current we can see that the couplings of Z’’ to the third family of quarks are different from the ones to the first two families. This induces FCNC at tree level transmitted by the Z’’ boson. The flavor changing interaction can be written, for ordinary up- and down-type quarks in the weak basis, as This shows that the strongest constraint comes from the d system, which puts on M Z 3 the lower bound 6.65 TeV. This Lagrangian produces the following efective Hamiltonian for the tree-level neutral meson mixing interactions where i=1,2 and α=1,2,3 are generation indexes. As we can see the mass of the new neutral gauge boson is compatible with the bound obtained in collisions at the Fermilab Tevatron [8]. where (α,β) must be replaced by (d,s), (d,b), (s,b) and (u,c) for the and systems, respectively, and V L must be replaced by U L for the neutral system. The effective Hamiltonian gives the following contribution to the mass differences Δm K, Δm B and Δm D : where B stands for B d or B s. B m and f m (m = K,B d,B s,D) are the bag parameter and decay constant of the corresponding neutral meson. The η's are QCD correction factors which, at leading order, can be taken equal to the ones of the SM, that is: [9]. Because there are various sources that may contribute to the mass differences, it is impossible to disentangle the Z 3 contribution from the other effects. Due to this, several authors consider reasonable to assume that the Z 3 exchange contribution must not be larger than the experimental values [10]. Since the complex numbers V Lij and U Lij can not be estimated from the present experimental, we assume the Fritzsch ansatz for the quark mass matrices [11], which implies (for i≤j), and similary for U L. To obtain bounds on M Z 3, we use updated experimental and theoretical values for the input parameters as shown in Table 5, where the quark masses are given at Z-pole. The results are CONCLUSIONS This model has the particular feature that, notwithstanding two families of quarks transform differently under the SU(4) L group, the three families have the same hypercharge X with respect to the U(1) X group. Therefore, the couplings of the fermion fields to the neutral currents Z 1 and Z 2 are family universal. Thus, the allowed region in the parameter space (θ − M Z 2 ) is: M Z 2 >0.89 TeV and − ≤ θ ≤ Additionally, FCNC present for this Model in the left-handed couplings of ordinary quarks to the Z 3 gauge boson allows us to conclude that the strongest constraint on M Z 3 comes from the system and turns to be M Z 3 > 6.65 TeV. These values show that the model studied here could be tested at the LHC facility.