Higgs Pair Production: Choosing Benchmarks With Cluster Analysis

TL;DR

This work tackles the challenge of probing large multi-parameter Higgs sectors by organizing the parameter space according to final-state kinematics. It introduces a clustering-based framework that uses a Poisson-binned likelihood ratio TS in the ($m_{hh}$, $|\cos\theta^*|$) plane to group parameter points into homogeneous regions and define representative benchmarks. Applied to non-resonant Higgs pair production in an EFT with anomalous couplings, the study shows that 12 benchmarks suffice to describe the main kinematic densities at 13 TeV, enabling extrapolation within clusters and guiding experimental searches. The method emphasizes shape information over rate, offering a practical, generalizable strategy for designing searches and interpreting results across complex multi-parameter spaces in BSM Higgs physics.

Abstract

New physics theories often depend on a large number of free parameters. The precise values of those parameters in some cases drastically affect the resulting phenomenology of fundamental physics processes, while in others finite variations can leave it basically invariant at the level of detail experimentally accessible. When designing a strategy for the analysis of experimental data in the search for a signal predicted by a new physics model, it appears advantageous to categorize the parameter space describing the model according to the corresponding kinematical features of the final state. A multi-dimensional test statistic can be used to gauge the degree of similarity in the kinematics of different models; a clustering algorithm using that metric may then allow the division of the space into homogeneous regions, each of which can be successfully represented by a benchmark point. Searches targeting those benchmark points are then guaranteed to be sensitive to a large area of the parameter space. In this document we show a practical implementation of the above strategy for the study of non-resonant production of Higgs boson pairs in the context of extensions of the standard model with anomalous couplings of the Higgs bosons. A non-standard value of those couplings may significantly enhance the Higgs pair production cross section, such that the process could be detectable with the data that the Large Hadron Collider will collect in Run 2.

Figures (12)

• Figure 1: Feynman diagrams that contribute to Higgs boson pair production by gluon-gluon fusion at leading order. Diagrams (a) and (b) correspond to SM-like processes, while diagrams (c), (d), and (e) correspond to pure BSM effects: (c) and (d) describe contact interactions between the Higgs boson and gluons, and (e) exploits the contact interaction of two Higgs bosons with top quarks.
• Figure 2: Cross section ratios ($\sigma_{BSM}/\sigma_{SM}$) in selected slices of parameter space. Left column: the plane of SM parameters, $\kappa_t : \kappa_\lambda$ (top), and the region allowing a Higgs boson contact interaction with gluons, $c_g : \kappa_\lambda$ (bottom). Middle column: planes spanned by the parameters describing non-vanishing one- and two-Higgs boson interactions with top quarks and with gluons, $\kappa_t : c_2$ (top) and $c_{2g} : c_g$ (bottom). Right column: the planes spanned by parameters governing interactions of the Higgs boson with gluons and top-quark pairs, $c_g : c_2$ (top) and $c_{2g}:c_2$ (bottom), for selected values of the other parameters. The cross section is computed with the fit discussed in the text.
• Figure 3: Graphical description of the clustering procedure.
• Figure 4: Distribution of the invariant mass $m_{hh}$ of Higgs boson pairs as pairs of clusters get merged into a single one, for different values of $N_{clus}$. The red distribution is the benchmark of the cluster. The merging of clusters due to the reduction in the number of $N_{clus}$ is highlighted. It is evident that passing from $N_{clus} = 13$ to $N_{clus} = 12$ the uniformity of the distributions inside the merged cluster remains good, while subsequent mergings worsen the intra-cluster homogeneity.
• Figure 5: Generation-level distributions of di-Higgs boson mass $m_{hh}$ (top three rows) and emission angle $|\cos \theta^{*}|$ (bottom three rows) for the clusters identified by the choice $N_{clus} = 12$. The red distributions correspond to the benchmark sample in each cluster, while the blue ones describe the other members of each cluster. Cluster 3 contains the SM sample.