Contributions to $$ZZV^*$$ ($$V=\gamma ,Z,Z'$$) couplings from CP violating flavor changing couplings

Abstract

The one-loop contributions to the trilinear neutral gauge boson couplings $$ZZV^*$$ Z Z V ∗ ($$V=\gamma ,Z,Z'$$ V = γ , Z , Z ′ ), parametrized in terms of one CP-conserving $$f_5^{V}$$ f 5 V and one CP-violating $$f_4^{V}$$ f 4 V form factors, are calculated in models with CP-violating flavor changing neutral current couplings mediated by the Z gauge boson and an extra neutral gauge boson $$Z'$$ Z ′ . Analytical results are presented in terms of Passarino-Veltman scalar functions. Constraints on the vector and axial couplings of the Z gauge boson $$\left| g_{{VZ}}^{tu}\right| < 0.0096$$ g VZ tu < 0.0096 and $$\left| g_{{VZ}}^{tc}\right| <0.011$$ g VZ tc < 0.011 are obtained from the current experimental data on the $$t\rightarrow Z q$$ t → Z q decays. It is found that in the case of the $$ZZ\gamma ^*$$ Z Z γ ∗ vertex the only non-vanishing form factor is $$f_5^{\gamma }$$ f 5 γ , which can be of the order of $$10^{-3}$$ 10 - 3 , whereas for the $$ZZZ^*$$ Z Z Z ∗ vertex both form factors $$f_5^{Z}$$ f 5 Z and $$f_4^{Z}$$ f 4 Z are non-vanishing and can be of the order of $$10^{-6}$$ 10 - 6 and $$10^{-5}$$ 10 - 5 , respectively. Our estimates for $$f_5^{\gamma }$$ f 5 γ and $$f_5^{Z}$$ f 5 Z are smaller than those predicted by the standard model, where $$f_4^{Z}$$ f 4 Z is absent up to the one loop level. We also estimate the $$ZZ{Z'}^{*}$$ Z Z Z ′ ∗ form factors arising from both diagonal and non-diagonal $$Z'$$ Z ′ couplings within a few extension models. It is found that in the diagonal case $$f_{5}^{Z'}$$ f 5 Z ′ is the only non-vanishing form factor and its real and imaginary parts can be of the order of $$10^{-1}$$ 10 - 1 –$$10^{-2}$$ 10 - 2 and $$ 10^{-2}$$ 10 - 2 –$$10^{-3}$$ 10 - 3 , respectively, with the dominant contributions arising from the light quarks and leptons. In the non-diagonal case $$f_{5}^{Z^\prime }$$ f 5 Z ′ can be of the order of $$10^{-4}$$ 10 - 4 , whereas $$f_4^{Z'}$$ f 4 Z ′ can reach values as large as $$10^{-7}$$ 10 - 7 –$$10^{-8}$$ 10 - 8 , with the largest contributions arising from the $$Z'tq$$ Z ′ t q couplings.

Non-diagonal contributions to $ZγV^\ast$ vertex and bounds on $Z\overline{t}q$ couplings

“…There are two kinds of TNGBCs: ZZV * and ZγV * (V = γ, Z), the former has been recently studied in Ref. [18], where new contributions to the CP -conserving form factors are induced. Also, new sources of CP violation through FCNCs mediated by the Z and a Z bosons can be found.…”

“…On the other hand, it has been pointed out that at low energies the real parts could be the dominant contribution. For non-diagonal contributions to TNGBCs, it has been also noted that the absorptive part could be bigger than the real one [5,18]. Moreover, this imaginary contribution is not exclusive to these vertexes as it is been founded in the Chromomagnetic (CMDM) and Chromoelectric (CEDM) dipole moments, where the gluon is off-shell [71,72].…”

“…Thus, corrections to TNGBCs from beyond SM (BSM) theories will play an important role, since they could be tested soon at the LHC. In the SM, a vertex with three neutral gauge bosons can only exist if at least one of them is off-shell (because of Bose statistics) and they are induced through dimension-six and dimension-eight operators [5,[7][8][9], which give rise to CP -conserving and CP -violating form factors, where the former is generated at the one-loop level in the SM, whereas the latter could be non-vanishing at the same level in models of new physics [5,18]. Therefore, new sources of CP violation are possible.…”

“…According to Sakharov's conditions [10], the violation of CP symmetry is necessary to explain the invariance between matter and antimatter in the universe. The TNGBCs have been studied within a lot of extensions of the SM, such as minimal supersymmetric standard model (MSSM) [5,6,11], the CPviolating two-Higgs doublet model (2HDM) [12][13][14], models with axial and vector fermion couplings [12], models with extended scalar sectors [15,16], the effective Lagrangian approach [7], models with CP violation [17] and models with flavor changing neutral currents (FCNCs) [18]. The effects of the TNGBCs in BSM theories at future colliders have been also studied very recently [19][20][21][22][23][24][25][26], whereas the first experimental results were obtained at the LEP [27][28][29] and the Tevatron [30][31][32] colliders.…”

“…New contributions to TNGBCs could arise from FCNCs couplings mediated by the Z gauge boson and those where there is mixing between the top quark and an up-type quark are of special interest [18]. Nevertheless, in the SM the channel t → Bq, where B = Z, γ, g and q = u, c can not be generated at tree level.…”