International Journal of Modern Physics A

Starting from a well-defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare parameters, respectively. We apply our formalism to the minimal subtraction scheme using dimensional regularization. We first argue that the relevant regularization scale in this case should be dimensionless. By relating bare and renormalized parameters to physical observables, we calculate the coefficients of the renormalization group equation up to two-loop order in the ${\varphi }^4$ theory. We show that the usual assumption, considering the bare parameters to be independent of the regularization scale, is not a direct consequence of any physical argument. The coefficients that we find in our two-loop calculation are identical to the standard practice. We finally comment on the decoupling properties of the renormalized coupling constant.

The physics related to the form factors of the energy–momentum tensor spans a wide spectrum of problems, and includes gravitational physics, hard-exclusive reactions, hadronic decays of heavy quarkonia, and the physics of exotic hadrons described as hadroquarkonia. It also provides access to the “last global unknown property:” the D-term. We review the physics associated with the form factors of the energy–momentum tensor and the D-term, their interpretations in terms of mechanical properties, their applications, and the current experimental status.

Recently, Borzou et al. (BSSY) generalized the Shiromizu–Maeda–Sasaki (SMS) formulation to $f(R)$-bulks. BSSY brane projected equation carries an additional stress tensor, besides SMS correction for Einstein’s theory on the brane. If we change this perspective, by requiring BSSY tensor in the geometrical side, acting as $f(R)$-brane generator, it is possible to relate $f(R)$-brane/bulk theories, by using curvature dynamical constraint (CDC), a concept that we developed. Since brane and bulk are $f(R)$, 5D/4D scalar curvatures also play a dynamical role and, thus, a dynamical version to Gauss equation trace, or CDC, must be offered. We will work yet in a specific case to obtain $f(R)$-unimodular gravity, formally identical with that obtained by Nojiri et al. (NOO). Therefore, two applications which consider cosmological scenarios in $f(R)$-unimodular gravity with dark radiation correction will be offered.

We study numerically the chromoelectric–chromomagnetic asymmetry of the dimension two gluon condensate and the longitudinal gluon propagator at $T\simeq T_c$ in the Landau-gauge $SU(2)$ lattice gauge theory. We show that substantial correlation between the asymmetry and the Polyakov loop as well as the correlation between the longitudinal propagator and the Polyakov loop pave the way to studies of the critical behavior of the asymmetry and the longitudinal propagator. The respective values of critical exponents and amplitudes are evaluated.

In the Standard Model (SM), the $\rho$ parameter is equal to 1 and the ratio ${\lambda }_{WZ}$ of Higgs $\to ZZ$ and Higgs $\to WW$ is also equal to 1 at the tree level. When going beyond the SM with more than one type of Higgs representations, these quantities may be different from the SM predictions which can provide crucial information about new physics. There may also exist a certain charged Higgs $h^{+}$ decays into a $W^{+}$ and a $Z$. Imposing a custodial symmetry can force the parameter $\rho$ to be equal to 1 with certain predictions for ${\lambda }_{WZ}$ and $h^{+}\to W^{+}Z$. However, imposing $\rho =1$ without custodial symmetry may have different predictions. We show how differences arise and how to use experimental data to obtain information about the underlying physics in a model with the SM, plus a real and a complex $SU{(2)}_L$ triplet.

The understanding of the basic properties of the ultrahigh-energy extensive air showers is dependent on the description of hadronic interactions in an energy range beyond that probed by the LHC. One of the uncertainties present in the modeling of air showers is the treatment of diffractive interactions, which are dominated by nonperturbative physics and usually described by phenomenological models. These interactions are expected to affect the development of the air showers, since they provide a way of transporting substantial amounts of energy deep in the atmosphere, modifying the global characteristics of the shower profile. In this paper, we investigate the impact of diffractive interactions in the observables that can be measured in hadronic collisions at high energies and ultrahigh-energy cosmic ray interactions. We consider three distinct phenomenological models for the treatment of diffractive physics and estimate the influence of these interactions on the elasticity, number of secondaries, longitudinal air shower profiles and muon densities for proton-air and iron-air collisions at different primary energies. Our results demonstrate that even for the most recent models, diffractive events have a non-negligible effect on the observables and that the distinct approaches for these interactions, present in the phenomenological models, still are an important source of theoretical uncertainty for the description of the extensive air showers.

We study the possibility of the existence of the electric current, formed by massive electrons and positrons, flowing along an external magnetic field. The charged fermions are supposed to have nonzero anomalous magnetic moments and electroweakly interact with background matter. The expression for the current is obtained on the basis of the exact solution of the Dirac equation in the corresponding external fields. We demonstrate that, in the state of equilibrium, such a current is vanishing for any characteristics of the electron–positron plasma as well as the external fields. Our results are compared with the recent findings of other authors.