Dilaton Interactions in QCD and in the Electroweak Sector of the Standard Model

We overview the structure of the effective action involving a dilaton and a Higgs in the Standard Model, which has been computed recently for the neutral currents sector. We discuss the role of the dilatation current ($J_D$) and of an effective degree of freedom appearing in the $J_D V V'$ correlator, with $V$ any neutral current, which can be interpreted as a Nambu-Goldstone mode generated by the anomalous breaking of the dilatation symmetry.Comment: 4 pages, presented at the workshop "QCD@work", Lecce June 18-21 201

Massless Scalar Degrees of Freedom in QCD and in the Electroweak Sector from the Trace Anomaly

The interaction of QCD and electroweak sector with gravity is characterized by the generation of a massless pole in a specific form factor present in the 1-loop effective action. We briefly illustrate how to single out this behaviour in perturbation theory, by taking as an example the $TJJ$ vertex, with $T$ denoting the energy momentum tensor of the Standard Model. The breaking of scale invariance, due to the trace anomaly, is then related to the appearance of a local degree of freedom in the effective action, which is of dilaton type.Comment: 5 pages, presented at the workshop "QCD@work", Lecce, June 18-21, 201

The Trace Anomaly and the Gravitational Coupling of an Anomalous U(1)

We extend a previous computation of the TJJ correlator, involving the energy-momentum tensor of an abelian gauge theory and two vector currents, to the case of mixed axial-vector/vector currents. The study is performed in analogy to the case of the $AVV$ vertex for the chiral anomaly. We derive the general structure of the anomalous Ward identities and provide explicit tests of their consistency using Dimensional Reduction. Mixed massive correlators of the form $TJ_V J_A$ are shown to vanish both by Ward identities and by C-invariance. The result is characterized by the appearance of massless scalar degrees of freedom in the coupling of chiral and vector theories to gravity, affecting both the soft and the ultraviolet region of the vertex. This is in agreement with previous studies of the effective action of gauge and conformal anomalies in QED and QCD.Comment: 30 pages, 3 figure

Conformal anomaly actions for dilaton interactions

We discuss, in conformally invariant field theories such as QCD with massless fermions, a possible link between the perturbative signature of the conformal anomaly, in the form of anomaly poles of the 1-particle irreducible effective action, and its description in terms of Wess-Zumino actions with a dilaton. The two descriptions are expected to capture the UV and IR behaviour of the conformal anomaly, in terms of fundamental and effective degrees of freedom respectively, with the dilaton effective state appearing in a nonlinear realization. As in the chiral case, conformal anomalies seem to be related to the appearance of these effective interactions in the 1PI action in all the gauge-invariant sectors of the Standard Model. We show that, as a consequence of the underlying anomalous symmetry, the infinite hierarchy of recurrence relations involving self-interactions of the dilaton is entirely determined only by the first four of them. This relation can be generalized to any even space-time dimension.Comment: 6 pages, 2 figure

Stability constraints of the scalar potential in extensions of the Standard Model with TeV scale right handed neutrinos

We investigate the stability of the scalar potential in a minimal $U(1)'$ extension of the Standard Model augmented by an extra complex scalar and three right handed neutrinos. We consider a type-I seesaw scenario for the generation of the small neutrino masses. Moreover, we focus our analysis on a class of models potentially accessible at the LHC experiment, in which the vacuum expectation value of the extra scalar is chosen in the TeV range. We show that the requirements of stability of the potential within the perturbative evolution under the renormalization group impose significant constraints on the Yukawa couplings of the right handed neutrinos.Comment: 6 pages, 2 figures, Presented at NOW 2014, 7-14 September 2014, Conca Specchiulla (Otranto-Italy

Three and Four Point Functions of Stress Energy Tensors in D=3 for the Analysis of Cosmological Non-Gaussianities

We compute the correlation functions of 3 and 4 stress energy tensors $(T)$ in D=3 in free field theories of scalars, abelian gauge fields, and fermions, which are relevant in the analysis of cosmological non-gaussianities. These correlators appear in the holographic expressions of the scalar and tensor perturbations derived for holographic cosmological models. The result is simply adapted to describe the leading contributions in the gauge coupling to the same correlators also for a non abelian SU(N) gauge theory. In the case of the bispectrum, our results are mapped and shown to be in full agreement with the corresponding expressions given in a recent holographic study by Bzowski, McFadden and Skenderis. In the 4-T case we present the completely traced amplitude plus all the contact terms. These are expected to appear in a fourth order extension of the holographic formulas for the 4-point functions of scalar metric perturbations.Comment: 29 pages, 3 figure

Trace Anomaly, Massless Scalars and the Gravitational Coupling of QCD

The anomalous effective action describing the coupling of gravity to a non-abelian gauge theory can be determined by a variational solution of the anomaly equation, as shown by Riegert long ago. It is given by a nonlocal expression, with the nonlocal interaction determined by the Green's function of a conformally covariant operator of fourth order. In recent works it has been shown that this interaction is mediated by a simple pole in an expansion around a Minkowski background, coupled in the infrared in the massless fermion limit. This result relies on the local formulation of the original action in terms of two auxiliary fields, one physical scalar and one ghost, which take the role of massless composite degrees of freedom. In the gravity case, the two scalars have provided ground in favour of some recent proposals of an infrared approach to the solution of the dark energy problem, entirely based on the behaviour of the vacuum energy at the QCD phase transition. As a test of this general result, we perform a complete one-loop computation of the effective action describing the coupling of a non-abelian gauge theory to gravity. We confirm the appearance of an anomaly pole which contributes to the trace part of the $TJJ$ correlator and of extra poles in its trace-free part, in the quark and gluon sectors, describing the coupling of the energy momentum tensor ($T$) to two non abelian gauge currents ($J$).Comment: 25 pages, 9 figures. Revised final version, to be published on Phys. Rev.

Prospects for Heavy Scalar Searches at the LHeC

In this article we study the prospects of the proposed Large Hadron electron Collider (LHeC) in the search for heavy neutral scalar particles. We consider a minimal model with one additional complex scalar singlet that interacts with the Standard Model (SM) via mixing with the Higgs doublet, giving rise to a SM-like Higgs boson $h_1$ and a heavy scalar particle $h_2$. Both scalar particles are produced via vector boson fusion and can be tested via their decays into pairs of SM particles, analogously to the SM Higgs boson. Using multivariate techniques we show that the LHeC is sensitive to $h_2$ with masses between 200 and 800 GeV down to scalar mixing of $\sin^2 \alpha \sim 10^{-3}$