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Abstract In the context of E6 Grand Unified Theories (GUTs), an intriguing possibility for symmetry breaking to the Standard Model (SM) group involves an intermediate stage characterized by either SU(3) × SU(3) × SU(3) (trinification) or SU(6) × SU(2). The more common choices of SU(5) and SO(10) GUT symmetry groups do not offer such breaking chains. We argue that the presence of a real (rank 2 tensor) representation 650 of E6 in the scalar sector is the minimal and likely only reasonable possibility to obtain one of the novel intermediate stages. We analyze the renormalizable scalar potential of a single copy of the 650 and find vacuum solutions that support regularly embedded subgroups SU(3) × SU(3) × SU(3), SU(6) × SU(2), and SO(10) × U(1), as well as specially embedded subgroups F4 and SU(3) × G2 that do not contain the SM gauge symmetry. We show that for a suitable choice of parameters, each of the regular cases can be obtained as the lowest among the analyzed minima in the potential.

Abstract We investigate the sensitivity of future high-energy muon colliders to neutral triple gauge couplings (nTGCs) through the process μ + μ − → γν ν ¯ μ⁺μ⁻→ γ ν ν̅ within the Standard Model Effective Field Theory (SMEFT) framework. Extending beyond previous studies, we consider a set of 14 dimension-8 operators, including both Higgs-related and pure gauge structures. By computing the cross sections and performing Monte Carlo simulations at multiple center-of-mass energies (3–30 TeV), we demonstrate that the annihilation process dominates over vector boson fusion (VBF) at TeV scales. We also explore the impact of beam polarization and show that the (– +) polarization enhances sensitivity to several operators. After the study of the event selection strategies, we show that muon colliders can impose stronger expected constraints on nTGCs operators than current LHC bounds, with two of the pure gauge operators yielding the most stringent expected constraints. We also evaluate the contribution of CP-violating pure gauge operators to the electron electric dipole moment (EDM), finding that the expected constraints from muon colliders are stronger than those from EDM measurements.

The so-called X17 particle has been proposed in order to explain a very significant resonant behaviour (in both the angular separation and invariant mass) of e+e- pairs produced during a nuclear transition of excited 8Be, 4He and 12C nuclei. Fits to the corresponding data point, as most probable explanation, to a spin-1 object, which is protophobic and has a mass of approximately 16.7 MeV, which then makes the X17 potentially observable in Coherent Elastic neutrino (nu) Nucleus Scattering (CE nu NS) at the European Spallation Source (ESS). By adopting as theoretical framework a minimal extension of the Standard Model (SM) with a generic U(1)' gauge group mixing with the hypercharge one of the latter, which can naturally accommodate the X17 state compliant with all available measurements from a variety of experiments, we predict that CE nu NS at the ESS will constitute an effective means to probe this hypothesis, even after allowing for the inevitable systematics associated to the performance of the planned detectors therein.

A bstract We perform a global fit of electroweak data, finding that the anomaly in the W mass claimed by the CDF collaboration can be reproduced as a universal new-physics correction to the T parameter or | H † D μ H | 2 operator. Contributions at tree-level from multi-TeV new physics can fit the anomaly compatibly with collider bounds: we explore which scalar vacuum expectation values (such as a triplet with zero hypercharge), Z ′ vectors (such as a Z ′ coupled to the Higgs only), little-Higgs models or higher-dimensional geometries provide good global fits. On the other hand, new physics that contributes at loop-level must be around the weak scale to fit the anomaly. Thereby it generically conflicts with collider bounds, that can be bypassed assuming special kinematics like quasi-degenerate particles that decay into Dark Matter (such as an inert Higgs doublet or appropriate supersymmetric particles).

A bstract We systematically explore ultraviolet complete models where flavour hierarchies emerge, via approximate accidental symmetries, from an underlying flavour non-universal gauge structure. In order to avoid large quantum corrections to the Higgs mass, the first layer of non-universality, separating the third generation from the light ones, should appear at the TeV scale. A handful of models survive the combined criteria of naturalness in the Higgs sector, having a semi-simple embedding in the UV, and compatibility with experiments. They all feature quark-lepton unification in the third family and a non-universal electroweak sector. We study in more detail the interesting option of having colour and hypercharge non-universal at the TeV scale, while SU(2) L remains universal up to high scales: this gauge structure turns to be very efficient in secluding the Higgs from large quantum corrections and predicting flavour mixing consistent with data. In all cases, these models imply a rich TeV-scale phenomenology within the reach of near-future direct and indirect experimental searches.

A bstract We construct two concrete examples of flavour non-universal gauge theories which, after the inclusion of all d ≤ 4 gauge invariant operators, allow to describe the observed pattern of flavour in the charged fermion sector without any small Yukawa coupling ( y ≳ 0 . 1). Guided by the criterium of minimality, we assume that flavour non universality is confined to the Abelian sector of the gauge group: the universal hypercharge emerges after a sequence of symmetry-breaking steps characterised by two high mass scales, Λ [23] < Λ [12] , where the second and the first fermion generations get their mass respectively. At least in one of the two models the smaller of these scales can be in the 10 TeV range, consistently with current bounds from flavour observables. Both models are extended to include as well neutrino masses and mixings.

A bstract The flavour puzzle is one of the greatest mysteries in particle physics. A ‘flavour deconstruction’ of the electroweak gauge symmetry, by promoting at least part of it to the product of a third family factor (under which the Higgs is charged) times a light family factor, allows one to address the flavour puzzle at a low scale due to accidentally realised U(2) 5 flavour symmetries. The unavoidable consequence is new heavy gauge bosons with direct couplings to the Higgs, threatening the stability of the electroweak scale. In this work, we propose a UV complete model of flavour based on deconstructing only hypercharge. We find that the model satisfies finite naturalness criteria, benefiting from the smallness of the hypercharge gauge coupling in controlling radiative Higgs mass corrections and passing phenomenological bounds. Our setup allows one to begin explaining flavour at the TeV scale, while dynamics solving the large hierarchy problem can lie at a higher scale up to around 10 TeV — without worsening the unavoidable little hierarchy problem. The low-energy phenomenology of the model is dominated by a single Z ′ gauge boson with chiral and flavour non-universal couplings, with mass as light as a few TeV thanks to the U(2) 5 symmetry. The natural parameter space of the model will be probed by the HL-LHC and unavoidably leads to large positive shifts in the W -boson mass, as well as an enhancement in B ( B s,d → μ + μ − ). Finally, we show that a future electroweak precision machine such as FCC-ee easily has the reach to fully exclude the model.

A bstract The interpretation of LHC data, and the assessment of possible hints of new physics, require the precise knowledge of the proton structure in terms of parton distribution functions (PDFs). We present a systematic methodology designed to determine whether and how global PDF fits might inadvertently ‘fit away’ signs of new physics in the high-energy tails of the distributions. We showcase a scenario for the High-Luminosity LHC, in which the PDFs may completely absorb such signs of new physics, thus biasing theoretical predictions and interpretations. We discuss strategies to single out the effects in this scenario, and disentangle the inconsistencies that stem from them. Our study brings to light the synergy between the high luminosity programme at the LHC and future low-energy non-LHC measurements of large- x sea quark distributions. The analysis code used in this work is made public so that any users can test the robustness of the signal associated to a given BSM model against absorption by the PDFs.

A bstract In view of both the latest LHCb measurement of R K ∗ and the new 2 . 7 σ deviation reported by Belle II on B + → K + ν ν ¯ decays, we present a fit to the B meson anomalies for various one and two dimensional hypothesis including complex Wilson coefficients. We show in a model-independent way that the generic non-universal U(1) ′ extensions of the SM, without flavour violation, fail to simultaneously fit those observables and corroborate that they can modify BR B + → K + ν ν ¯ up to only a 10%. In view of this deficit, we propose a new way in which those models can accommodate the data at tree level by introducing lepton flavour violating couplings and non-diagonal elements of the charged lepton mixing matrix, with implications in future charged lepton flavour violation searches.

Abstract Lepton flavor violation (LFV), observed conclusively in neutrino oscillations, remains a pivotal area of investigation due to its absence in the Standard Model (SM). Beyond the Standard Model (BSM) physics explores charged lepton flavor violation (CLFV), particularly through new particle candidates such as the Z ′. This article focuses on maximal LFV interactions facilitated by the Z ′ boson, specifically targeting its off-diagonal interactions with the first and second generations of charged and neutral leptons. In our ultraviolet (UV) model for the origin of the Z ′, inspired by the work of [R.Foot et al., Phys.Rev. D50 (1994) 4571-4580], we utilize the discrete Z 2 symmetry to investigate the maximal LFV mediated by the Z ′ between the muon (μ) and electron (e) arising from the additional scalars. This symmetry prohibits flavor-conserving interactions between Z ′ and μ + μ − , e + e − . In conjunction with collider, (g – 2) μ , (g – 2) e , inverse μ decay, Muonium-to-Antimuonium conversion and LFV decay constraints, we provide forecasts for anticipated limits derived from processes such as ν μ N → ν e μ + e − N in neutrino trident experiments like the DUNE search at the first time. These limits highlight the prospective scope and significance of LFV investigations within these experimental frameworks. Within the mass range of 0.01 GeV to 10 GeV, the most stringent limit arises from B μ → e + X + γ$$ \\mathcal{B}\\left(\\mu \\to e+X+\\gamma \\right) $$when M Z ′ < m μ$$ {M}_{Z^{\\prime }}<{m}_{\\mu } $$, while ∆a e provides effective constraints as M Z ′$$ {M}_{Z^{\\prime }} $$approaches 10 GeV. Looking ahead, the proposed Muonium-to-Antimuonium Conversion Experiment (MACE) is expected to impose the most stringent constraints on Muonium-to-Antimuonium oscillation, improving sensitivity by about one order of magnitude against ∆a e .