Modern Physics Letters A

The precise knowledge of the QED initial state corrections is of instrumental importance in studying high-luminosity measurements in $e^{+}{e}^{-}$ annihilation at facilities like LEP, the International Linear Collider ILC, CLIC, a Giga-$Z$ facility, and the planned FCC_ee. Logarithmic corrections of up to $O({\alpha }^6{L}^5)$ are necessary with various subleading terms taken into account. This applies to both the inclusive measurement of processes like $e^{+}{e}^{-}\to {\gamma }^{\ast }/Z^{\ast }$ and also the forward–backward asymmetry. As has been shown recently, techniques from massive QCD, such as the computation of massive on-shell operator matrix elements, can be used for these calculations. We give an introduction to this topic and present both the calculation methods and the numerical corrections having been reached so far.

In this paper, we verify a method which allows to obtain the $\beta$-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general renormalizable ${𝒩}=1$ supersymmetric gauge theory, a part of the three-loop $\beta$-function depending on the Yukawa couplings is constructed in the general $\xi$-gauge. The result is written in the form of an integral of double total derivatives with respect to the loop momenta. It is demonstrated that all gauge-dependent terms cancel each other in agreement with the general statements. The result in the Feynman gauge (found earlier) coincides with the one obtained by the standard technique which requires to calculate the sum of superdiagrams with two external gauge lines. This fact confirms the correctness of the considered method by a highly nontrivial multiloop calculation.

In this paper, we show how a modified Friedmann equation, originating from a model of the universe built from a certain $W_3$ algebra, has the potential to explain the difference between the Hubble constants extracted from CMB data and from supernova data.

In this paper, the energy density of plane gravitational wave is studied by using Einstein and Møller’s prescription of energy–momentum pseudotensors. The linearly polarized plane gravitational wave solution of Einstein field equation, which has been defined by Bondi et al., is represented by four kinds of different coordinates. The energy distributions of gravitational wave solution in Einstein and Møller’s prescription are obtained. Particularly, the energy component is zero in null coordinates.

In this paper, we update the standard model $d=6$ operators of Weinberg (1979) using a modified notation which accommodates the bilepton extension of the standard model. This may lead to an enhancement of the proton lifetime by orders of magnitude due to mixing first-family with third-family quarks. By contrast, $d=5$ operators which can provide Majorana neutrino masses retain the family structure of their counterparts in the standard model.

In this paper, we generalize the application of the Levi-Civita (L-C) and Kustaanheimo–Stiefel (K-S) regularization methods to quantum mechanical systems in two and three dimensions. Schrödinger equations in two and three dimensions, describing a particle moving under the combined influence of $\frac{1}{r}$ and $r^2$ potentials are mapped to that of a harmonic oscillator with inverted sextic potential, and interactions, in two and four dimensions, respectively. Using the perturbative solutions of the latter systems, we derive the eigen spectrum of the former systems. Using Bohlin–Sundmann transformation, a mapping between the Schrödinger equations describing shifted harmonic oscillator and H-atom is also derived. Exploiting this equivalence, the solution to the former is obtained from the solution of the latter.

In this paper, we use the tridiagonal representation approach to obtain a finite series solution of the radial Schrödinger equation in three dimensions for a spiked oscillator with inverse quartic singularity.