If dark matter couples directly to a light force mediator, then it may form bound states in the early universe and in the non-relativistic environment of haloes today. In this work, we establish a field-theoretic framework for the computation of bound-state formation cross-sections, de-excitation and decay rates, in theories with long-range interactions. Using this formalism, we carry out specific computations for scalar particles interacting either via a light scalar or vector mediator. At low relative velocities of the interacting particles, the formation of bound states is enhanced by the Sommerfeld effect. For particle-antiparticle pairs, we show that bound-state formation can be faster than annihilation into radiation in the regime where the Sommerfeld effect is important. The field-theoretic formalism outlined here can be generalised to compute bound-state formation cross-sections in a variety of theories, including theories featuring non-Abelian (albeit non-confining) interactions, such as the electroweak interactions.Comment: 36 pages + appendices + references, 9 figures, 1 table; v2: published versio

Abstract:We consider the generation of the hierarchical charged lepton spectrum and anarchic neutrino masses and mixing angles in warped extra dimensional models with Randall-Sundrum metric. We have classified all possible cases giving rise to realistic spectra for both Dirac and Majorana neutrinos. An anarchic neutrino spectrum requires a convenient bulk symmetry broken by boundary conditions on both UV and IR branes. We have in particular considered the case of Majorana neutrinos with a continuous bulk symmetry. To avoid unwanted massless extra gauge bosons the 4D group should be empty. If the 4D coset is not vanishing it can provide a Wilson Line description of the neutrino Majorana mass matrix. We have studied an example based on the bulk gauge group U(3) ℓ ⊗ U(3) N ⊗ i U(1) E i with the Wilson Line in SO(3) N satisfying all required conditions. A χ 2 -fit to experimental data exhibits 95% CL region in the parameter space with no finetuning. As a consequence of the symmetries of the theory there is no tree-level induced lepton flavor violation and so one-loop processes are consistent with experimental data for KK-modes about a few TeV. The model is easily generalizable to models with IR deformed metrics with similar conclusions.

Traditionally, education has been largely delivered in an in-person format; however, an increasing number of courses are being delivered entirely online or with a blend of online and in-person components. These formats differ along various dimensions, such as the quantity and quality of interpersonal interactions and connections, which will likely lead to different student experiences. Using a sample of 200 undergraduate student responses from an online survey, we compared five different course formats (in-person, synchronous online, asynchronous online, blended with alternating weeks and blended exam only) on students’ perceptions of various elements of their learning environment, including teaching presence, cognitive presence, social presence, sense of community and teamwork. A between groups ANOVA demonstrated significant differences for seven of the eight variables examined. In each case, the in-person format was rated the most positively and the blended exam only format tended to receive the poorest ratings. Overall, our results suggest that live interaction among students, and between students and instructors, whether it is from an in-person format or a blended alternating format, appears to be linked to more positive perceptions of the social learning environment.