No abstract

We consider the Standard Model, including a light scalar boson h, as an effective theory at the weak scale v = 246 GeV of some unknown dynamics of electroweak symmetry breaking. This dynamics may be strong, with h emerging as a pseudo-Goldstone boson. The symmetry breaking scale Λ is taken to be at 4πv or above. We review the leading-order Lagrangian within this framework, which is nonrenormalizable in general. A chiral Lagrangian can then be constructed based on a loop expansion. A systematic power counting is derived and used to identify the classes of counterterms that appear at one loop order. With this result the complete Lagrangian is constructed at next-to-leading order, O(v 2 /Λ 2 ). This Lagrangian is the most general effective description of the Standard Model containing a light scalar boson, in general with strong dynamics of electroweak symmetry breaking. Scenarios such as the SILH ansatz or the dimension-6 Lagrangian of a linearly realized Higgs sector can be recovered as special cases.

We discuss the systematics of power counting in general effective field theories, focussing on those that are nonrenormalizable at leading order. As an illuminating example we consider chiral perturbation theory gauged under the electromagnetic U (1) symmetry. This theory describes the low-energy interactions of the octet of pseudo-Goldstone bosons in QCD with photons and has been discussed extensively in the literature. Peculiarities of the standard approach are pointed out and it is shown how these are resolved within our scheme. The presentation follows closely our recent discussion of power counting for the electroweak chiral Lagrangian. The systematics of the latter is reviewed and shown to be consistent with the concept of chiral dimensions. The results imply that naive dimensional analysis (NDA) is incomplete in general effective field theories, while still reproducing the correct counting in special cases.

We present a novel integrator based on normalizing flows which can be used to improve the unweighting efficiency of Monte-Carlo event generators for collider physics simulations. In contrast to machine learning approaches based on surrogate models, our method generates the correct result even if the underlying neural networks are not optimally trained. We exemplify the new strategy using the example of Drell-Yan type processes at the LHC, both at leading and partially at nextto-leading order QCD. I. INTRODUCTIONNumerical simulation programs are a cornerstone of collider physics. They are used for the planning of future experiments, analysis of current measurements and, finally, reinterpretation based on an improved theoretical understanding of nature. They employ Monte Carlo methods to link theory and experiment by generating virtual collider events, which can then be analyzed like actual events observed in detectors [1,2].With more and more data available from the Large Hadron Collider (LHC) and the high-luminosity upgrade, the task of simulating collisions at high precision becomes a matter of concern for the high-energy physics community. The projected amount of computational resources falls far short of the needs for precision event generation [3]. Past studies of the scaling behavior of multi-jet simulations have shown that the compute needs are largely determined by the gradually decreasing unweighting efficiency [4,5]. Except for dedicated integrators, which require a detailed understanding of the physics problem at hand, adaptive Monte-Carlo methods seem the only choice to address this problem [6][7][8][9][10][11][12][13].With the rise of machine learning, this topic has seen a resurgence of interest recently. The possibility of using these techniques for integration in high-energy physics was first discussed in Ref. [14]. Boosted Decision Trees and Generative Adversarial Networks (GANs) were investigated as possible general purpose integrators. This new technique improved the integration of non-separable high dimensional functions, for which traditional algorithms failed. The first true physics application was presented in Ref. [15]. The authors used Dense Neural Networks (DNN) in order to perform a variable transformation and demonstrate that they obtain significantly larger efficiencies for three body decay integrals than standard approaches [16]. The major drawback of this method is its computational cost. Since the network acts as a variable transformation, its gradient must be computed for each inference point in order to determine the Jacobian. This becomes computationally heavy for high multiplicity processes.A completely orthogonal approach utilizes machine learning techniques directly for amplitude evaluation [17] or event generation [18][19][20][21][22][23][24]. Training data for these approaches are obtained from traditional event generation techniques, and hence the problem of efficient event generation still remains. In addition, one needs to ensure that the neural networks are trained well ...

We perform a Bayesian statistical analysis of the constraints on the nonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. We obtain bounds on the effective coefficients entering in Higgs observables at the leading order, using all available Higgs-boson signal strengths from the LHC runs 1 and 2. Using a prior dependence study of the solutions, we discuss the results within the context of natural-sized Wilson coefficients. We further study the expected sensitivities to the different Wilson coefficients at various possible future colliders. Finally, we interpret our results in terms of some minimal composite Higgs models.

If the electroweak phase transition (EWPT) is of strongly first order due to higher dimensional operators, the scale of new physics generating them is at the TeV scale or below. In this case the effective-field theory (EFT) neglecting operators of dimension higher than six may overlook terms that are relevant for the EWPT analysis. In this article we study the EWPT in the EFT to dimension eight. We estimate the reach of the future gravitational wave observatory LISA for probing the region in which the EWPT is strongly first order and compare it with the capabilities of the Higgs measurements via doubleHiggs production at current and future colliders. We also match different UV models to the previously mentioned dimension-eight EFT and demonstrate that, from the top-down point of view, the double-Higgs production is not the best signal to explore these scenarios.

In a recent paper we showed that the electroweak chiral Lagrangian at leading order is equivalent to the conventional formalism used by ATLAS and CMS to test Higgs anomalous couplings. Here we apply this fact to fit the latest Higgs data. The new aspect of our analysis is a systematic interpretation of the fit parameters within an EFT. Concentrating on the processes of Higgs production and decay that have been measured so far, six parameters turn out to be relevant: , , , , , . A global Bayesian fit is then performed with the result , , , , , . Additionally, we show how this leading-order parametrization can be generalized to next-to-leading order, thus improving the formalism systematically. The differences with a linear EFT analysis including operators of dimension six are also discussed. One of the main conclusions of our analysis is that since the conventional formalism can be properly justified within a QFT framework, it should continue to play a central role in analyzing and interpreting Higgs data.

We consider the Standard Model extended by a heavy scalar singlet in different regions of parameter space and construct the appropriate low-energy effective field theories up to first nontrivial order. This top-down exercise in effective field theory is meant primarily to illustrate with a simple example the systematics of the linear and nonlinear electroweak effective Lagrangians and to clarify the relation between them. We discuss power-counting aspects and the transition between both effective theories on the basis of the model, confirming in all cases the rules and procedures derived in previous works from a bottom-up approach.