One light composite Higgs boson facing electroweak precision tests

We study analytically and numerically the bounds imposed by the electroweak precision tests on a minimal composite Higgs model. The model is based on spontaneous SO(5)/SO(4) breaking, so that an approximate custodial symmetry is preserved. The Higgs arises as a pseudo-Goldstone boson at a scale below the electroweak symmetry breaking scale. We show that one can satisfy the electroweak precision constraints without much fine-tuning. This is the case if the left-handed top quark is fully composite, which gives a mass spectrum within the reach of the LHC. However a composite top quark is strongly disfavoured by flavour physics. The alternative is to have a singlet top partner at a scale much lighter than the rest of the composite fermions. In this case the top partner would be light enough to be produced significantly at the LHC.Comment: 15 pages, 4 figures; v2: figures and discussion improved, references added; v3: minor changes, final version to appear in PR

Scale Anomalies, States, and Rates in Conformal Field Theory

This paper presents two methods to compute scale anomaly coefficients in conformal field theories (CFTs), such as the c anomaly in four dimensions, in terms of the CFT data. We first use Euclidean position space to show that the anomaly coefficient of a four-point function can be computed in the form of an operator product expansion (OPE), namely a weighted sum of OPE coefficients squared. We compute the weights for scale anomalies associated with scalar operators and show that they are not positive. We then derive a different sum rule of the same form in Minkowski momentum space where the weights are positive. The positivity arises because the scale anomaly is the coefficient of a logarithm in the momentum space four-point function. This logarithm also determines the dispersive part, which is a positive sum over states by the optical theorem. The momentum space sum rule may be invalidated by UV and/or IR divergences, and we discuss the conditions under which these singularities are absent. We present a detailed discussion of the formalism required to compute the weights directly in Minkowski momentum space. A number of explicit checks are performed, including a complete example in an 8-dimensional free field theory.Comment: 39 pages, 7 figure

Vector-like Bottom Quarks in Composite Higgs Models

Like many other models, Composite Higgs Models feature the existence of heavy vector-like quarks. Mixing effects between the Standard Model fields and the heavy states, which can be quite large in case of the top quark, imply deviations from the SM. In this work we investigate the possibility of heavy bottom partners. We show that they can have a significant impact on electroweak precision observables and the current Higgs results if there is a sizeable mixing with the bottom quark. We explicitly check that the constraints from the measurement of the CKM matrix element $V_{tb}$ are fulfilled, and we test the compatibility with the electroweak precision observables. In particular we evaluate the constraint from the $Z$ coupling to left-handed bottom quarks. General formulae have been derived which include the effects of new bottom partners in the loop corrections to this coupling and which can be applied to other models with similar particle content. Furthermore, the constraints from direct searches for heavy states at the LHC and from the Higgs search results have been included in our analysis. The best agreement with all the considered constraints is achieved for medium to large compositeness of the left-handed top and bottom quarks.Comment: additional figures, extended discussion of numerical result

Constraining new coloured matter from the ratio of 3- to 2-jets cross sections at the LHC

The Large Hadron Collider experiments are probing the evolution of the strong coupling $\alpha_s$ up to the TeV scale. We show how the ratio of 3- to 2-jets cross sections is affected by the presence of new physics and argue that it can be used to place a model-independent bound on new particles carrying QCD color charge. The current data potentially constrains such states to be heavier than a few hundred GeVs.Comment: 9 pages, 7 figure