In this work, we review the history and current role of global fits in the search for physics beyond the Standard Model (BSM), including precision tests of the Standard Model (SM). Although BSM global fits were initially focused on minimal supersymmetric models, we describe how fits have evolved in response to new data from the Large Hadron Collider (LHC) and elsewhere, expanding to encompass a broad spectrum of BSM scenarios including non-minimal supersymmetry, axion-like particles, extended Higgs sectors, dark matter models, and effective field theories such as SMEFT. We discuss how the role of global fits has shifted from forecasting possible signals of new physics at the LHC to understanding the impact of null results from LHC run-I and II and the discovery of the Higgs boson, and how interest has shifted from global fits for parameter estimation to comprehensive model comparison. We close by discussing potential trends and future applications, emphasizing the potential for machine learning and artificial intelligence to enhance the efficiency of sampling algorithms and comparison between theory and experiment, as well as collaboration and software development.

We review the role of the anomalous magnetic moment of the muon aμ as a powerful probe of physics beyond the Standard Model (BSM), taking advantage of the final result of the Fermilab g−2 experiment and the recently updated Standard Model value. This review provides both a comprehensive summary of the current status, as well as an accessible entry point for phenomenologists with interests in dark matter, Higgs and electroweak or neutrino and flavour physics in the context of a wide range of BSM scenarios. It begins with a qualitative overview of the field and a collection of key properties and typical results. It then focuses on model-independent, generic formulas and classifies types of BSM scenarios with or without chiral enhancements. A strong emphasis of the review are the connections to a large number of other observables — ranging from the muon mass and the muon–Higgs coupling and related dipole observables to dark matter, neutrino masses and high-energy collider observables. Finally, we survey a number of well-motivated BSM scenarios such as dark photons, axion-like particles, the two-Higgs doublet model, supersymmetric models and models with leptoquarks, vector-like leptons or neutrino mass models. We discuss the impact of the updated Standard Model value for aμ and of complementary constraints, exploring the phenomenology and identifying excluded and viable parameter regions.

Abstract We explore the cosmological dynamics of a supercooled first-order phase transition in the classically conformal U(1) B−L extension of the Standard Model, where radiative symmetry breaking simultaneously generates the right-handed neutrino (RHN) masses, and a strong stochastic gravitational-wave (GW) background. The slow decay of the scalar field into RHNs can induce an early matter-dominated (EMD) era whose duration is sensitive to the RHN mass and gauge coupling g′. This non-standard cosmological phase reshapes the GW spectrum and leaves a distinctive RHN-mass-dependent spectral distortion that correlates with the flavour regime of thermal leptogenesis. Within this framework, one RHN can serve as a dark matter candidate produced from gauge-mediated freeze-in or nonthermally from scalar decays, while the remaining states generate the baryon asymmetry via thermal leptogenesis. For g′ = 0.5, we identify such a parameter region, and show that with singlet extensions, even with a smaller gauge coupling, one can realise this mechanism for the three-flavour regime. The resulting GW signals, amplified by supercooling and modified by EMD, provide a unique window to probe the scale and flavour structure of leptogenesis in future high frequency GW observations.

We discuss the landscape of flavor physics at the Circular Electron-Positron Collider (CEPC), based on the nominal luminosity outlined in its Technical Design Report. The CEPC is designed to operate in multiple modes to address a variety of tasks. At the Z pole, the expected production of 4 Tera Z bosons will provide unique and highly precise measurements of Z boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean Z decays will facilitate investigations into their flavor physics with unprecedented precision. We investigate the prospects of measuring various physics benchmarks and discuss their implications for particle theories and phenomenological models. Our studies indicate that, with its highlighted advantages and anticipated excellent detector performance, the CEPC can explore beauty and tau physics in ways that are superior to or complementary with the Belle II and Large-Hadron-Collider-beauty experiments, potentially enabling the detection of new physics at energy scales of 10 TeV and above. This potential also extends to the observation of yet-to-be-discovered rare and exotic processes, as well as testing fundamental principles such as lepton flavor universality, lepton and baryon number conservation, etc., making the CEPC a vibrant platform for flavor physics research. The WW threshold scan, Higgs-factory operation and top-pair productions of the CEPC further enhance its merits in this regard, especially for measuring the Cabibbo-Kobayashi-Maskawa matrix elements, and Flavor-Changing-Neutral-Current physics of Higgs boson and top quarks. We outline the requirements for detector performance and considerations for future development to achieve the anticipated scientific goals. The role of machine learning for innovative detector design and advanced reconstruction algorithms is also stressed. The CEPC flavor physics program not only develops new capabilities for exploring flavor physics beyond existing projects but also enriches the physics opportunities of this machine. It should be remarked that, given the richness of the CEPC flavor physics, this manuscript is not meant to be a comprehensive survey, but rather an investigation of representative cases. Uncovering the full potential of flavor physics at the CEPC will require further dedicated explorations in the future.

The Circular Electron-Positron Collider (CEPC), a proposed next-generation Higgs factory, provides new opportunities to explore physics beyond the Standard Model (SM). With its clean electron-positron collision environment and the ability to collect large samples of Higgs, W, and Z bosons, the CEPC enables precision measurements and searches for new physics. This white paper outlines the CEPC's discovery potential, including studies of exotic decays of the Higgs, Z, and top quarks, dark matter and dark sector phenomena, long-lived particles, supersymmetry, and neutrino-related signatures. Advanced detector technologies and reconstruction techniques, such as one-to-one correspondence reconstruction and jet origin identification, significantly improve sensitivity to rare and weakly interacting processes. The CEPC is particularly well suited to probe the electroweak phase transition and test models of electroweak baryogenesis and dark sector interactions. In addition, global fit analyses highlight the CEPC's complementary role in constraining a wide range of new physics scenarios. These features position the CEPC as a powerful tool for exploring the next frontier in fundamental particle physics in the post-Higgs discovery era.

We demonstrate for the first time that new physics explaining the long standing charged B meson anomalies, R(D^(*)), can be the source of CP violation that explains the observed baryon asymmetry of the universe (BAU). We consider the general two Higgs doublet model with complex Yukawa couplings and compute the BAU in the semiclassical formalism, using a novel analytic approximation for the latter. After imposing constraints from both flavor observables and the electron electric dipole moment (eEDM), we find that a significant BAU can still be generated for a variety of benchmark points in the parameter space, assuming the occurrence of a sufficiently strong first order electroweak phase transition. These scenarios, which explain both the R(D^(*)) flavor anomalies and the BAU, can be probed with future eEDM experiments and Higgs factories measurements.

Blue-tilted Gravitational Waves (BGWs) have been proposed as a potential candidate for the cosmic gravitational waves detected by Pulsar Timing Arrays (PTA). In the standard cosmological framework, BGWs are constrained in their frequency range by the Big Bang Nucleosynthesis (BBN) limit on GW amplitude, which precludes their detection at interferometer scales. However, introducing a phase of early matter domination dilutes BGWs at higher frequencies, ensuring compatibility with both the BBN and LIGO constraints on stochastic GWs. This mechanism allows BGWs to align with PTA data while producing a distinct and testable GW signal across a broad frequency spectrum. Ultralight Primordial Black Holes (PBHs) could provide the required early matter-dominated phase to support this process. Interpreted through the lens of BGWs, the PTA results offer a way to constrain the parameter space of a new scenario involving modified Hawking radiation, known as the “memory burden" effect, associated with ultralight PBHs. This interpretation can be further probed by high-frequency GW detectors. Specifically, we demonstrate that PBHs as light as 10^2-3 g can leave detectable imprints on BGWs at higher frequencies while remaining consistent with PTA observations.

In recent years, the prospect of detecting gravitational waves sourced from a strongly first-order cosmological phase transition has emerged as one of the most exciting frontiers of gravitational wave astronomy. Cosmological phase transitions are an essential ingredient in the Standard Model of particle cosmology, and help explain the mechanism for creation of matter in the early Universe, provide insights into fundamental theories of physics, and shed light on the nature of dark matter. This underscores the significance of developing robust end-to-end tools for determining the resulting gravitational waves from these phase transitions. In this article we present PhaseTracer2, an improved version of the C++ software package PhaseTracer, designed for mapping cosmological phases and transitions in Standard Model extensions of multiple scalar fields. Building on the robust framework of its predecessor, PhaseTracer2 extends its capabilities by including new features crucial for a more comprehensive analysis of cosmological phase transitions. It can calculate more complex properties, such as the bounce action through the path deformation method or an interface with BubbleProfiler, thermodynamic parameters, and gravitational wave spectra. Its applicability has also been broadened via incorporating the dimensionally reduced effective potential for models obtained from DRalgo, as well as calculations in the MSbar and OS-like renormalisation schemes. This modular, flexible, and practical upgrade retains the speed and stability of the original PhaseTracer, while significantly expanding its utility.

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^+νν 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^+νν) up to only a 10

A bstract In view of both the latest LHCb measurement of $$ {R}_{K^{\left(\ast \right)}} $$ R K ∗ and the new 2 . 7 σ deviation reported by Belle II on $$ {B}^{+}\to {K}^{+}\nu \overline{\nu} $$ 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 $$ \textrm{BR}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right) $$ 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.

We demonstrate that existing gravitational wave data from LIGO already places constraints on well motivated Pati-Salam models that allow the Standard Model to be embedded within grand unified theories. For the first time in these models we also constrain the parameter space by requiring that the phase transition completes, with the resulting constraint being competitive with the limits from LIGO data. Both constraints are complementary to the LHC constraints and can exclude scenarios that are much heavier than can be probed in colliders. Finally we show that results from future LIGO runs, and the planned Einstein telescope, will substantially increase the limits we place on the parameter space.

Gravitational waves (GWs) were recently detected for the first time. This revolutionary discovery opens a new way of learning about particle physics through GWs from first-order phase transitions (FOPTs) in the early Universe. FOPTs could occur when new fundamental symmetries are spontaneously broken down to the Standard Model and are a vital ingredient in solutions of the matter anti-matter asymmetry problem. The purpose of our work is to review the path from a particle physics model to GWs, which contains many specialized parts, so here we provide a timely review of all the required steps, including: (i) building a finite-temperature effective potential in a particle physics model and checking for FOPTs; (ii) computing transition rates; (iii) analyzing the dynamics of bubbles of true vacuum expanding in a thermal plasma; (iv) characterizing a transition using thermal parameters; and, finally, (v) making predictions for GW spectra using the latest simulations and theoretical results and considering the detectability of predicted spectra at future GW detectors. For each step we emphasize the subtleties, advantages and drawbacks of different methods, discuss open questions and review the state-of-art approaches available in the literature. This provides everything a particle physicist needs to begin exploring GW phenomenology.

We perform a global statistical analysis of the two-Higgs-doublet model with generic sources of flavour violation using GAMBIT. This is particularly interesting in light of deviations from the Standard Model predictions observed in b→ cτν and b → sℓ+ℓ− transitions as well as the indications for a charged Higgs with a mass of 130 GeV in top quark decays. Including all relevant constraints from precision, flavour and collider observables, we find that it is possible to simultaneously explain both the charged and neutral current B anomalies. We study the impact of using different values for the W mass and the Standard Model prediction for the anomalous magnetic moment of the muon and provide predictions for observables that can probe our model in the future such as lepton flavour violation searches at Belle II and Higgs coupling strength measurements at the high-luminosity LHC.

Gravitational wave (GW) predictions of cosmological phase transitions are almost invariably evaluated at either the nucleation or percolation temperature. We investigate the effect of the transition temperature choice on GW predictions, for phase transitions with weak, intermediate and strong supercooling. We find that the peak amplitude of the GW signal varies by a factor of a few for weakly supercooled phase transitions, and by an order of magnitude for strongly supercooled phase transitions. The variation in amplitude for even weakly supercooled phase transitions can be several orders of magnitude if one uses the mean bubble separation, while the variation is milder if one uses the mean bubble radius instead. We also investigate the impact of various approximations used in GW predictions. Many of these approximations introduce at least a 10% error in the GW signal, with others introducing an error of over an order of magnitude.

Several pulsar timing array collaborations recently reported evidence of a stochastic gravitational wave background (SGWB) at nHz frequencies. Whilst the SGWB could originate from the merger of supermassive black holes, it could be a signature of new physics near the 100 MeV scale. Supercooled first-order phase transitions (FOPTs) that end at the 100 MeV scale are intriguing explanations, because they could connect the nHz signal to new physics at the electroweak scale or beyond. Here, however, we provide a clear demonstration that it is not simple to create a nHz signal from a supercooled phase transition, due to two crucial issues that could rule out many proposed supercooled explanations and should be checked. As an example, we use a model based on non-linearly realized electroweak symmetry that has been cited as evidence for a supercooled explanation. First, we show that a FOPT cannot complete for the required transition temperature of around 100 MeV. Such supercooling implies a period of vacuum domination that hinders bubble percolation and transition completion. Second, we show that even if completion is not required or if this constraint is evaded, the Universe typically reheats to the scale of any physics driving the FOPT. The hierarchy between the transition and reheating temperature makes it challenging to compute the spectrum of the SGWB.

We investigate the extent to which perturbative calculations of the electroweak phase transition are arbitrary and uncertain, owing to their gauge, renormalisation scale and scheme dependence, as well as treatments of the Goldstone catastrophe and daisy diagrams. Using the complete parameter space of the Standard Model extended by a real scalar singlet with a ℤ 2 symmetry as a test, we explore the properties of the electroweak phase transition in general R ξ and covariant gauges, OS and MS renormalisation schemes, and for common treatments of the Goldstone catastrophe and daisy diagrams. Reassuringly, we find that different renormalisation schemes and different treatments of the Goldstone catastrophe and daisy diagrams typically lead to only modest changes in predictions for the critical temperature and strength of the phase transition. On the other hand, the gauge and renormalisation scale dependence may be significant, and often impact the existence of the phase transition altogether.

There are now two single measurements of precision observables that have major anomalies in the Standard Model: the recent CDF measurement of the $W$ mass shows a $7σ$ deviation and the Muon $g-2$ experiment at FNAL confirmed a long-standing anomaly, implying a $4.2 σ$ deviation. Doubts regarding new physics interpretations of these anomalies could stem from uncertainties in the common hadronic contributions. We demonstrate that these two anomalies pull the hadronic contributions in opposite directions by performing electroweak fits in which the hadronic contribution was allowed to float. The fits show that including the $g - 2$ measurement worsens the tension with the CDF measurement and conversely that adjustments that alleviate the CDF tension worsen the $g-2$ tension beyond $5 σ$. This means that if we adopt the CDF $W$ mass measurement, the case for new physics in either the $W$ mass or muon $g-2$ is inescapable regardless of the size of the SM hadronic contributions. Lastly, we demonstrate that a mixed scalar leptoquark extension of the Standard Model could explain both anomalies simultaneously.