Invitation to composition

In 1963 [Ann. of Math. {\bf 78}, 267-288], Gerstenhaber invented a \emph{comp(osition)} calculus in the Hochschild complex of an associative algebra. In this paper, the first steps of the Gerstenhaber theory are exposed in an abstract (comp system) setting. In particular, as in the Hochschild complex, a graded Lie algebra and a pre-coboundary operator can be associated to every comp system. A derivation deviation of the pre-coboundary operator over the total composition is calculated in two ways, (the long) one of which is essentially new and can be seen as an example and elaboration of the auxiliary variables method proposed by Gerstenhaber in the early days of the comp calculus.Comment: 18 pages, AMSLaTe

Light Colored Scalar as Messenger of Up-Quark Flavor Dynamics in Grand Unified Theories

The measured forward-backward asymmetry in the t tbar production at the Tevatron might be explained by the additional exchange of a colored weak singlet scalar. Such state appears in some of the grand unified theories and its interactions with the up-quarks are purely antisymmetric in flavor space. We systematically investigate the resulting impact on charm and top quark physics. The constraints on the relevant Yukawa couplings come from the experimentally measured observables related to D0--D0bar oscillations, as well as di-jet and single top production measurements at the Tevatron. After fully constraining the relevant Yukawa couplings, we predict possible signatures of this model in rare top quark decays. In a class of grand unified models we demonstrate how the obtained information enables to constrain the Yukawa couplings of the up-quarks at very high energy scale.Comment: 13 pages, 11 figures, version as published in PR