Some Features of the Direct and Inverse Double-Compton Effect as Applied to Astrophysics

In the present paper, the process of inverse double-Compton (IDC) scattering is considered in the context of astrophysical applications. It is assumed that the two hard X-ray photons emitted from an astrophysical source are scattered on a free electron and converted into a single soft photon of optical range. Using the QED S-matrix formalism for the derivation of a cross-section of direct double-Compton (DDC) scattering and assuming detailed balance conditions, an analytical expression for the cross-section of the IDC process is presented. It is shown that at fixed energies of incident photons, the inverse cross-section has no infrared divergences, and its behavior is completely defined by the spectral characteristics of the photon source itself, in particular by the finite interaction time of radiation with an electron. Thus, even for the direct process, the problem of resolving infrared divergence actually refers to a real physical source of radiation in which photons are never actually plane waves. As a result, the physical frequency profile of the scattered radiation for DDC as well as for IDC processes is a function of both the intensity and line shape of the incident photon field.

Renormalization group improvement of the effective potential: an EFT approach

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.

All-loop-orders relation between Regge limits of $$ \mathcal{N} $$ = 4 SYM and $$ \mathcal{N} $$ = 8 supergravity four-point amplitudes

We examine in detail the structure of the Regge limit of the (nonplanar) $$ \mathcal{N} $$ N = 4 SYM four-point amplitude. We begin by developing a basis of color factors Cik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through $$ \mathcal{O}\left({\upepsilon}^2\right) $$ O ϵ 2 at two loops, and through $$ \mathcal{O}\left({\upepsilon}^0\right) $$ O ϵ 0 at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the $$ \mathcal{N} $$ N = 8 supergravity four-point amplitude.

Stuckelberg SUSY QED and infrared problem

We review gauge invariant [Formula: see text] supersymmetric massive U(1) gauge theory coupled to matter and Stuckelberg superfields. We focus on the leading order self-energy and vertex correction to the matter field in the massless limit of both the U(1) vector superfield and the Stuckelberg superfield. We explicitly verify that the theory is infrared divergence free in the massless limit. Hence the Stuckelberg mechanism appears to be the efficient route to handle infrared divergences seen in supersymmetric quantum electrodynamics. Since these additional particles have very small masses they can serve as dark matter candidates through “Ultralight particles” mechanism.

Light-front QED, Stueckelberg field and infrared divergence

Stueckelberg mechanism introduces a scalar field, known as Stueckelberg field, so that gauge symmetry is preserved in the massive Abelian gauge theory. In this work, we show that the role of the Stueckelberg field is similar to the Kulish and Faddeev coherent state approach to handle infrared (IR) divergences. We expect that the light-front quantum electrodynamics (LFQED) with Stueckelberg field must be IR finite in the massless limit of the gauge boson. We have explicitly shown the cancellation of IR divergences in the relevant diagrams contributing to self-energy and vertex correction at leading order.

Reduction of gravity-matter and dS gravity to hypersurface

The quantization scheme based on reduction of the physical states I. Y. Park, Hypersurface foliation approach to renormalization of ADM formulation of gravity, Eur. Phys. J. C 75(9) (2015) 459, arXiv:1404.5066 [hep-th] is extended to two gravity-matter systems and pure de Sitter (dS) gravity. For the gravity-matter systems, we focus on quantization in a flat background for simplicity, and renormalizability is established through gauge-fixing of matter degrees of freedom. Quantization of pure dS gravity has several new novel features. It is noted that the infrared divergence does not arise in the present scheme of quantization. The lapse function constraint plays a crucial role.