On pion mass and decay constant from theory

We calculate the pion mass from Goldstone modes in the Higgs mechanism related to the neutron decay. The Goldstone pion modes acquire mass by a vacuum misalignment of the Higgs field. The size of the misalignment is controlled by the ratio between the electronic and the nucleonic energy scales. The nucleonic energy scale is involved in the neutron to proton transformation and the electronic scale is involved in the related creation of the electronic state in the course of the electroweak neutron decay. The respective scales influence the mapping of the intrinsic configuration spaces used in our description. The configuration spaces are the Lie groups U(3) for the nucleonic sector and U(2) for the electronic sector. These spaces are both compact and lead to periodic potentials in the Hamiltonians in coordinate space. The periodicity and strengths of these potentials control the vacuum misalignment and leads to a pion mass of 135.2(1.5) MeV with an uncertainty mainly from the fine structure coupling at pionic energies. The pion decay constant 92 MeV results from comparing the fourth order self-coupling in an effective pion field theory with the corresponding fourth order term in the Higgs potential. We suggest analogies with the Goldberger-Treiman relation.

Abundant solutions of an extended KPII equation combined with a new fourth-order term

An extension of the KPII equation is studied. Adding a new fourth-order derivative term and some second-order derivative terms, we formulate an extended KPII equation. Different types of solutions of the extended equation are obtained by the Hirota bilinear method, and the presented solutions include soliton solutions, lump solutions and interaction solutions. Their dynamical behaviors are analyzed through plots.

Lump Solutions of a Nonlinear PDE Combining with a New Fourth-Order Term Dx2Dt2∗

A nonlinear PDE combining with a new fourth-order term Dx2Dt2 is studied. Adding three new fourth-order derivative terms and some second-order derivative terms, we formulate a combined fourth-order nonlinear partial differential equation, which possesses a Hirota’s bilinear form. The class of lump solutions is constructed explicitly through Hirota’s bilinear method. Their dynamical behaviors are analyzed through plots.

Deflection of light in equatorial plane due to Kerr-Taub-NUT body

According to General Relativity, there are factors like mass, rotation, charge and presence of Cosmological constant that can influence the path of light ray. Apart from these factors, many authors have also reported the influence of gravitomagnetism on the path of light ray. In this study we have discussed the effect of a rotating Kerr-Taub-NUT body where the strength of the gravitomagnetic monopole is represented by the NUT factor or magnetic mass. We use the null geodesic of photon method to obtain the deflection angle of light ray for a Kerr-Taub-NUT body in equatorial plane upto the fourth order term. Our study shows that the NUT factor has a noticeable effect on the path of the light ray. By considering the magnetism to be zero, the expression of bending angle gets reduced to the Kerr bending angle. However, we obtained a non-zero bending angle for a hypothetical massless, magnetic body.

Spectral Calibration Requirements of Radio Interferometers for Epoch of Reionisation Science with the SKA

Spectral features introduced by instrumental chromaticity of radio interferometers have the potential to negatively impact the ability to perform Epoch of Reionisation and Cosmic Dawn (EoR/CD) science. We describe instrument calibration choices that influence the spectral characteristics of the science data, and assess their impact on EoR/CD statistical and tomographic experiments. Principally, we consider the intrinsic spectral response of the antennas, embedded within a complete frequency-dependent primary beam response, and instrument sampling. The analysis is applied to the proposed SKA1-Low EoR/CD experiments. We provide tolerances on the smoothness of the SKA station primary beam bandpass, to meet the scientific goals of statistical and tomographic (imaging) of EoR/CD programs. Two calibration strategies are tested: (1) fitting of each fine channel independently, and (2) fitting of annth-order polynomial for each ~ 1 MHz coarse channel with (n+1)th-order residuals (n= 2, 3, 4). Strategy (1) leads to uncorrelated power in the 2D power spectrum proportional to the thermal noise power, thereby reducing the overall sensitivity. Strategy (2) leads to correlated residuals from the fitting, and residual signal power with (n+1)th-order curvature. For the residual power to be less than the thermal noise, the fractional amplitude of a fourth-order term in the bandpass across a single coarse channel must be < 2.5% (50 MHz), < 0.5% (150 MHz), < 0.8% (200 MHz). The tomographic experiment places constraints on phase residuals in the bandpass. We find that the root-mean-square variability over all stations of the change in phase across any fine channel (4.578 kHz) should not exceed 0.2 degrees.

Scale-invariant scalar spectrum from the nonminimal derivative coupling with fourth-order term

In this paper, an exactly scale-invariant spectrum of scalar perturbation generated during de Sitter spacetime is found from the gravity model of the nonminimal derivative coupling with fourth-order term. The nonminimal derivative coupling term generates a healthy (ghost-free) fourth-order derivative term, while the fourth-order term provides an unhealthy (ghost) fourth-order derivative term. The Harrison–Zel’dovich spectrum obtained from Fourier transforming the fourth-order propagator in de Sitter space is recovered by computing the power spectrum in its momentum space directly. It shows that this model provides a truly scale-invariant spectrum, in addition to the Lee–Wick scalar theory.

The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water

A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.

GAUGED LIFSHITZ MODEL WITH CHERN–SIMONS TERM

We present a gauged Lifshitz Lagrangian including second- and fourth-order spatial derivatives of the scalar field and a Chern–Simons term, and study nontrivial solutions of the classical equations of motion. While the coefficient β of the fourth-order term should be positive in order to guarantee positivity of the energy, the coefficient α of the quadratic one need not be. We investigate the parameter domains and find significant differences in the field behaviors. Apart from the usual vortex field behavior of the ordinary relativistic Chern–Simons–Higgs model, we find in certain parameter domains oscillatory solutions reminiscent of the modulated phases of Lifshitz systems.