Top-pair production via gluon fusion in the Standard Model effective field theory

We compute the leading corrections to the differential cross section for top-pair production via gluon fusion due to third-generation dimension-six operators at leading order in QCD. The Standard Model fields are assumed to couple only weakly to the hypothetical new sector. A systematic approach then suggests treating single insertions of the operator class containing gluon field strength tensors on the same footing as explicitly loop suppressed contributions from four-fermion operators. This is in particular the case for the chromomagnetic operator $Q_{(uG)}$ and the purely bosonic operators $Q_{(G)}$ and $Q_{(\phi G)}$. All leading order dimension-six contributions are consequently suppressed with a loop factor $1/16{\pi }^2$.

Figure 1

Kinematic setup for gluon fusion top-pair production with incoming momenta $k_1$ and $k_2$ and outgoing momenta $p_1$ and $p_2$. The circle in the middle represents all possible interactions for the theory under consideration. There are three Feynman diagrams within the SM at leading order. The SMEFT diagrams will be discussed below.

Figure 2

Feynman diagrams for the tree contributions in SMEFT, where dimension-six insertions are denoted by black squares. Crossings are not displayed. (a)–(c) Contributions from $Q_{(uG)}$. The local interaction (c) does not appear in the SM. (d) Contribution from $Q_{(G)}$ which modifies the s-channel process of the SM. (e) New contribution from $Q_{(\phi G)}$.

Figure 3

Feynman diagrams for the one-loop contributions in SMEFT. Again, crossings are not displayed. These diagrams are needed to cancel the implicit dependence on the renormalization scale $\mu$ in the diagrams of Figs. 2.

Figure 4

(a) SM differential cross section $(d\sigma /d\cos \theta {)}_{\mathrm{SM}}$. (b)–(d) Selected SMEFT corrections to the SM result (b) $(d\sigma /d\cos \theta {)}_{Q_{(\phi G)}}$, (c) $(d\sigma /d\cos \theta {)}_{Q_{(uG)}}$, and (d) $(d\sigma /d\cos \theta {)}_{Q_{(uu)}}$. The differential cross sections $d\sigma /d\cos \theta$ are given in units of pb. The center-of-mass energy was chosen to be $\sqrt{s}=1\mathrm{TeV}$.

Figure 5

Selected relative corrections to the SM differential cross section at $\sqrt{s}=1\mathrm{TeV}$ with (a) $f=(d\sigma /d\cos \theta {)}_{Q_{(\phi G)}}/(d\sigma /d\cos \theta {)}_{\mathrm{SM}}$, (b) $f=(d\sigma /d\cos \theta {)}_{Q_{(uG)}}/(d\sigma /d\cos \theta {)}_{\mathrm{SM}}$ and (c) $f=(d\sigma /d\cos \theta {)}_{Q_{(uu)}}/(d\sigma /d\cos \theta {)}_{\mathrm{SM}}$.

Figure 6

(a) SM total cross section ${\sigma }_{\mathrm{SM}}$. (b)–(d) Selected SMEFT corrections to the SM result (b) ${\sigma }_{Q_{(\phi G)}}$, (c) ${\sigma }_{Q_{(uG)}}$, and (d) ${\sigma }_{Q_{(uu)}}$. The center-of-mass energies $\sqrt{s}$ are given in units of GeV, whereas the total cross sections $\sigma$ are again given in units of pb.