Supergroup BF action for supergravity

General relativity can be formulated as a SU(2) BF-theory with constraints, as has been shown, by Pleba\'nski. The cosmological constant term can be obtained from the constraint term, following from the consistency of the equations of motion, as recently shown by Krasnov. We consider an $OSp(2|1)$ invariant, supergravity extension of this theory, for which the consistency of the equations of motion and the constraints contribute as well to the cosmological constant terms of Townsend's supergravity. The Kalb-Ramond invariance is shortly discussed.Comment: 14 page

Top quark forward-backward asymmetry from the 3−3−13-3-1 model

The forward-backward asymmetry $A_{FB}$ in top quark pair production, measured at the Tevatron, is probably related to the contribution of new particles. The Tevatron result is more than a $2\sigma$ deviation from the standard model prediction and motivates the application of alternative models introducing new states. However, as the standard model predictions for the total cross section $\sigma_{tt}$ and invariant mass distribution $M_{tt}$ for this process are in good agreement with experiments, any alternative model must reproduce these predictions. These models can be placed into two categories: One introduces the s-channel exchange of new vector bosons with chiral couplings to the light quarks and to the top quark and another relies on the t-channel exchange of particles with large flavor-violating couplings in the quark sector. In this work we employ a model which introduces both s- and t-channel nonstandard contributions for the top quark pair production in proton antiproton collisions. We use the minimal version of the $SU(3)_C \otimes SU(3)_L \otimes U (1)_X$ model (3-3-1 model) that predicts the existence of a new neutral gauge boson, called $Z^\prime$. This gauge boson has both flavor-changing couplings to up and top quarks and chiral coupling to the light quarks and to the top quark. This very peculiar model coupling can correct the $A_{FB}$ for top quark pair production for two ranges of $Z^\prime$ mass while leading to cross section and invariant mass distribution quite similar to the standard model ones. This result reinforces the role of the 3-3-1 model for any new physics effect.Comment: 12 pages, 4 figures, 2 table

Quantum Backflow States from Eigenstates of the Regularized Current Operator

We present an exhaustive class of states with quantum backflow -- the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. They are characterized by a general function of momenta subject to very weak conditions. Such a family of states is of interest in the light of a recent experimental proposal to measure backflow. We find one particularly simple state which has surprisingly large backflow -- about 41 percent of the lower bound on flux derived by Bracken and Melloy. We study the eigenstates of a regularized current operator and we show how some of these states, in a certain limit, lead to our class of backflow states. This limit also clarifies the correspondence between the spectrum of the regularized current operator, which has just two non-zero eigenvalues in our chosen regularization, and the usual current operator.Comment: 16 pages, 2 figure