Constraining the top-Higgs sector of the standard model effective field theory

Working in the framework of the Standard Model effective field theory, we study chirality-flipping couplings of the top quark to Higgs and gauge bosons. We discuss in detail the renormalization-group evolution to lower energies and investigate direct and indirect contributions to high- and low-energy $CP$-conserving and $CP$-violating observables. Our analysis includes constraints from collider observables, precision electroweak tests, flavor physics, and electric dipole moments. We find that indirect probes are competitive or dominant for both $CP$-even and $CP$-odd observables, even after accounting for uncertainties associated with hadronic and nuclear matrix elements, illustrating the importance of including operator mixing in constraining the Standard Model effective field theory. We also study scenarios where multiple anomalous top couplings are generated at the high scale, showing that while the bounds on individual couplings relax, strong correlations among couplings survive. Finally, we find that enforcing minimal flavor violation does not significantly affect the bounds on the top couplings.

Figure 1

Representative diagrams contributing to the mixing of $C_{\gamma }$ into $C_{\phi \tilde{W},\phi \tilde{B},\phi \tilde{W}B,quqd,lequ}$ (top panel), and the mixing of the latter into light fermion electroweak dipoles (bottom panel). The square (circle) represents an operator (quark mass) insertion. Solid, wavy, and dotted lines represent fermions, electroweak gauge bosons, and the Higgs, respectively.

Figure 2

Contribution of $C_{Wt}$ and $C_{Wb}$ to $t$-channel single top production. Solid lines denote light quarks, double lines the top quark, and wavy lines the $W$ boson. SM vertices are denoted by a dot, while an insertion of a $C_{Wt}$ or $C_{Wb}$ is denoted by a square.

Figure 3

The 90% C.L. allowed regions in the $v^2{c}_{\gamma }-v^2{\tilde{c}}_{\gamma }$ (left panel) and $v^2{c}_{Wt}-v^2{\tilde{c}}_{Wt}$ planes (right panel), with couplings evaluated at $\mathrm{\Lambda }=1\mathrm{TeV}$. In both cases, the inset zooms into the current combined allowed region and shows projected future sensitivities.

Figure 4

The 90% C.L. allowed regions in the $v^2{c}_{Wb}-v^2{\tilde{c}}_{Wb}$ (left panel), $v^2{c}_g-v^2{\tilde{c}}_g$ (center panel), and $v^2{c}_Y-v^2{\tilde{c}}_Y$ (right panel) planes, with couplings evaluated at $\mathrm{\Lambda }=1\mathrm{TeV}$.

Figure 5

Same as Fig. 3, showing the 90% C.L. allowed regions in the $v^2{c}_{\gamma }-v^2{\tilde{c}}_{\gamma }$ (left panel) and $v^2{c}_{Wt}-v^2{\tilde{c}}_{Wt}$ planes (right panel), but now assuming central values for the relevant nuclear and hadronic matrix elements. Both the allowed regions in the single coupling case (solid lines) and marginalized case (dashed lines) are shown.

Figure 6

Same as Fig. 4, showing the 90% C.L. allowed regions in the $v^2{c}_{Wb}-v^2{\tilde{c}}_{Wb}$ (left panel), $v^2{c}_g-v^2{\tilde{c}}_g$ (center panel), and $v^2{c}_Y-v^2{\tilde{c}}_Y$ (right panel) planes, but now assuming central values for the relevant nuclear and hadronic matrix elements. Both the allowed regions in the single coupling case (solid lines) and marginalized case (dashed lines) are shown.

Figure 7

The 90% C.L. allowed regions in the $v^2{\tilde{c}}_{\gamma }-v^2{\tilde{c}}_{Wt}$ plane. We marginalized over the remaining couplings and assumed central values for the relevant nuclear and hadronic matrix elements.

Figure 8

The 90% C.L. allowed regions in the $v^2{c}_g-v^2{c}_Y$ plane, with couplings evaluated at $\mathrm{\Lambda }=1\mathrm{TeV}$. We assume that only $C_g$ and $C_Y$ are generated at the high scale, and the theoretical uncertainties are dealt with using the R-fit procedure.

Figure 9

The 90% C.L. allowed regions in the $v^2{\tilde{c}}_{\gamma }\text{−}{v}^2{\tilde{c}}_{\gamma }^{\prime }$ plane, using the R-fit method to treat theoretical uncertainties in the relevant hadronic matrix elements.