Decays Z → γγ and Z → gg in the Standard Model Extension

Abstract

The Z → γγ and Z → gg decays are studied in the context of the renormalizable version of the Standard Model Extension. The CP T -oddψγ 5 / bψ bilinear interaction, which involves the constant background field bα and which has been a subject of interest in literature, is considered. It is shown that the Z → γγ and Z → gg decays, which are strictly zero in the standard model, can be generated radiatively at the one-loop level. It is found that these decays are gauge invariant and free of ultraviolet divergences, and that the corresponding decay widths only depend on the spatial component of the background field b. IntroductionThe trilinear V V V (V = γ, Z) and quartic V V V V neutral couplings are quite suppressed, as they first arise at the one-loop level a in the Standard Model (SM) and in most of its renormalizable extensions. Since new physics effects could be more apparent in those processes which are quite suppressed or forbidden in the SM, these couplings constitute a good mechanism for investigating possible signals of physics beyond the Fermi scale. The charged counterparts W W V and W W V V , of these neutral couplings, arise at the tree level and are related by gauge invariance in the sense that they are simultaneously induced by1, 2 However, this type of gauge connection does not exist between the V V V and V V V V couplings.3, 4 While the V V V V couplings receive one-loop contributions from both fermionic and bosonic particles b , the V V V ones are exclusively generated by fermionic triangles.38-40 Intimately related with the absence of a gauge link between the V V V and V V V V couplings is the fact that none of the V V V vertices reflects the non-Abelian nature of the electroweak group, as the Yang-Mills sector neither induces these couplings at the tree-level nor contribute to them at the one-loop order. This is in contrast with the quartic V V V V couplings, which are generated by the Yang-Mills sector at the one-loop level.5-37 The trilinear V V V couplings are indeed severely restricted by the Bose and Lorentz symmetries. It turns out that if both Bose symmetry and Lorentz invariance are simultaneously respected, the V V V coupling vanishes when the three bosons are real, though they can exist when at least one of the particles is off-shell.38-40 As a consequence, the Z → γγ decay is forbidden. This result is known as the Landau-Yang's theorem, 41,42 which establishes that a vector particle cannot decay into two massless vector particles. This means that the Z decay into two gluons is also forbidden c . This theorem invokes Bose symmetry and rotational invariance arguments. Nevertheless, as soon as this requirement is relaxed, the V V V vertex with the three bosons on-shell can exist. In particular, the rare decays of the Z gauge boson Z → γγ and Z → gg are allowed.In this paper, we are interested in studying the decays Z → γγ and Z → gg in the context of the minimal Lorentz-and CP T -violating Standard Model Extension 45,46 (SME), which is a renormalizable extension of the SM that incorporat...

General CPT-even dimension-five nonminimal couplings between fermions and photons yielding EDM and MDM

“…The investigation of Lorentz symmetry violation is indeed a rich line of research, much developed in the framework of the Standard Model extension (SME) [21][22][23][24][25][26], whose developments have scrutinized the Lorentzviolating effects in distinct physical systems and served to state tight upper bounds on the LV coefficients, including photon-fermion interactions [27] and electroweak processes [28], [29]. Beyond the minimal SME, there is its nonminimal extension encompassing nonminimal couplings with higher-order derivatives [30].…”

Constraining CPT -odd nonminimal interactions in the electroweak sector

“…Some works also examined the possibility of LV electroweak terms to make feasible forbidden processes (Z 0 −→ γ + γ) [19] or modify the reactions such as γ + e → W + ν e , γ + γ → W + W [20]. Lepton flavor violating decays triggered by renormalizable and nonrenormalizable (dimension five) terms belonging to the Higgs sector were recently considered as well [21].…”

Bounds on Lorentz-violating Yukawa couplings via lepton electromagnetic moments

“…A couple decades ago, an effective-Lagrangian description of Lorentz-symmetry nonconservation, known as the Lorentz-and CPT-violating SM Extension (SME), was devised [12,13]. The SME has since become a useful tool to comprehensively study this sort of new physics 1 , which induces unconventional phenomena such as vacuum birefringence [15,16], vacuum Čerenkov radiation [17][18][19][20][21][22], oscillations of massless neutrinos [24][25][26][27], exotic electromagnetic properties of SM particles [28,29], and violations of standard theorems [30,31]. The dynamic variables of the SME and its gauge-symmetry group are the same as those of the sole SM, the key element being a large set of coefficients, characterized by fullycontracted spacetime indices within Lagrangian terms and which transform as tensors under observer Lorentz transformations [12,13], thus implying that Lorentzviolating physics is observer independent.…”

“…[10], which, moreover, is updated every year. Lorentz-violating Lagrangian terms constituting the SME are classified into two types, according to whether they are power-counting renormalizable or not [16,28,29,[31][32][33][34][35][36]. The full set of renormalizable SME terms define the so-called minimal SME (mSME).…”