B physics constraints on a flavor symmetric scalar model to account for the tt¯ asymmetry and Wjj excess at CDF

Recently Nelson et al. proposed an interesting flavor symmetric model to account for the top quark forward-backward asymmetry and the dijet anomaly at CDF simultaneously with just three parameters: a coupling constant of order one, and two scalar masses of 160 GeV and 220 GeV. However these fiducial values of the parameters lead to the branching ratio of a almost pure penguin B→πK decay about one hundred times larger than the experimental results. Consider also the precision electroweak constraints, the scalar masses should be at least around 500 GeV. Actually with the coupling constant larger than one, it is impossible to explain either of the two CDF measurements consistently in this model. But one may raise the charged scalar mass to, for example, 250 GeV and reduce the coupling strength to 0.6 to meet the B physics constraints. With this parameter set, the Wjj cross section is found to be in the right range. But due to the scalar mass splitting, its correction to T-parameter is about 3σ away from the precision electroweak constraints. In addition, the top quark forward-backward asymmetry should be well below 0.1 with this small coupling constant.