Light colored scalar as messenger of up-quark flavor dynamics in grand unified theories

The measured forward-backward asymmetry in the $t\overline{t}$ 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 $D^0\mathrm{\text{−}}{\overline{D}}^0$ oscillations, as well as dijet 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.

Figure 1

Contribution of order $(g_6^{13}{g}_6^{23*}{)}^2$ to $\Delta C=2$ effective Hamiltonian.

Figure 2

The 1 and $2\sigma$ confidence level regions (dark and light-shaded regions, respectively) in the plane $x_{12}\mathrm{\text{−}}{x}_{12}|\sin {\varphi }_{12}|$.

Figure 3

Allowed regions of $|g_6^{23}|$ and $\omega$ for different values of $m_{{\Delta }_6}$.

Figure 4

Partonic contribution to dijet production at the Tevatron from a $u$-channel ${\Delta }_6$ exchange. The analogous $s$- and $t$-channel contributions can simply be obtained via crossing.

Figure 5

Partonic contribution to the single-top production at the Tevatron from a $u$-channel ${\Delta }_6$ exchange. The analogous $s$-channel contribution can simply be obtained by crossing.

Figure 6

Constraint on the $|g_6^{12}|$ coupling and ${\Delta }_6$ mass from the single-top production and dijet at the Tevatron. The shaded areas are excluded.

Figure 7

Ratio of top quark decay widths $t\to c\gamma$, $cG$ and ${\Delta }_6$ contribution to the single-top production at the Tevatron. See text for explanation.

Figure 8

Plot of $|U_{31}|$ vs $|S_{33}^{\prime }|/|A_{13}^{\prime }|$. Squares represent results of our numerical analysis as described in the text whereas the curve stands for approximate analytic expression $2\sqrt{1-|U_{31}{|}^2}/|U_{31}|$. The observed agreement implies that $|U_{32}|$ is negligible.

Figure 9

Plot of $\log |S_{12}^{\prime }|/|A_{12}^{\prime }|$ vs $|U_{31}|$. There exist a lower bound on $|U_{31}|$ due to the fact that $|A_{13}^{\prime }|>|A_{23}^{\prime }|$. See text for details.

Figure 10

Plot of $\log |S_{11}^{\prime }|/|S_{22}^{\prime }|$ vs $|U_{31}|$. $|S_{11}^{\prime }|/|S_{22}^{\prime }|\to m_u/m_c$ for small $|U_{31}|$.

Figure 11

The dependence of upper bound on $v_{45}$ as a function of $m_{{\Delta }_6}$. Note that $v_{45}$ drops as $m_{{\Delta }_6}$ grows to decrease the influence of the antisymmetric components of $g_6$ towards the up-quark mass relations.