We perform a comprehensive study of the allowed range for the Tevatron t tbar forward-backward asymmetries in six representative new physics models: a flavour-changing Z' boson, a scalar isodoublet, a W' boson, a heavy axigluon, a colour-triplet and a colour-sextet scalar. We devote special attention to the constraints from the t tbar tail at LHC on the parameter space, which will be dramatic if the measurements agree with the SM prediction, specially for Z' and W' bosons. We also study the predictions for the charge asymmetries at LHC and compare several proposed definitions.This work has been partially supported by projects FPA2010-17915 (MICINN), FQM 101 and FQM 437 (Junta de Andalucía) and CERN/FP/116397/2010 (FCT)
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