Employing Helicity Amplitudes for Resummation

Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in $4$- and $d$-dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard matching coefficients, for $pp\to H + 0,1,2$ jets, $pp\to W/Z/\gamma + 0,1,2$ jets, and $pp\to 2,3$ jets. These operator bases are completely crossing symmetric, so the results can easily be applied to processes with $e^+e^-$ and $e^-p$ collisions.Comment: 41 pages + 20 pages in Appendices, 1 figure, v2: journal versio

Spatiotemporal symmetries in the disynaptic canal-neck projection

The vestibular system in almost all vertebrates, and in particular in humans, controls balance by employing a set of six semicircular canals, three in each inner ear, to detect angular accelerations of the head in three mutually orthogonal coordinate planes. Signals from the canals are transmitted to eight (groups of) neck motoneurons, which activate the eight corresponding muscle groups. These signals may be either excitatory or inhibitory, depending on the direction of head acceleration. McCollum and Boyle have observed that in the cat the relevant network of neurons possesses octahedral symmetry, a structure that they deduce from the known innervation patterns (connections) from canals to muscles. We rederive the octahedral symmetry from mathematical features of the probable network architecture, and model the movement of the head in response to the activation patterns of the muscles concerned. We assume that connections between neck muscles can be modeled by a “coupled cell network,” a system of coupled ODEs whose variables correspond to the eight muscles, and that this network also has octahedral symmetry. The network and its symmetries imply that these ODEs must be equivariant under a suitable action of the octahedral group. It is observed that muscle motoneurons form natural “push-pull pairs” in which, for given movements of the head, one neuron produces an excitatory signal, whereas the other produces an inhibitory signal. By incorporating this feature into the mathematics in a natural way, we are led to a model in which the octahedral group acts by signed permutations on muscle motoneurons. We show that with the appropriate group actions, there are six possible spatiotemporal patterns of time-periodic states that can arise by Hopf bifurcation from an equilibrium representing an immobile head. Here we use results of Ashwin and Podvigina. Counting conjugate states, whose physiological interpretations can have significantly different features, there are 15 patterns of periodic oscillation, not counting left-right reflections or time-reversals as being different. We interpret these patterns as motions of the head, and note that all six types of pattern appear to correspond to natural head motions

The Employment Contract

This article consists of Professors Ian Ayres and Stewart Schwab \u27s presentation given at the Economic Analysis of State Employment Law Issues Symposium. Following the presentation, audience members and the presenters participated in a discussion concerning employment contracts. The Journal staff and Professors Ayres and Schwab compiled and edited some of these questions and responses

The Employment Contract

This article consists of Professors Ian Ayres and Stewart Schwab \u27s presentation given at the Economic Analysis of State Employment Law Issues Symposium. Following the presentation, audience members and the presenters participated in a discussion concerning employment contracts. The Journal staff and Professors Ayres and Schwab compiled and edited some of these questions and responses

Foam patches behind spilling breakers

Previous theoretical and laboratory studies of spilling breakers on a beach are described and discussed, paying particular attention to models that emphasize the importance of air bubbles in the spill. At first such a spill forms at a sharp crest, and accelerates down the front of the wave as it propagates towards the shore. Then the crest becomes more rounded and this allows part of the aerated water to flow backwards over or under the crest, leaving a foam patch behind. Laboratory experiments in channels of constant width have documented many features of these flows. But recent new observations on gently sloping beaches have revealed another three-dimensional phenomenon, which is not possible in laboratory channels, and which has rarely been described or properly explained. Initially the spill forms nearly simultaneously over a wide front and extends down the forward face of the wave. Then at some point on the spill some of the foam flows over the crest and is left behind in a continuous patch of increasing length. At the same time the rounded portion of the crest propagates sideways in both directions, as the shear flow at its edge entrains fluid from the sharp crests on either side. This leads to a patch that is triangular in shape, with a peak directly behind the initial instability and of zero length where the backward flow has just begun. This idea has been quantitatively tested using selected photos taken from a headland above a beach, rectified to produce plan views. The patches are indeed triangular, sometimes distorted by a shear flow parallel to the wave crest but with a narrow range of peak angles, and on this beach which has a very uniform slope there is no systematic dependence on other parameters such as the wave height at breaking or the bathymetry conditions

N-Jettiness Subtractions for gg→Hgg\to H at Subleading Power

$N$-jettiness subtractions provide a general approach for performing fully-differential next-to-next-to-leading order (NNLO) calculations. Since they are based on the physical resolution variable $N$-jettiness, $\mathcal{T}_N$, subleading power corrections in $\tau=\mathcal{T}_N/Q$, with $Q$ a hard interaction scale, can also be systematically computed. We study the structure of power corrections for $0$-jettiness, $\mathcal{T}_0$, for the $gg\to H$ process. Using the soft-collinear effective theory we analytically compute the leading power corrections $\alpha_s \tau \ln\tau$ and $\alpha_s^2 \tau \ln^3\tau$ (finding partial agreement with a previous result in the literature), and perform a detailed numerical study of the power corrections in the $gg$, $gq$, and $q\bar q$ channels. This includes a numerical extraction of the $\alpha_s\tau$ and $\alpha_s^2 \tau \ln^2\tau$ corrections, and a study of the dependence on the $\mathcal{T}_0$ definition. Including such power suppressed logarithms significantly reduces the size of missing power corrections, and hence improves the numerical efficiency of the subtraction method. Having a more detailed understanding of the power corrections for both $q\bar q$ and $gg$ initiated processes also provides insight into their universality, and hence their behavior in more complicated processes where they have not yet been analytically calculated.Comment: 16 pages, 12 figure

Exploiting jet binning to identify the initial state of high-mass resonances

If a new high-mass resonance is discovered at the Large Hadron Collider, model-independent techniques to identify the production mechanism will be crucial to understand its nature and effective couplings to Standard Model particles. We present a powerful and model-independent method to infer the initial state in the production of any high-mass color-singlet system by using a tight veto on accompanying hadronic jets to divide the data into two mutually exclusive event samples (jet bins). For a resonance of several hundred GeV, the jet binning cut needed to discriminate quark and gluon initial states is in the experimentally accessible range of several tens of GeV. It also yields comparable cross sections for both bins, making this method viable already with the small event samples available shortly after a discovery. Theoretically, the method is made feasible by utilizing an effective field theory setup to compute the jet cut dependence precisely and model independently and to systematically control all sources of theoretical uncertainties in the jet binning, as well as their correlations. We use a 750 GeV scalar resonance as an example to demonstrate the viability of our method.Comment: 6 pages, 2 figures, v2: journal versio

The Gloucester Tabulae set : its discovery and interpretation.

In 2 vols. Maps/charts relating to this thesis have not been filmed; please apply direct to issuing universityAvailable from British Library Document Supply Centre- DSC:DX185508 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Hydrodynamic Fin Function of Brief Squid, Lolliguncula Brevis

Although the pulsed jet is often considered the foundation of a squid\u27s locomotive system, the lateral fins also probably play an important role in swimming, potentially providing thrust, lift and dynamic stability as needed. Fin morphology and movement vary greatly among squid species, but the locomotive role of the fins is not well understood. To begin to elucidate the locomotive role of the fins in squids, fin hydrodynamics were studied in the brief squid Lolliguncula brevis, a species that exhibits a wide range of fin movements depending on swimming speed. Individual squid were trained to swim in both the arms-first and tail-first orientations against currents in a water tunnel seeded with light-reflective particles. Particle-laden water around the fins was illuminated with lasers and videotaped so that flow dynamics around the fins could be analyzed using digital particle image velocimetry (DPIV). Time-averaged forces generated by the fin were quantified from vorticity fields of the fin wake. During the low swimming speeds considered in this study [\u3c2.5 dorsal mantle lengths (DML) per second], L. brevis exhibited four unique fin wake patterns, each with distinctive vortical structures: (1) fin mode I, in which one vortex is shed with each downstroke, generally occurring at low speeds; (2) fin mode II, an undulatory mode in which a continuous linked chain of vortices is produced; (3) fin mode III, in which one vortex is shed with each downstroke and upstroke, and; (4) fin mode IV, in which a discontinuous chain of linked double vortex structures is produced. All modes were detected during tail-first swimming but only fin modes II and III were observed during arms-first swimming. The fins produced horizontal and vertical forces of varying degrees depending on stroke phase, swimming speed, and swimming orientation. During tail-first swimming, the fins functioned primarily as stabilizers at low speeds before shifting to propulsors as speed increased, all while generating net lift. During arms-first swimming, the fins primarily provided lift with thrust production playing a reduced role. These results demonstrate the lateral fins are an integral component of the complex locomotive system of L. brevis, producing lift and thrust forces through different locomotive modes