We present a methodology for performing scans of beyond the standard model (BSM) parameter spaces with reinforcement learning. We identify a novel procedure using graph neural networks that is capable of exploring spaces of models without the user specifying a fixed particle content, allowing broad classes of BSM models to be explored—in theory, the technique is applicable to nearly any model space with a prespecified gauge group. We provide a generic procedure by which a suitable graph grammar can be developed for any BSM model that features user-specified symmetry groups and a finite number of different possible particle species, the use of which is applicable to a variety of machine learning tasks over the actions of BSM theories beyond our particular reinforcement learning use case. As a proof of concept, we construct the graph grammar for theories with vectorlike leptons that may or may not be charged under a dark U(1) group, inspired by portal matter extensions of the sub-GeV vector portal/kinetic mixing simplified dark matter models. We then use this graph grammar to create a reinforcement learning environment tasked with creating models with these vectorlike leptons that are consistent with a list of a variety of precision observables. The reinforcement learning agent succeeds in developing models that can address the observed muon anomalous magnetic moment discrepancy while remaining consistent with flavor violation and electroweak precision observables, including both constructions that have previously been studied as well as new models that have not, to our knowledge, previously been identified. By inspecting the resulting ensembles of models that the agent produces and experimenting with different configurations for our reinforcement learning environment and graph grammar, we also infer various lessons about the development of these environments that can be transferable to reinforcement learning scans of more complicated model spaces and comment on future directions for the development of this technique into a more mature tool. Published by the American Physical Society 2025

We provide a framework for exploring physics beyond the Standard Model with reinforcement learning using graph representations of new physics theories. The graph structure allows for model-building without a priori specifying definite numbers of new particles. As a case study, we apply our method to a simple class of theories involving vectorlike leptons and a dark U(1) inspired by the portal matter paradigm. Using modern policy gradient methods, the agent successfully explores a model space consisting of both continuous and discrete parameters and identifies consistent theories. The minimal models found include both known and previously unstudied examples that can accommodate the muon anomalous magnetic moment and satisfy precision electroweak and flavor constraints. The method represents a step forward in enabling an automated model-building process for physics beyond the Standard Model.

We present a methodology for performing scans of BSM parameter spaces with reinforcement learning (RL). We identify a novel procedure using graph neural networks that is capable of exploring spaces of models without the user specifying a fixed particle content, allowing broad classes of BSM models to be explored. In theory, the technique is applicable to nearly any model space with a pre-specified gauge group. We provide a generic procedure by which a suitable graph grammar can be developed for any BSM model which features user-specified symmetry groups and a finite number of different possible particle species. As a proof of concept, we construct the graph grammar for theories with vector-like leptons that may or may not be charged under a dark U(1) group, inspired by portal matter extensions of the sub-GeV vector portal/kinetic mixing simplified dark matter models. We then use this graph grammar to create a RL environment tasked with creating models with these vector-like leptons that are consistent with a list of a variety of precision observables. The RL agent succeeds in developing models that can address the observed muon anomalous magnetic moment discrepancy while remaining consistent with flavor violation and electroweak precision observables, including both constructions that have previously been studied as well as new models which have not, to our knowledge, previously been identified. By inspecting the resulting ensembles of models that the agent produces and experimenting with different configurations for our RL environment and graph grammar, we also infer various lessons about the development of these environments that can be transferable to RL scans of more complicated model spaces, and comment on future directions for the development of this technique into a more mature tool.

We present a minimal construction using leptonic portal matter that addresses the muon $g-2$ anomaly. While the chiral enhancement mechanism is reminiscent of that of fermiophobic $Z'$ gauge models, the parameter space motivated by the kinetic mixing/vector portal dark matter model paradigm is vastly different and can be readily explored in current and forthcoming experiments.

The paradigm of portal matter represents a well-motivated extension to models with kinetic mixing/vector portal dark matter. In previous work, we constructed a simple leptonic portal matter model in which the portal matter fields could mediate a new physics correction to the anomalous magnetic moment of the muon consistent with the observed discrepancy between the measured value for this quantity and the SM prediction. Here, we present a version of this mechanism by constructing a model with an extended dark gauge sector in which SM and portal matter fields exist as members of the same dark gauge multiplets, which provides a natural extension of simple portal matter models. We find a rich phenomenology in this extended model, including nontrivial novel characteristics that do not appear in our earlier minimal construction, and discuss current experimental constraints and future prospects for this model. We find that a multi-TeV muon collider has excellent prospects for constraining or measuring the crucial parameters of this model.

We investigate flavored gauge mediation models in which the Higgs and messenger doublets are embedded in multiplets of the discrete non-Abelian symmetry S3. In these theories, the S3 symmetry correlates the flavor structure of the quark and lepton Yukawa couplings with the structure of the messenger Yukawa couplings that contribute to the soft supersymmetry breaking mass parameters. We provide a systematic exploration of possible scenarios within this framework that can accommodate hierarchical quark and charged lepton masses, and examine the resulting phenomenological implications in each case. We find a heavier spectrum for the superpartner masses compared to flavored gauge mediation models controlled by Abelian symmetries, which can be directly traced back to the need in our scenarios for two vectorlike pairs of messenger fields for viable electroweak symmetry breaking.

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community.

This is the report for the topical group Theory of Neutrino Physics (TF11/NF08) for Snowmass 2021. This report summarizes the progress in the field of theoretical neutrino physics in the past decade, the current status of the field, and the prospects for the upcoming decade.

We explore the theoretical constraints on the observable parameters of neutrino mixing on predictions for the leptonic Dirac CP-violating phase within a well-studied class of simple theoretical models that includes a single source of CP violation due to charged lepton corrections. The approach guarantees that a physically meaningful prediction for the most likely values for the leptonic Dirac CP-violating phase is obtained.

We explore scenarios within grand unification in which proton decay can be suppressed and possibly eliminated due to novel embeddings of the Standard Model matter fields into irreducible representations of the grand unified group and residual symmetries. The scenarios are based on an $SU(7)$ gauge group, in which the matter fields are embedded within an anomaly-free set of fields that can be realized as a natural subgroup of the fundamental spinor representation of an $SO(14)$ gauge symmetry. Depending on the embedding, proton decay can either be forbidden at tree level and generated via one-loop diagrams, or the proton can be made stable by forcing it to decay channels that must have an even number of leptons, independently of the bosonic content of the theory. We describe the theoretical and phenomenological implications of such scenarios, including their implications for dark matter and neutrino masses.

We analyze a minimal flavored gauge mediation model in which the electroweak Higgs and messenger doublets are embedded in multiplets of a discrete non-Abelian symmetry. In this scenario, the minimal Higgs-messenger sector that is consistent with the 125 GeV Higgs mass has two vectorlike pairs of messenger fields. This scenario is obtained in a specific limit of the superpotential interactions of the Higgs-messenger fields and the matter fields. Due to the structure of the messenger-matter Yukawa couplings in this limit, sizable stop mixing and flavor diagonal soft supersymmetry breaking parameters are achieved. In most of the parameter space, the masses of the colored superpartners are at most in the 5--6 TeV range.

We explore the implications of recent results relating the Dirac CP-violating phase to predicted and measured leptonic mixing angles within a standard set of theoretical scenarios in which charged lepton corrections are responsible for generating a nonzero value of the reactor mixing angle. We employ a full set of leptonic sum rules as required by the unitarity of the lepton mixing matrix, which can be reduced to predictions for the observable mixing angles and the Dirac CP-violating phase in terms of model parameters. These sum rules are investigated within a given set of theoretical scenarios for the neutrino sector diagonalization matrix for several known classes of charged lepton corrections. The results provide explicit maps of the allowed model parameter space within each given scenario and assumed form of charged lepton perturbations.

We explore the generation of fermion masses and quark mixing angles within flavored gauge mediation models of supersymmetry breaking in which the Higgs and messenger doublets are connected by a discrete non-Abelian symmetry. In this framework, the Higgs-messenger symmetry, which we take for concreteness to be the discrete group $\mathcal{S}_3$, also plays the role of a (partial) family symmetry. We investigate mechanisms for generating mass hierarchies for the lighter quark generations and generating the Cabibbo angle within this class of models. While perturbations of the couplings at the renormalizable level do not lead to phenomenologically viable quark mixing parameters, we show that the Cabibbo angle can be generated via couplings at the nonrenormalizable level and explore the phenomenological implications of this scenario.

The research at the energy frontier was to explore high energy and luminosity collisions at the LHC using the ATLAS and CMS detectors to lead physics analyses in characterization of the Higgs Boson, to search for its potential partners, to lead searches for Dark Matter and to make extensive studies of Electroweak phenomena. The objectives are also to operate and upgrade the ATLAS and CMS detectors and their computing to optimize their physics performance in the present data taking and to enable the full exploitation of planned High Luminosity LHC. The research for the theory frontier was to analyze and interpret the new data from the experimental frontiers: energy, cosmic and intensity (Phenomenology), to investigate new theories of high energy physics extending the standard model by including gravity within consistent frameworks such as string theory, and examine their phenomenological and cosmological implications (String Theory and Theoretical Cosmology.)

We study the effects of considering nontrivial unphysical lepton sector phases on the group theoretical properties of the flavor and generalized CP symmetry elements in the case where there are three light, distinct Majorana neutrino species. We highlight the similarities and differences between the charged lepton and neutrino sectors and further elucidate the group properties of the flavor and generalized CP symmetry elements. We show how the inclusion of these leptonic phases affects the bottom-up constructions of these symmetry elements and discuss the implications for top-down model building based on discrete symmetry groups.

We investigate the question of electroweak naturalness within the deflected mirage mediation (DMM) framework for supersymmetry breaking in the minimal supersymmetric standard model (MSSM). The class of DMM models considered are nine-parameter theories that fall within the general classification of the 19-parameter phenomenological MSSM (pMSSM). Our results show that these DMM models have regions of parameter space with very low electroweak fine-tuning, at levels comparable to the pMSSM. These parameter regions should be probed extensively in the current LHC run.

We complete the study of a class of string-motivated effective supergravity theories in which modulus-induced soft supersymmetry breaking is sufficiently suppressed in the observable sector so as to be competitive with anomaly-mediated supersymmetry breaking. Here we consider deflected mirage mediation (DMM), where contributions from gauge mediation are added to those arising from gravity mediation and anomaly mediation. We update previous work that surveyed the rich parameter space of such theories, in light of data from the CERN Large Hadron Collider (LHC) and recent dark matter detection experiments. Constraints arising from LHC superpartner searches at $\sqrt{s} = 8\,{\rm TeV}$ are considered, and discovery prospects at $\sqrt{s} = 14\,{\rm TeV}$ are evaluated. We find that deflected mirage mediation generally allows for SU(3)-charged superpartners of significantly lower mass (given current knowledge of the Higgs mass and neutralino relic density) than was found for the `pure' mirage mediation models of Kachru et al. Consequently, discovery prospects are enhanced for many combinations of matter multiplet modular weights. We examine the experimental challenges that will arise due to the prospect of highly compressed spectra in DMM, and the correlation between accessibility at the LHC and discovery prospects at large-scale liquid xenon dark matter detectors.

A study group was formed in Beijing in September 2013 to investigate the feasibility of a high energy Circular Electron Positron Collider (CEPC) as a Higgs and/or Z factory, and a subsequent Super proton-proton Collider (SPPC). A provisional organization structure and a management team, consisted mostly of Chinese physicists, were established to guide the initial study [1]. The group aims at establishing an international collaboration on CEPC-SPPC after sufficient progress has been made in China or it has been given government funding for RD Volume 2 describes the CEPC accelerator design and SPPC consideration, and the associated civil engineering [2]. The contents presented are preliminary and are predominately focused on the CEPC. Formal CDR and TDR work will follow.