3.2.A simulation of the dark matter distribution in the universe13.6 billion years ago.

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... this reason, most experts think dark matter to be ubiquitous in the universe and to have had a strong influence on its structure and evolution. Dark matter is called dark because it does not appear to interact with observable electromagnetic radiation, such as light, and is thus invisible to the entire electromagnetic spectrum, making it extremely difficult to detect using usual astronomical equipment Fig.2.3.1.Dark matter map for a patch of sky based on gravitational lensing analysis [18]. ...

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... 2.3.1.In order to explain physical nature of dark matter sector we assume that main part of dark matter,i.e., 23% 4. 6% 18% (see Fig.2.3.3) formed by supermassive ghost particles vith masess such that mc 2 . ...

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... us consider now the one-loop divergent diagrams in the SM. Besides the familiar diagrams in QED and QCD discussed below in section IV.5 one has the diagrams presented in Fig.2.3.5. The diagrams containing the goldstone bosons are omitted. ...

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... we show only the results for the renormalization constants of the fields and the coupling constants. They have the form (for the gauge fields we use the Feynman gauge) Fig.2.3.5. Fig.2.3.5.Some divergent one-loop diagrams in the SM. ...

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... have the form (for the gauge fields we use the Feynman gauge) Fig.2.3.5. Fig.2.3.5.Some divergent one-loop diagrams in the SM. The dotted line denotes the Higgs field, the solid line -the quark and lepton fields, and the wavy line -the gauge fields Remark 2.3.3.In standard sector the renormalization constants of the fields and the coupling constants reads (see Sect.IV.1-IV.8): ...

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... find the renormalization of the mass itself, one should know how the v.e.v. is renormalized or find explicitly the mass counter-term from Feynman diagrams. In this case, one has also to take into account the tad-pole diagrams shown in Fig.2.3.5, including the diagrams with goldstone bosons. For illustration we present the renormalization constant of the b-quark mass in the SM ...

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... vertex: Here one also has only one diagram but the external momenta can be adjusted in several ways (see Fig.4.2.2). As a result the total contribution to the vertex function consists of three parts Is, t, u I 1 s I 1 t I 1 u, where we introduced the commonly accepted notation for the Mandelstam variables (we assume here that the momenta p 1 and p 2 are incoming and the momenta p 3 and p 4 are outgoing) s p 1 p 2 2 p 3 p 4 2 , t p 1 p 3 2 p 2 p 4 2 , u p 1 p 4 2 p 2 p 3 2 , and the integral equals Fig.4 which holds in arbitrary noncritical dimension D and any power of the propagator as follows [32]: ...

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... vertex: In the given order there are two diagrams (remind that in the massless case the tad-poles equal to zero) shown in Fig.4.3.2. ...

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... us to catalog three different types of divergent structures involving ghosts. These are illustrated in Fig.5.1.2. Each of the three types has degree of divergence D 1 2n E . ...

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... only in the replacement of the factors of 2 k 4 in the graviton propagator by 4 k 6 . This change brings about a reduction in the degree of divergence of those parts of diagrams which depend on the parameter . The degree of divergence is reduced by 2 for each factor of , so that once again all three types of diagram involving ghosts shown in Fig. 6.1.2 are convergent. The renormalization equation then implies that all the divergences in 6 div n are gauge ...