Solving the strong CP problem with non-conventional CP

A very simple model is presented where all CP violation in Nature is spontaneous in origin. The CKM phase is generated unsuppressed and the strong CP problem is solved with only moderately small couplings between the SM and the CP violation sector or mediator sector because corrections to $\bar{\theta}$ arise only at two loops. The latter feature follows from an underlying unconventional CP symmetry of order 4 imposed in the sectors beyond the SM composed of only two vector-like quarks of charge $-1/3$ and one complex scalar singlet. No additional symmetry is necessary to implement the Nelson-Barr mechanism.Comment: Comments added, comply with published versio

Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints

We compute the Coulomb correction $\mathcal{C}$ to the a. c. conductivity of interacting massless Dirac particles in graphene in the collisionless limit using the polarization tensor approach in a regularization independent framework. Arbitrary parameters stemming from differences between logarithmically divergent integrals are fixed on physical grounds exploiting only spatial $O(2)$ rotational invariance of the model which amounts to transversality of the polarization tensor. Consequently $\mathcal{C}$ is unequivocally determined to be $(19- 6\pi)/12$ within this effective model. We compare our result with explicit regularizations and discuss the origin of others results for $\mathcal{C}$ found in the literature

Subtleties in the beta function calculation of N=1 supersymmetric gauge theories

We investigate some peculiarities in the calculation of the two-loop beta-function of $N=1$ supersymmetric models which are intimately related to the so-called "Anomaly Puzzle". There is an apparent paradox when the computation is performed in the framework of the covariant derivative background field method. In this formalism, it is obtained a finite two-loop effective action, although a non-null coefficient for the beta-function is achieved by means of the renormalized two-point function in the background field. We show that if the standard background field method is used, this two-point function has a divergent part which allows for the calculation of the beta-function via the renormalization constants, as usual. Therefore, we conjecture that this paradox has its origin in the covariant supergraph formalism itself, possibly being an artifact of the rescaling anomaly.Comment: Few misprintings corrected and comments added. To meet the version to be published at European Physical Journal

On the viability of a light scalar spectrum for 3-3-1 models

In this work we study an effective version of the 3-3-1 model, in which the particle content is the same of the 2HDM. We show that the inherited structure from the $SU(3)_C \otimes SU(3)_L \otimes U(1)_X$ gauge group has a series of consequences, the most relevant one being the prediction of the masses of the neutral scalar to be of the order or lower than the mass of the charged scalar. Given current constraints from collider searches, B-physics, as well as theoretical constraints such as perturbativity of quartic couplings and stability of the scalar potential, we find that the new scalars cannot be lighter than 350 GeV.Comment: Complies with the accepted version at JHE

Explicit parametrization of more than one vector-like quark of Nelson-Barr type

Nelson-Barr models solve the strong CP problem based on spontaneous CP violation and generically requires vector-like quarks (VLQs) mixing with standard quarks to transmit the CP violation. We devise an explicit parametrization for the case of two VLQs of either down-type or up-type and quantitatively study several aspects including the hierarchy of the VLQ Yukawas and their irreducible contribution to $\bar{\theta}$. In particular, with the use of the parametrization, we show that a big portion of the parameter space for two up-type VLQs at the TeV scale is still allowed by the constraint on $\bar{\theta}$, although this case had been previously shown to be very restricted based on estimates

Dimensional regularization vs methods in fi xed dimension with and without y5

We study the Lorentz and Dirac algebra, including the antisymmetric e tensor and the y 5 matrix, in implicit gauge-invariant regularization/renormalization methods de ned in xed integer dimensions. They include constrained differential, implicit and four-dimensional renormalization. We nd that these xed-dimension methods face the same di culties as the different versions of dimensional regularization. We propose a consistent procedure in these methods, similar to the consistent version of regularization by dimensional reduction.The work of A.M.B. and M.P.V. has been supported by the Spanish MINECO project FPA2016-78220-C3-1-P (Fondos FEDER) and the Junta de Andalucía grant FQM101. The work of M.P.V. has also been supported by the European Commission, through the contract PITN-GA-2012-316704 (HIGGSTOOLS). A.L.C. acknowledges nancial support from CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), Brazil, as well as networking support by the COST Action CA16201

Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams

Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IReg program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multi-loop amplitude in a well defined set of basic divergent integrals in one loop momentum only which is the essence of IReg. Moreover, we conjecture that momentum routing invariance in the loops, which has been shown to be connected with gauge symmetry, is a fundamental symmetry of any Feynman diagram in a renormalizable quantum field theory