Constrained Differential Renormalization of Yang-Mills Theories

We renormalize QCD to one loop in coordinate space using constrained differential renormalization, and show explicitly that the Slavnov-Taylor identities are preserved by this method.Comment: LaTex, 13 pages with 2 ps figure

Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics

We examine the nonperturbative structure of the radiatively induced Chern-Simons term in a Lorentz- and CPT-violating modification of QED. Although the coefficient of the induced Chern-Simons term is in general undetermined, the nonperturbative theory appears to generate a definite value. However, the CPT-even radiative corrections in this same formulation of the theory generally break gauge invariance. We show that gauge invariance may yet be preserved through the use of a Pauli-Villars regulator, and, contrary to earlier expectations, this regulator does not necessarily give rise to a vanishing Chern-Simons term. Instead, two possible values of the Chern-Simons coefficient are allowed, one zero and one nonzero. This formulation of the theory therefore allows the coefficient to vanish naturally, in agreement with experimental observations.Comment: 8 page

Electroweak Precision Observables and the Unhiggs

We compute one-loop corrections to the S and T parameters in the Unhiggs scenario. In that scenario, the Standard Model Higgs is replaced by a non-local object, called the Unhiggs, whose spectral function displays a continuum above the mass gap. The Unhiggs propagator has effectively the same UV properties as the Standard Model Higgs propagator, which implies that loop corrections to the electroweak precision observables are finite and calculable. We show that the Unhiggs is consistent with electroweak precision tests when its mass gap is at the weak scale; in fact, it then mimics a light SM Higgs boson. We also argue that the Unhiggs, while being perfectly visible to electroweak precision observables, is invisible to detection at LEP.Comment: 13 pages; v2: references added, discussion of production cross-section expande

Wilsonian renormalisation of CFT correlation functions: Field theory

We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space allows us to select convenient non-linear parametrisations that serve different purposes. First, we identify normal parameters in which the renormalisation group flows take their simplest form; normal correlators are defined by functional differentiation with respect to these parameters. The renormalised correlation functions are given by the continuum limit of correlators associated to a cutoff-dependent parametrisation, which can be related to the renormalisation group flows. The necessary linear and non-linear counterterms in any arbitrary parametrisation arise in a natural way from a change of coordinates. We show that, in a class of minimal subtraction schemes, the renormalised correlators are exactly equal to normal correlators evaluated at a finite cutoff. To illustrate the formalism and the main results, we compare standard diagrammatic calculations in a scalar free-field theory with the structure of the perturbative solutions to the Polchinski equation close to the Gaussian fixed point.This work has been supported by the Spanish MICINN project FPA 2013-47836-C3-2-P, the MINECO project FPA2016-78220-C3-1-P and by the European Commission through the contract PITN-GA-2012-316704 (HIGGSTOOLS)

Impact of extra particles on indirect Z' limits

We study the possibility of relaxing the indirect limits on extra neutral vector bosons by their interplay with additional new particles. They can be systematically weakened, even below present direct bounds at colliders, by the addition of more vector bosons and/or scalars designed for this purpose. Otherwise, they appear to be robust.Comment: Latex 23 pages, 8 eps figures. Minor changes, version published in Phys. Rev.

Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED

We consider a Lorentz-violating modification to the fermionic Lagrangian of QED that is known to produce a finite Chern-Simons term at leading order. We compute the second order correction to the one-loop photon self-energy in the massless case using an exact propagator and a nonperturbative formulation of the theory. This nonperturbative theory assigns a definite value to the coefficient of the induced Chern-Simons term; however, we find that the theory fails to preserve gauge invariance at higher orders. We conclude that the specific nonperturbative value of the Chern-Simons coefficient has no special significance.Comment: 8 pages, very minor change