Two-current correlations in the pion in the Nambu and Jona-Lasinio model

We present an analysis of two-current correlations for the pion in the Nambu–Jona-Lasinio model, with Pauli–Villars regularization. We provide explicit expressions in momentum space for two-current correlations corresponding to the zeroth component of the vector Dirac bilinear in the quark vertices, which has been evaluated on the lattice, thinking to applications in a high energy framework, as a step towards the calculation of pion double parton distributions. The numerical results show a remarkable qualitative agreement with recent lattice data. The factorization approximation into one-body currents is discussed based on previous evaluation of the relevant low energy matrix elements in the Nambu–Jona-Lasinio model, confirming the lattice result.

Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model

In this article, we study the two-flavor Nambu and Jona-Lasinio (NJL) phase diagrams on the T–μ plane through three regularization methods. In one of these, we introduce an infrared three-momentum cutoff in addition to the usual ultraviolet regularization to the quark loop integrals and compare the obtained phase diagrams with those obtained from the NJL model with proper time regularization and Pauli–Villars regularization. We have found that the crossover appears as a band with a well-defined width in the T–μ plane. To determine the extension of the crossover zone, we propose a novel criterion, comparing it to another criterion that is commonly reported in the literature; we then obtain the phase diagrams for each criterion. We study the behavior of the phase diagrams under all these schemes, focusing on the influence of the regularization procedure on the crossover zone and the presence or absence of critical end points.

Pauli–Villars regularization elucidated in Bopp–Podolsky’s generalized electrodynamics

We discuss an inherent Pauli–Villars regularization in Bopp–Podolsky’s generalized electrodynamics. Introducing gauge-fixing terms for Bopp–Podolsky’s generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli–Villars regularization independent of the gauge choice made in Maxwell’s usual electromagnetism. According to our realization, the length dimensional parameter a associated with Bopp–Podolsky’s higher order derivatives corresponds to the inverse of the Pauli–Villars regularization mass scale $$\Lambda $$Λ, i.e. $$a = 1/\Lambda $$a=1/Λ. Solving explicitly the classical static Bopp–Podolsky’s equations of motion for a specific charge distribution, we explore the physical meaning of the parameter a in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics.

Axial-anomaly in noncommutative QED and Pauli–Villars regularization

We calculate the [Formula: see text](1) axial-anomaly in two and four dimensions using a modified path integral method coupled to a Pauli–Villars regulator field in the noncommutative QED. Pauli–Villars regularization method provides us with unambiguous way to connect the modified path integral formalism with perturbative axial Ward identities at each step of calculations.

Light front Hamiltonian for boson form of QED (1 + 1) in Pauli–Villars regularization

Light front (LF) Hamiltonian for QED in [Formula: see text] dimensions is constructed using the boson form of this model with additional Pauli–Villars-type ultraviolet regularization. Perturbation theory, generated by this LF Hamiltonian, is proved to be equivalent to usual covariant chiral perturbation theory. The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some renormalization of coupling constants. The obtained results can be useful when one attempts to apply LF Hamiltonian approach for [Formula: see text]-dimensional models like QCD.

Gravitational Friedel oscillations in higher-derivative and infinite-derivative gravity?

When a positively charged impurity is placed inside a cold metal, the resulting charge density around that object exhibits characteristic ripples to negative values, known as Friedel oscillations. In this essay, we describe a somewhat analogous effect in (i) linearized higher-derivative gravity and (ii) linearized infinite-derivative “ghost-free” gravity: when a gravitational impurity (point particle) is placed in Minkowski vacuum, the local energy density [Formula: see text] (with [Formula: see text]) exhibits oscillations to negative values. The wavelength of these oscillations is roughly given by (i) the Pauli–Villars regularization scale and (ii) the scale of nonlocality. We hence dub this phenomena gravitational Friedel oscillations.

The use of Pauli–Villars regularization in string theory

The proper-time regularization of bosonic string reproduces the results of canonical quantization in a special scaling limit where the length in target space has to be renormalized. We repeat the analysis for the Pauli–Villars regularization and demonstrate the universality of the results. In the mean-field approximation, we compute the susceptibility anomalous dimension and show it equals 1/2. We discuss the relation with the previously known results on lattice strings.

Meson and diquark condensates in the NJL model and the Fermi momentum

Quark–anti quark and diquark condensation have been investigated in the framework of the NJL model. The Pauli–Villars regularization scheme have been used for the investigation of meson condensation in three dimension whereas the four dimensional case has been studied using the Schwinger–Dyson equation considering the Hartree approximation. Diquark condensation in three and four dimension have also been studied considering the Pauli–Villars regularization scheme. Using the Fermi momentum [Formula: see text] of the particle as cut-off parameter, the gap energy/coherence length for meson condensation [Formula: see text] have been investigated whereas for diquark [Formula: see text] the critical gap energy/critical coherence length (the distance over which there would be no diquark condensation) have been extracted. The variation of the coherence length/gap energy with [Formula: see text] have also been investigated. The results are compared with exciting data. Some interesting observations are made.