Zero-Range Effective Field Theory for Resonant Wino Dark Matter III. Annihilation Effects

Near a critical value of the wino mass where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold, low-energy winos can be described by a zero-range effective field theory (ZREFT) in which the winos interact nonperturbatively through a contact interaction and through Coulomb interactions. The effects of wino-pair annihilation into electroweak gauge bosons are taken into account through the analytic continuation of the real parameters for the contact interaction to complex values. The parameters of ZREFT can be determined by matching wino-wino scattering amplitudes calculated by solving the Schr\"odinger equation for winos interacting through a real potential due to the exchange of electroweak gauge bosons and an imaginary potential due to wino-pair annihilation into electroweak gauge bosons. ZREFT at leading order gives an accurate analytic description of low-energy wino-wino scattering, inclusive wino-pair annihilation, and a wino-pair bound state. ZREFT can also be applied to partial annihilation rates, such as the Sommerfeld enhancement of the annihilation rate of wino pairs into monochromatic photons.Comment: 57 pages, 25 figures. Published version in JHEP. Final part of a 3 part series. Part 1: arXiv:1706.02253 and 10.1007/JHEP11(2017)108. Part 2: arXiv:1708.07155 and 10.1007/JHEP02(2018)15

Zero-Range Effective Field Theory for Resonant Wino Dark Matter II. Coulomb Resummation

Near a critical value of the wino mass where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold, low-energy winos can be described by a zero-range effective field theory (ZREFT) in which the winos interact nonperturbatively through a contact interaction and charged winos also have electromagnetic interactions. At energies near the wino-pair thresholds, the Coulomb interaction from photon exchange between charged winos must also be treated nonperturbatively. The parameters of ZREFT can be determined by matching wino-wino scattering amplitudes calculated by solving the Schr\"odinger equation for winos interacting through a potential due to the exchange of electroweak gauge bosons. With Coulomb resummation, ZREFT at leading order gives a good description of the low-energy two-body observables for winos.Comment: 46 pages, 21 figures. Corrected typos in version 1. Published version in JHE

Planar and oblique shock wave interaction with a droplet seeded gas cylinder

We present an experimental study of a shock interaction with an initially diffuse heavy-gas cylinder seeded with submicron-scale glycol droplets. Unlike most earlier studies, the investigation covers not just a quasi-two-dimensional geometry, where the axis of the cylinder is parallel to the plane of the shock, but also the oblique interaction at an angle of 15\u25e6 between the cylinder axis and the plane of the shock wave. Our experimental data cover the range of Mach numbers from 1.2 to 2.4. The heavy gas cylinder is produced by injecting sulfur hexafluoride pre-mixed with glycol vapor into the test section of a tiltable shock tube through a co-flowing nozzle, with the gravity-driven flow of the heavy gas stabilized by an annular flow of air in the downward direction. Droplets in the gas cylinder are visualized via Mie scattering of diffuse white light. Two views of the flow—side and top— are simultaneously captured by a high-speed gated and intensified CCD camera, producing a spatially and temporally resolved description of the evolution of the gas cylinder upon impul- sive acceleration. While the observations for the planar interaction reveal that the large-scale flow structure remains largely two-dimensional, confirming the assump- tions of earlier studies, during the oblique shock interaction, we observe evidence of flow evolution in three dimensions, including asymmetric interaction of the gas cylin- der with the boundary layers forming on the walls of the shock tube, and rotation of this cylinder in the vertical plane parallel to the streamwise direction

Equal Entries in Totally Positive Matrices

We show that the maximal number of equal entries in a totally positive (resp. totally nonsingular) $n\textrm{-by-}n$ matrix is $\Theta(n^{4/3})$ (resp. $\Theta(n^{3/2}$)). Relationships with point-line incidences in the plane, Bruhat order of permutations, and $TP$ completability are also presented. We also examine the number and positionings of equal $2\textrm{-by-}2$ minors in a $2\textrm{-by-}n$ $TP$ matrix, and give a relationship between the location of equal $2\textrm{-by-}2$ minors and outerplanar graphs.Comment: 15 page

Doubly stochastic continuous-time hidden Markov approach for analyzing genome tiling arrays

Microarrays have been developed that tile the entire nonrepetitive genomes of many different organisms, allowing for the unbiased mapping of active transcription regions or protein binding sites across the entire genome. These tiling array experiments produce massive correlated data sets that have many experimental artifacts, presenting many challenges to researchers that require innovative analysis methods and efficient computational algorithms. This paper presents a doubly stochastic latent variable analysis method for transcript discovery and protein binding region localization using tiling array data. This model is unique in that it considers actual genomic distance between probes. Additionally, the model is designed to be robust to cross-hybridized and nonresponsive probes, which can often lead to false-positive results in microarray experiments. We apply our model to a transcript finding data set to illustrate the consistency of our method. Additionally, we apply our method to a spike-in experiment that can be used as a benchmark data set for researchers interested in developing and comparing future tiling array methods. The results indicate that our method is very powerful, accurate and can be used on a single sample and without control experiments, thus defraying some of the overhead cost of conducting experiments on tiling arrays.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS248 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org