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With the physical Higgs mass the Standard Model symmetry restoration phase transition is a smooth cross-over. We study the thermodynamics of the cross-over using numerical lattice Monte Carlo simulations of an effective SU(2) X U(1) gauge + Higgs theory, significantly improving on previously published results. We measure the Higgs field expectation value, thermodynamic quantities like pressure, energy density, speed of sound and heat capacity, and screening masses associated with the Higgs and Z fields. While the cross-over is smooth, it is very well defined with a width of only approximately 5 GeV. We measure the cross-over temperature from the maximum of the susceptibility of the Higgs condensate, with the result $T_c = 159.5 pm 1.5$ GeV. Outside of the narrow cross-over region the perturbative results agree well with non-perturbative ones.
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Estimates of the CP violating observable $varepsilon/varepsilon$ have gained some attention in the past few years. Depending on the long-distance treatment used, they exhibit up to $2.9sigma$ deviation from the experimentally measured value. Such a deviation motivates the investigation of New Physics (NP) effects in the process $Ktopipi$. In my talk I will review the Standard Model (SM) prediction for $varepsilon/varepsilon$, with a special focus on the Dual QCD approach. On the NP side, I will discuss a recent computation of the hadronic matrix elements of NP operators. Furthermore a master formula for BSM effects in $varepsilon/varepsilon$ is presented. Finally, a treatment of $varepsilon/varepsilon$ using the SM effective theory (SMEFT) will be discussed together with possible correlations to other observables.
We present for the first time a model-independent anatomy of the ratio $varepsilon/varepsilon$ in the context of the $Delta S = 1$ effective theory with operators invariant under QCD and QED and in the context of the Standard Model Effective Field Theory (SMEFT) with the operators invariant under the full SM gauge group. Our goal is to identify the new physics scenarios that are probed by this ratio and which could help to explain a possible deviation from the SM that is hinted by the data. To this end we derive a master formula for $varepsilon/varepsilon$, which can be applied to any theory beyond the Standard Model (BSM) in which the Wilson coefficients of all contributing operators have been calculated at the electroweak scale. The relevant hadronic matrix elements of BSM operators are from the Dual QCD approach and the SM ones from lattice QCD. Within SMEFT, the constraints from $K^0$ and $D^0$ mixing as well as electric dipole moments limit significantly potential new physics contributions to $varepsilon/varepsilon$. Correlations of $varepsilon/varepsilon$ with $Ktopi ubar u$ decays are briefly discussed. Building on our EFT analysis and the model-independent constraints, we discuss implications of a possible deviation from the SM in $varepsilon/varepsilon$ for model building, highlighting the role of the new scalar and tensor matrix elements in models with scalar mediators.
We show that the leading coupling between a shift symmetric inflaton and the Standard Model fermions leads to an induced electroweak symmetry breaking due to particle production during inflation, and as a result, a unique oscillating feature in non-Gaussianities. In this one parameter model, the enhanced production of Standard Model fermions dynamically generates a new electroweak symmetry breaking minimum, where the Higgs field classically rolls into. The production of fermions stops when the Higgs expectation value and hence the fermion masses become too large, suppressing fermion production. The balance between the above-mentioned effects gives the Standard Model fermions masses that are uniquely determined by their couplings to the inflaton. In particular, the heaviest Standard Model fermion, the top quark, can produce a distinct cosmological collider physics signature characterised by a one-to-one relation between amplitude and frequency of the oscillating signal, which is observable at future 21-cm surveys.
We demonstrate that light spectator fields can source sizeable CMB anisotropies through modulated reheating even in the absence of direct couplings to the inflaton. The effect arises when the phase space of the inflaton decay is modulated by the spectator which generates masses for the decay products. We call the mechanism textit{indirect modulation} and show that it can source perturbations even four orders of magnitude larger than the observed. Importantly, the indirect mechanism is present in the Standard Model extended with right-handed neutrinos. For a minimally coupled Higgs boson this leads to a novel lower bound on the quartic coupling and constrains the neutrino Yukawas below unity.
We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $alpha$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $mathcal{O}(alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $mathcal{O}(alpha^2)$ and is due to hadronic vacuum polarization, whereas at $mathcal{O}(alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_mu^text{SM}=116,591,810(43)times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.
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