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Register a new userThree-loop calculations in non-Abelian gauge theories
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A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-Abelian gauge theories with fermions in the three-loop approximation. A three-loop expression for the effective charge of QCD is given. Charge renormalization effects in the SU(4)-supersymmetric gauge model is shown to vanish at this level. A complete list of required formulas is given in Appendix. The above-mentioned results of three-loop calculations have been published by the present authors (with A.Yu., Zharkov and L.V., Avdeev) in 1980 in Physics Letters B. The present text, which treats the subject in more details and contains a lot of calculational techniques, has also been published in 1980 as the JINR Communication E2-80-483.
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The infrared divergences of QCD scattering amplitudes can be derived from an anomalous dimension Gamma, which is a matrix in color space and depends on the momenta and masses of the external partons. It has recently been shown that in cases where there are at least two massive partons involved in the scattering process, starting at two-loop order Gamma receives contributions involving color and momentum correlations between three (and more) partons. The three-parton correlations can be described by two universal functions F_1 and f_2. In this paper these functions are calculated at two-loop order in closed analytic form and their properties are studied in detail. Both functions are found to be suppressed like O(m^4/s^2) in the limit of small parton masses, in accordance with mass factorization theorems proposed in the literature. On the other hand, both functions are O(1) and even diverge logarithmically near the threshold for pair production of two heavy particles. As an application, we calculate the infrared poles in the q qbar --> t tbar and g g --> t tbar scattering amplitudes at two-loop order.
We construct chiral theories with the smallest number $n_chi$ of Weyl fermions that form an anomaly-free set under various Abelian gauge groups. For the $U(1)$ group, where $n_chi = 5$, we show that the general solution to the anomaly equations is a set of charges given by cubic polynomials in three integer parameters. For the $U(1) times U(1)$ gauge group we find $n_chi = 6$, and derive the general solution to the anomaly equations, in terms of 6 parameters. For $U(1) times U(1) times U(1)$ we show that $n_chi = 8$, and present some families of solutions. These chiral gauge theories have potential applications to dark matter models, right-handed neutrino interactions, and other extensions of the Standard Model. As an example, we present a simple dark sector with a natural mass hierarchy between three dark matter components.
Using elementary considerations of Lorentz invariance, Bose symmetry and BRST invariance, we argue why the decay of a massive color-octet vector state into a pair of on-shell massless gluons is possible in a non-Abelian SU(N) Yang-Mills theory, we constrain the form of the amplitude of the process and offer a simple understanding of these results in terms of effective-action operators.
We investigate a gauge theory realization of non-Abelian discrete flavor symmetries and apply the gauge enhancement mechanism in heterotic orbifold models to field-theoretical model building. Several phenomenologically interesting non-Abelian discrete symmetries are realized effectively from a $U(1)$ gauge theory with a permutation symmetry. We also construct a concrete model for the lepton sector based on a $U(1)^2 rtimes S_3$ symmetry.
We study the solution to the Slavnov-Taylor (ST) identities in spontaneously broken effective gauge theories for a non-Abelian gauge group. The procedure to extract the $beta$-functions of the theory in the presence of (generalized) non-polynomial field redefinitions is elucidated.
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