Rotation-equivariant graph neural network for learning hadronic SMEFT effects

We introduce a graph neural network architecture designed to extract novel phenomena in the standard model effective field theory (SMEFT) context from LHC collision data. The proposed infrared- and collinear-safe architecture is sensitive to the angular orientation of radiation patterns in jets from hadronic decays of highly energetic massive particles. Equivariance with respect to rotations around the jet axis allows for extracting the information on the angular orientation decoupled from the jet substructure. We demonstrate the robustness of the approach and its potential for future probes of the SMEFT at the LHC through toy studies and with realistic event simulations of the associated production of a W and a Z boson in the semileptonic decay channel.

Figure 1

Sketch of the $\mathrm{p}\mathrm{p}\to \mathrm{W}\mathrm{Z}$ process, the decay plane, the decay plane angle ${\phi }_{\text{decay}}$ of the $\mathrm{W}$ boson decay. The $\mathrm{\Delta }{R}_i$ and ${\phi }_i$ coordinates of a constituent $i$ from a highly energetic jet are defined with respect to the beam plane and the jet axis.

Figure 1

Sketch of the $\mathrm{p}\mathrm{p}\to \mathrm{W}\mathrm{Z}$ process, the decay plane, the decay plane angle ${\phi }_{\text{decay}}$ of the $\mathrm{W}$ boson decay. The $\mathrm{\Delta }{R}_i$ and ${\phi }_i$ coordinates of a constituent $i$ from a highly energetic jet are defined with respect to the beam plane and the jet axis.

Figure 2

Sketch of the network configuration as explained in the text. The equivariant feature is represented by a double line and the algorithms output by $\widehat{f}$.

Figure 3

Left: contours of the probability density functions used in the toy example, along with an illustrative single event. Middle: median of the MLP output score (black) in scenario (A) as well as the medians of the 20 gNN outputs that serve as inputs to the redout MLP (gray) in arbitrary units. The equivariant feature $h_{\gamma }$ is shown in blue. Right: median of the MLP output score (black) in scenario (B) as well as the medians of the first seven pooled gNN outputs that serve as inputs to the redout MLP (gray) in arbitrary units. The median of ${\sin }^2{\mathrm{h}}_{\phi }$ is shown in blue.

Figure 4

Two-dimensional distribution of the true and regressed angle ${\phi }_{\text{decay}}$ in the test dataset.

Figure 5

Left: mean score as a function of ${\phi }_{\text{decay}}$, obtained with the true model and the regressed surrogate model. Center and right: likelihood scan as a function of $C_{\mathrm{W}}$ (center) and $C_{\tilde{\mathrm{W}}}$ (right) using different likelihood models, assuming 2000 observed events. The surrogate model described in this paper is compared with a MLP that takes as an only input the ${\phi }_{\text{decay}}$ and the likelihood function of a counting experiment considering ten bins in ${\phi }_{\text{decay}}$. We also compare to a strategy based on the soft-drop mass $M_{\mathrm{SD}}$ [63] and N-subjettiness ratio ${\tau }_{21}$ [64].