B physics constraints on a flavor symmetric scalar model to account for the ttbar 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 ->pi K 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 3 sigma 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.

The CDF collaboration has recently updated the measurements on the forward-backward asymmetry in top quark pair production with a larger data sample about 5.3 fb −1 [1,2].
Interestingly, deviations from the Standard Model (SM) predictions are observed in the total forward-backward asymmetry both in the semi-leptonic tt data and in the di-lepton channel.
In addition, A distributional measurement found that A tt F B (M tt > 450 GeV) = 0.475 ± 0.112 in the tt rest frame, which deviates from the QCD correction prediction 0.088 ± 0.013 by 3.5 σ. The CDF collaboration has also reported another 3.2 σ anomaly in the 120 − 160 GeV range of the invariant dijet mass distribution in association with a W boson [3]. A flavor symmetric model was proposed in [4] to explain simultaneously the tt asymmetry and Wjj excess at CDF 1 . A Z 3 triplet of complex scalar fields Φ = (Φ 1 , Φ 2 , Φ 3 ) is introduced in [4]. These color-singlet weak-doublet scalars respect the flavor symmetry: where q Li and u Ri have charge +1 under U(1) q Li and U(1) u Ri , respectively, while d R is in a fundamental representation of U(3). This flavor symmetry is also preserved in the SM without Yukawa interactions.
In this model the interaction of the scalars Φ with the SM quarks are completely determined by the flavor symmetry with a universal coupling strength. The W jj anomaly can then be interpreted as us → W + Φ 0 3 via a s-channel Φ + 3 exchange, and Φ 0 3 decays subsequently to a jet pair with its mass to be around 160 GeV. The top quark forward-backward asymmetry can be explained by uū → tt via a t-channel Φ 0 2 exchange and dd → tt via a tchannel Φ + 2 exchange. At first glance, this seems to be in contradiction with the observation of [7] that t-channel exchange of a color-singlet scalar has great difficulty to produce a large positive contribution to the top quark forward-backward asymmetry. However a closer look at Fig. 2 of [7] reveals that there does have a narrow window with the scalar mass lighter than 250 GeV.
However this flavor symmetry model also contributes to hadronic b decays. Although there is no new CP phase introduced, we will show in the following that the effective operator (b L u R )(u R s L ) via an exchange of such a light Φ is constrained severely by the penguin dominant processes, such as B → πK decays 2 .
In this flavor symmetry model, the color-singlet weak-doublet scalars Φ are charged −1/2 under U(1) Y and singlets under U(3) d R . The interaction between Φ i and the SM quarks [4] is completely determined by the flavor symmetry in which Φ i (i = 1, 2, 3) are charged as , and charged as Then the only free parameters are the coupling constant λ and the scalar masses m Φ 0 and m Φ − .
However in the mass basis, Eq.
(2) also generates effective four fermion operators, among which contains As noticed in [4], this operator contributes to the charmless process b → sūu in comparison to the relevant effective Hamiltonian of the SM (where electroweak penguin operators have been neglected) [10] with 2 The implications of rare B decays on t-channel models to account for the Tevatron top-pair asymmetry have been discussed recently in [8]. 3 The same-sign tops production is extremely suppressed in this model. Otherwise such light scalars might be severely constrained, see e.g. [9].
Since Eq. (5) is obtained at tree level, we will also consider the Wilson coefficients in the SM at leading order. Matching the effective operators to the full theory at µ = M W , one finds C 1 (M W ) = 1 and other Wilson coefficients to be zero at leader order in the SM. But the flavor symmetry model contributes to C 6 as Running the scale down from M W to m b , one finds in the SM But when the new scalar contributions are included, the Wilson coefficients are changed to be One may easily notice that C 6 (m b ) is surprisingly large in this flavor symmetry model.
Even considering the theoretical uncertainties on hadronic B decays, it will lead to too large branching ratios on the penguin dominant decays, such as B → πK channels as we will show immediately.
For charmless B decays, there are three factorization approaches being widely used: QCD factorization [11][12][13], the perturbative QCD method (PQCD) [14][15][16] and soft collinear effective theory (SCET) [17][18][19]. Here we will adopt QCD factorization method. Notice that the new physics amplitude is calculated at tree level, correspondingly the Wilson coefficients are calculated at leading logarithm. To be consistent, the decay amplitudes of QCD factorization are also evaluated at leading order of α s . Let's consider the almost pure penguin process B + → π + K 0 decay. Taking f K = 160 MeV, the form factor F Bπ 0 (0) = 0.26 [20,21], the current quark mass m s (2GeV) = 100 MeV [22] and the relevant CKM parameters [23] A = 0.812, λ = 0.2254, we obtain which is about one hundred times larger than the experimental measurement (23.1 ± 1.0) × 10 −6 [22]. Therefore the fiducial values of λ = 1.4, m Φ − = 220 GeV taken by Nelson et al. In Fig. 1, we show the branching ratio of B + → π + K 0 decay as a function of m Φ − with the coupling strength λ fixed. It indicates that the charged scalars should be heavier than about 540 GeV to be consistent with the charmless B decays. Noticed that the leading order SM prediction is about half less than the experimental measurements, as shown in Fig. 1. This is because next-to-leading order amplitudes are not small in QCD factorization method, especially for chirally enhanced power corrections and annihilation diagrams (see, e.g., [13,[24][25][26]). But for the purpose of this paper, it should be enough to be confined at leading order.
The CDF dijet anomaly was explained in this flavor symmetry model by the process us → W − Φ 0 3 via s-channel Φ − 3 exchange, with the cross section to be about 2 pb. Now to satisfy B physics constraints, the charged scalar masses have to be raised from 220 GeV to around 540 GeV. As a result, the corresponding cross section must be well below 1 pb, which is too small to account for the CDF dijet excess. In addition, keeping λ = 1.4 and m Φ 0 = 160 GeV unchanged while rasing the mass of charged scalars to m Φ − = 540 GeV, one might worry about its correction to the electroweak parameter [4] αT = 3 where m H,ref denotes the reference value of the Higgs mass. This means, for the SM Higgs as heavy as 1 TeV, the precision electroweak constraint on T parameter would be around T ≃ 0.40 ± 0.08, which is consistent with the flavor symmetric model with m Φ − = 250 GeV.
In any case, it is unlikely for the charged scalar mass in this model to be heavier than 250 GeV. One may observe from Fig. 2 that, taking m Φ − = 250 GeV, λ should be around 0.6 to satisfy the restriction of B + → π + K 0 decay. Notice that it was shown in [4] that in this model the top quark forward-backward asymmetry A tt ≃ 0.13 for M tt > 450 GeV with λ = 1.4. It is then clear that this asymmetry must be well below 0.1 if the coupling constant λ is lowered to around 0.6. Therefore it should be really hard, if not impossible, to explain the measured large forward-backward asymmetry of produced top pair under this circumstance.
As to the Wjj anomaly, the resonant productionūs → Φ − 3 which subsequently decays to  2. Branching ratio of B + → π + K 0 decay as a function of the coupling strength λ, with the charged and neutral scalar masses taken at 250 GeV and 160 GeV, respectively. The meaning of the lines is the same as in Fig. 1.
with the phase factor λ(x, y, z) = x 2 + y 2 + z 2 − 2(xy + xz + yz). Correspondingly, the Wjj cross section is found to be 3.0 pb for λ = 0.6. Actually, the Wjj cross section from resonant Φ − 3 production is not very sensitive to the value of λ, because the total width of Φ − 3 also changes with λ. For instance, the cross section is calculated to be 2.5 pb with even smaller λ = 0.4.
In summary, we consider the constraints of charmless B decays on a flavor symmetric scalar model proposed in [4]. The color-singlet weak-doublet scalars are introduced in the model which respects the flavor symmetry of It was shown in [4] that the top quark forward-backward asymmetry and the dijet excess at CDF could be explained simultaneously with the parameters chosen as λ = 1.4, m Φ 0 = 160 GeV and m Φ − = 220 GeV. However the flavor symmetry of the scalars also contributes to b → sūu decays. With the above fiducial values of the parameters, the pure penguin decay B + → π + K 0 is predicted to have a branching ratio about one hundred times larger than the experimental results. To avoid this constraint, the charged scalars should be heavier than around 540 GeV with λ = 1.4 fixed. As a result, the production cross section of dijet plus a W boson would be too small to account for the CDF dijet excess. Furthermore, the precision electroweak constraints force the neutral scalar masses to be also around 500 GeV.
Then it also becomes hard for this model to account for the forward-backward asymmetry in top quark pair production.
Another possibility is to raise the charged scalar mass so that Φ − 3 → Φ 0 3 W − decay channel is allowed kinematically. In this scenario the Wjj cross section is enhanced due to the resonant production of Φ − 3 so that the coupling constant λ may be lowered to evade the B physics constraint. Specifically, one may take m Φ − = 250 GeV, m Φ 0 = 160 GeV and λ = 0.6. With this parameter set, the Wjj cross section is found to be 3 pb, which is in the right range to explain the CDF dijet excess. But the scalar mass splitting will contribute to αT = 3.4 × 10 −3 , which is about 3σ deviation from the precision electroweak constraint. In addition, the smaller coupling strength will lead to too small tt forward-backward asymmetry to account for the experimental measurements.