Dilepton production in the SMEFT at $\mathcal{O}(1/{\mathrm{\Lambda }}^4)$

We study the inclusion of $\mathcal{O}(1/{\mathrm{\Lambda }}^4)$ effects in the Standard Model effective field theory in fits to the current Drell-Yan data at the LHC. Our analysis includes the full set of dimension-6 and dimension-8 operators contributing to the dilepton process, and is performed to next-to-leading-order in the QCD coupling constant at both $\mathcal{O}(1/{\mathrm{\Lambda }}^2)$ and $\mathcal{O}(1/{\mathrm{\Lambda }}^4)$. We find that the inclusion of dimension-6 squared terms and certain dimension-8 operators has significant effects on fits to the current data. Neglecting them leads to bounds on dimension-6 operators off by large factors. We find that dimension-8 four-fermion operators can already be probed to the several-TeV level by LHC results, and that their inclusion significantly changes the limits found for dimension-6 operators. We discuss which dimension-8 operators should be included in fits to the LHC data. Only a manageable subset of two-derivative dimension-8 four-fermion operators need to be included at this stage given current LHC uncertainties.

Figure 1

$a^{(6)}$ and $b^{(6)}$ coefficients for the operators $C_{eu}$ and $C_{\ell u}$, for $\mathrm{\Lambda }=4\mathrm{TeV}$.

Figure 2

Contributions of vector and axial operators to dilepton production. The colored bands denote the deviation from the Standard Model cross sections, as the couplings vary between $\pm 1$ for $\mathrm{\Lambda }=4\mathrm{TeV}$.

Figure 3

Contributions of scalar, tensor and dipole operators to dilepton production. The colored bands denote the deviation from the Standard Model cross sections, as the couplings vary between 0 and 1 for $C_{\ell equ}^{(1,3)}({\mu }_0)$ and between 0 and 20 for $C_{eW,eB}({\mu }_0)$, with $\mathrm{\Lambda }=4\mathrm{TeV}$. The Wilson coefficients are defined at the initial scale ${\mu }_0=1\mathrm{TeV}$.

Figure 4

Contributions of dimension-8 operators to dilepton production. The colored bands denote the deviation from the Standard Model cross sections, as the couplings vary between $\pm 10$ for $C_{e^2{u}^2{D}^2}$, $\pm 100$ for $C_{e^2{u}^2{H}^2}$ and $\pm {10}^4$ for $C_{e^2{H}^2{D}^3}$ and $C_{u^2{H}^2{D}^3}$, with $\mathrm{\Lambda }=4\mathrm{TeV}$.

Figure 5

Comparison between the SM prediction (blue) and the measurement of the Drell-Yan invariant mass distribution of Ref. [72] (black). In the top panel, the grey shaded area and blue error bars denote, respectively, the experimental and theoretical errors. In the bottom panel, the error on the ratio ${\sigma }_{\mathrm{th}}/\mathrm{data}$ is dominated, at high invariant mass, by the experimental uncertainties.

Figure 6

95% CL intervals for the dimension-6 four-fermion operators that interfere with the SM. Both the limits obtained by considering only $\mathcal{O}(1/{\mathrm{\Lambda }}^2)$ effects, as well as those including the $\mathcal{O}(1/{\mathrm{\Lambda }}^4)$ corrections, are shown.

Figure 7

95% CL intervals for dimension-6 dipole, scalar and tensor interactions that first contribute at $\mathcal{O}(1/{\mathrm{\Lambda }}^4)$. The Wilson coefficients are defined at the scale ${\mu }_0=1\mathrm{TeV}$.

Figure 8

95% CL intervals for the dimension-8 momentum-dependent four-fermion operators.

Figure 9

95% CL intervals for the dimension-8 momentum-independent four-fermion operators. A combination such as $(1)+(2)$ in a superscript indicates that the indicated linear combination of the two relevant operators has been considered.

Figure 10

95% CL intervals for a selection of dimension-8 $Z$-boson vertex corrections. A combination such as $(1)-(2)$ in a superscript indicates that the indicated linear combination of the two relevant operators has been considered.