Family dependence in 331 models

Abstract

Using experimental results at the Z-pole, and considering the ansatz of Matsuda as an specific texture for the quark mass matrices, we perform a chi2 fit at 95% CL to obtain family-dependent bounds to Z' mass and Z-Z' mixing angle in the framework of the main versions of 331 models. The allowed regions depend on the assignment of the physical quark families into different representations that cancel anomalies. Allowed regions on other possible 331 models are also obtained.

Standart model; Gauge bosons

POSTERS

Family dependence in 331 models

R. Martínez; F. Ochoa

Universidad Nacional de Colombia, Ciudad Universitaria, Carrera 30, No. 45-03, Edificio 405 Oficina 218, Bogota, Colombia

ABSTRACT

Using experimental results at the Z-pole, and considering the ansatz of Matsuda as an specific texture for the quark mass matrices, we perform a c² fit at 95% CL to obtain family-dependent bounds to Z' mass and Z-Z' mixing angle in the framework of the main versions of 331 models. The allowed regions depend on the assignment of the physical quark families into different representations that cancel anomalies. Allowed regions on other possible 331 models are also obtained.

Keywords: Standart model; Gauge bosons

I. INTRODUCTION

In most of extensions of the standard model (SM), new massive and neutral gauge bosons, called Z', are predicted. The presence of this boson is sensitive to experimental observations at low and high energies, and will be of great interest in the next generation of colliders (LHC, ILC, TESLA) [1]. In particular, it is possible to study some phenomenological features associated to Z' through models with gauge symmetry SU(3)_c Ä SU(3)_L Ä U(1)_X, also called 331 models. These models arise as an interesting alternative to explain the origin of generations [2-4], where the three families are required in order to cancel chiral anomalies. The electric charge is defined as a linear combination of the diagonal generators of the group

where b allow classify the different 331 models. The two main versions corresponds to b = - [2] and b = - [3]. In the quark sector, each 331-family can be assigned in 3 different ways. Therefore, in a phenomenological analysis, the allowed region associated with the Z-Z' mixing angle and the physical mass M_Z' of Z' will depend on the family assignment. We adopt the texture structure proposed in ref. [5] in order to obtain allowed regions for the Z-Z' mixing angle, the mass of the Z' boson and the values of b for 3 different assignments of the quark families in mass eigenstates. The above analysis is performed through a c² statistics at 95% CL.

II. THE QUARK AND NEUTRAL GAUGE SPECTRUM

The fermion representations under SU(3)_c Ä SU(3)_L Ä U(1)_X read

The second equality comes from the branching rules SU(2)_L Ì SU(3)_L. The X_p refers to the quantum number associated with U(1)_X. The generator of U(1)_X conmute with the matrices of SU(3)_L; hence, it should take the form X_pI_3×3, the value of X_p is related with the representations of SU(3)_L and the anomalies cancellation. On the other hand, this fermionic content shows that the left-handed multiplets lie in either the 3 or 3* representations. In the framework of three family model, we recognize 3 different possibilities to assign the physical quarks in each family representation as shown in Table I in weak eigenstates.

On the other hand, we obtain the following mass eigenstates associated to the neutral gauge spectrum

where a small mixing angle q between the neutral currents Z_m and appears, with

where the Weinberg angle is defined as S_W = g'/ and g, g' correspond to the coupling constants of the groups SU(3)_L and U(1)_X, respectively.

III. THE NEUTRAL GAUGE COUPLINGS

The neutral Lagrangian associated to the SM-boson Z_1µ in the weak basis of the SM quarks U⁰ = (u⁰,c⁰,t⁰)^T and D⁰ = (d⁰,s⁰,b⁰)^T, is

The couplings of the Z_1µ have the same form as the SM couplings, where the usual vector and axial vector couplings are replaced by , where

which corresponds to the correction due to the small Z_m - mixing angle q, the coupling constants, and r = (A,B,C) each representation from Table I. The couplings for leptons are

while for the quark couplings we get

with q = U⁰,D⁰, M = 1/diag[1 + /, 1 + /, -1 + /] and where we define for each representation from table I

We will consider linear combinations among the three families to obtain couplings in mass eigenstates by adopting an ansatz on the texture of the quark mass matrix in agreement with the CKM matrix. We take the structure of mass matrix suggested in ref. [5] given by , with P_q = diag(exp(a₁),exp(a₂),exp(a₃)), and where M is written in the basis (u⁰,c⁰,t⁰) or (d⁰,s⁰,b⁰) as

For up-type quarks, A_U = , B_U = (m_t+m_c-m_u)/2 and C_U = (m_t-m_c-m_u)/2; for down-type quarks A_D = , B_D = (m_b+m_s-m_d)/2 and C_D = -(m_b-m_s+m_d)/2. The above ansatz is diagonalized by [5]

with c = , s = , c' = and s' = . The complex matrix is then diagonalized by the bi-unitary transformation with U_Lq = and U_Rq = P_qR_q. Then, the diagonal couplings in Eq. (5) in mass eigenstates have terms of the form where any effect of the CP violating phases P disappears. Thus, we can write the Eq. (5) in mass eigenstates as

where the couplings of quarks depend on the rotation matrix, with

We obtain flavor changing couplings in the quark sector due to the family dependence shown by . All the analytical parameters (O) at the Z pole have the same SM-form (O_SM) but with small correction factors (dO) which are expressed in terms of the coupling corrections that depend on the family assignment from table I. Each observable predicted by the 331 model takes the form O₃₃₁ = O_SM(1 + dO) . For the analysis, we take into account the observables at the Z pole shown in Table II from ref. [7], including data from atomic parity violation. The 331 corrections are

where

IV. PRECISION FIT TO THE Z-POLE OBSERVABLES

With the expressions for the Z-pole observables and the experimental data from the LEP [7], we perform a c² fit for each representation A,B and C at 95% CL and 3 d.o.f, where the free quantities S_q, and b can be constrained at the Z₁ peak. Figs. 1 and 2 show the allowed region for the main versions of 331 models corresponding to b = - [2] and b = - [3], respectively, which exhibits family-dependent regions. First of all, we note that A and B representations display broader mixing angles than representation C. For the model b = -, we see that the lowest bound in the value is about 4000 GeV for A and B cases, while for the C representation this bound increses to 10000 GeV, showing an strong dependence on the family representation. The model b = - exhibits a lower bound in the Z₂ mass, where the lowest bound is about 1400 GeV for A and B regions, and 2100 GeV for the C spectrum. We also see that the mixing angle in this model is smaller by about one order of magnitude than the angles predicted by the b = - model.

On the other hand, we get the best allowed region in the plane S_q - b for two different values of . The lowest bound that display an allowed region is about 1200 GeV, which appears only for the C assignments such as Fig. 3 shows. We can see in this case that the usual 331 models are excluded, and only those 331 models with 1.1 b 1.75 are allowed with small mixing angles (S_q ~ 10^-4). Fig. 4 display the allowed region in the - b plane for a small mixing angle (S_q = -0.0002). It is noted that the smallest bounds in is obtained for b > 0.

[1] S. Godfrey arXiv: hep-ph/0201093; G. Weiglein et. al., arXiv: hep-ph/0410364; R.D. Heuer et. al, arXiv: hep-ph/0106315.

[3] R. Foot, H.N. Long, and T.A. Tran, Phys. Rev. D 50, R34 (1994).

[4] L.A. Sánchez, W.A. Ponce, and R. Martínez, Phys. Rev. D 64, 075013 (2001); Rodolfo A. Diaz, R. Martinez, and F. Ochoa, Phys. Rev. D 69, 095009 (2004); Rodolfo A. Diaz, R. Martinez, and F. Ochoa, Phys. Rev. D 72, 035018 (2005).

[5] K. Matsuda, H. Nishiura, Phys. Rev. D 69, 053005 (2004).

[6] Fredy Ochoa and R. Martinez, Phys. Rev. D 72, 035010 (2005).

[7] S. Eidelman et. al. Particle Data Group, Phys. Lett. B 592, 120 (2004); S. Schael et. al. arXiv: hep-ph/0509008 (submitted to Physics Reports)

Received on 16 October, 2006

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• Rodolfo A. Diaz, R. Martinez, and F. Ochoa, Phys. Rev. D 69, 095009 (2004);
• Rodolfo A. Diaz, R. Martinez, and F. Ochoa, Phys. Rev. D 72, 035018 (2005).
• [5] K. Matsuda, H. Nishiura, Phys. Rev. D 69, 053005 (2004).
• [6] Fredy Ochoa and R. Martinez, Phys. Rev. D 72, 035010 (2005).
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Publication Dates

• Publication in this collection
  13 Aug 2007
• Date of issue
  July 2007

History

• Received
  16 Oct 2006