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Register a new userProbing Effective Field Theory Approach in the CP Violating Minimal Linear $sigma$ Model
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The Minimal Linear $sigma$ Model is a useful theoretical laboratory. One can investigate in a perturbative renormalisable model the properties of the Higgs boson as a pseudo-Goldstone boson, the phenomenological effects of the radial mode of the field $mathtt{s}$ which spontaneously breaks the global $SO(5)$ symmetry and the validity of conclusions based on the Effective Field Theory approach with the field $mathtt{s}$ in the spectrum, after the decoupling of heavy degrees of freedom. In this paper all those issues are discussed in the framework of the Minimal Linear $sigma$ Model with CP violating phases leading to pseudoscalar components in the effective Standard Model Yukawa couplings. Also the character of the electroweak phase transition in the presence of the field $mathtt{s}$ is investigated.
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Extensions of the Standard Model that include vector-like quarks commonly also include additional particles that may mediate new production or decay modes. Using as example the minimal linear $sigma$ model, that reduces to the minimal $SO(5)/SO(4)$ composite Higgs model in a specific limit, we consider the phenomenology of vector-like quarks when a scalar singlet $sigma$ is present. This new particle may be produced in the decays $T to t sigma$, $B to b sigma$, where $T$ and $B$ are vector-like quarks of charges $2/3$ and $-1/3$, respectively, with subsequent decay $sigma to W^+ W^-, ZZ, hh$. By scanning over the allowed parameter space we find that these decays may be dominant. In addition, we find that the presence of several new particles allows for single $T$ production cross sections larger than those expected in minimal models. We discuss the observability of these new signatures in existing searches.
We quantify and examine the uncertainties in predictions of the lightest $CP$ even Higgs boson pole mass $M_h$ in the Minimal Supersymmetric Standard Model (MSSM), utilising current spectrum generators and including some three-loop corrections. There are two broadly different approximations being used: effective field theory (EFT) where an effective Standard Model (SM) is used below a supersymmetric mass scale, and a fixed order calculation, where the MSSM is matched to QCD$times$QED at the electroweak scale. The uncertainties on the $M_h$ prediction in each approach are broken down into logarithmic and finite pieces. The inferred values of the stop mass parameters are sensitively dependent upon the precision of the prediction for $M_h$. The fixed order calculation appears to be more accurate below a supersymmetry (SUSY) mass scale of $M_S approx 1.2$ TeV, whereas above this scale, the EFT calculation is more accurate. We also revisit the range of the lightest stop mass across fine-tuned parameter space that has an appropriate stable vacuum and is compatible with the lightest $CP$ even Higgs boson $h$ being identified with the one discovered at the ATLAS and CMS experiments in 2012; we achieve a maximum value of $sim 10^{11}$ GeV.
We develop the geometric formulation of the Standard Model Effective Field Theory (SMEFT). Using this approach we derive all-orders results in the $sqrt{2 langle H^dagger H rangle}/Lambda$ expansion relevant for studies of electroweak precision and Higgs data.
If the Standard Model is understood as the first term of an effective field theory, the anomaly-cancellation conditions have to be worked out and fulfilled order by order in the effective field-theory expansion. We bring attention to this issue and study in detail a subset of the anomalies of the effective field theories at the electroweak scale. The end result is a set of sum rules for the operator coefficients. These conditions, which are necessary for the internal consistency of the theory, lead to a number of phenomenological consequences when implemented in analyses of experimental data. In particular, they not only decrease the number of free parameters in different physical processes but have the potential to relate processes with different flavor content. Conversely, a violation of these conditions would necessarily imply the existence of undetected non-decoupling new physics associated with the electroweak energy scale.
We use a new weak basis invariant approach to classify all the observable phases in any extension of the Standard Model (SM). We apply this formalism to determine the invariant CP phases in a simplified version of the Minimal Supersymmetric SM with only three non-trivial flavour structures. We propose four experimental measures to fix completely all the observable phases in the model. After these phases have been determined from experiment, we are able to make predictions on any other CP-violating observable in the theory, much in the same way as in the Standard Model all CP-violation observables are proportional to the Jarlskog invariant.
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