CSW rules for massive matter legs and glue loops

Cachazo-Svrcek-Witten-type Feynman rules for massive matter scalar legs and pure glue loops are presented, obtained by deriving them directly from the space-time action. We comment on the derivation and some sample applications, in particular to calculating one loop effects in pure Yang-Mills theory. Furthermore, we derive CSW rules for effective Higgs-gluon couplings studied in the literature. In addition, it is shown how twistor techniques for deriving canonical field transformations explored for massless scalars extend to massless fermions.Comment: 6 pages, to appear in the proceedings of the international conference on Loops and Legs in Quantum Field Theory, Sondershausen, 20-25 April 200

Perturbative expansion of N<8 Supergravity

We characterise the one-loop amplitudes for N=6 and N=4 supergravity in four dimensions. For N=6 we find that the one-loop n-point amplitudes can be expanded in terms of scalar box and triangle functions only. This simplification is consistent with a loop momentum power count of n-3, which we would interpret as being n+4 for gravity with a further -7 from the N=6 superalgebra. For N=4 we find that the amplitude is consistent with a loop momentum power count of n, which we would interpret as being n+4 for gravity with a further -4 from the N=4 superalgebra. Specifically the N=4 amplitudes contain non-cut-constructible rational terms.Comment: 13 pages. v2 adds analytic expression for rational parts of 5-pt 1-loop N=4 SUGRA amplitude; v3 normalisations clarifie

Obtaining One-loop Gravity Amplitudes Using Spurious Singularities

The decomposition of a one-loop scattering amplitude into elementary functions with rational coefficients introduces spurious singularities which afflict individual coefficients but cancel in the complete amplitude. These cancellations create a web of interactions between the various terms. We explore the extent to which entire one-loop amplitudes can be determined from these relationships starting with a relatively small input of initial information, typically the coefficients of the scalar integral functions as these are readily determined. In the context of one-loop gravity amplitudes, of which relatively little is known, we find that some amplitudes with a small number of legs can be completely determined from their box coefficients. For increasing numbers of legs, ambiguities appear which can be determined from the physical singularity structure of the amplitude. We illustrate this with the four-point and N=1,4 five-point (super)gravity one-loop amplitudes.Comment: Minor corrections. Appendix adde

The n-point MHV one-loop Amplitude in N=4 Supergravity

We present an explicit formula for the n-point MHV one-loop amplitude in a N=4 supergravity theory. This formula is derived from the soft and collinear factorisations of the amplitude.Comment: 8 pages; v2 References added. Minor changes to tex

Statistical Analysis of Observed Iceberg Drift

Eight iceberg trajectories observed by the U.S. Coast Guard during 1965, 1967, and 1968 have been subjected to preliminary analysis. The data were obtained by tracking the icebergs relative to fixed reference markers using visual bearings and radar ranges. Speed ratios and drift angles were calculated for each half hour of iceberg trajectory. It was found that at low wind speeds the effects of permanent currents, older wind-driven currents, and tidal currents predominate over wind drag and new wind-driven currents, whereas at wind speeds of over 10 knots the wind has a significant effect on the drift of an iceberg. The ratio of the drag coefficient for the iceberg's above-water portion to the drag coefficient for its submerged portion was found to range from 1.5 to approximately 7

Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation

Soft and collinear factorisations can be used to construct expressions for amplitudes in theories of gravity. We generalise the "half-soft" functions used previously to "soft-lifting" functions and use these to generate tree and one-loop amplitudes. In particular we construct expressions for MHV tree amplitudes and the rational terms in one-loop amplitudes in the specific context of N=4 supergravity. To completely determine the rational terms collinear factorisation must also be used. The rational terms for N=4 have a remarkable diagrammatic interpretation as arising from algebraic link diagrams.Comment: 18 pages, axodraw, Proof of eq. 4.3 adde

KLT relations from the Einstein-Hilbert Lagrangian

The Kawai-Lewellen-Tye (KLT) relations derived from string theory tell us that perturbative gravity amplitudes are the "square" of the corresponding amplitudes in gauge theory. Starting from the light-cone Lagrangian for pure gravity we make these relations manifest off-shell, for three- and four-graviton vertices, at the level of the action.Comment: 9 page

CSW rules for a massive scalar

We derive the analog of the Cachazo-Svrcek-Witten (CSW) diagrammatic Feynman rules for four dimensional Yang-Mills gauge theory coupled to a massive colored scalar. The mass term is shown to give rise to a new tower of vertices in addition to the CSW vertices for massless scalars in non-supersymmetric theories. The rules are derived directly from an action, once through a canonical transformation within light-cone Yang-Mills and once by the construction of a twistor action. The rules are tested against known results in several examples and are used to simplify the proof of on-shell recursion relations for amplitudes with massive scalars.Comment: 12 pages, 2 figures; v2: minor typos corrected and clarifications added, published versio

Investigations on the replacement of maize products in rations for dairy cows and fattening bulls

For different reasons as for example the occurrence of pests like Diabrotica virgifera there may be a shortage in availability of maize products for ruminant feeding. Therefore, different feeding studies on replacement of maize products in rations for dairy cows and fattening bulls were conducted as a part of the “Diabrotica research programme” set up by the federal government of Germany and the federal state of Bavaria. The main focus was set to on suitability of alfalfa as well as grass silage as a roughage source for dairy cows and fattening bulls. It is shown that partial replacement of maize silage by these products allows producing at high production level in Simmental cows and fattening bulls. A decisive advantage is the possibility to reduce the portion of protein concentrates like soybean or rape meal in the diets. Moreover, other beneficial aspects for ruminant feeding such as the high structural value of alfalfa silage are discussed. In ruminant feeding, corn is used as an energy rich dietary component. As a part of the programme a dairy cow feeding trial was conducted to evaluate whether replacement of corn by wheat is a promising possibility to reduce portion of maize products in ruminant diets. Results of the study demonstrate the limits of these feeding strategies, especially in maize silage based diets high in energy concentration and in the concentration of soluble carbohydrates. In these diets, concentrations of degradable starch and sugar are often near or above the maximum recommended amounts. For these reasons use of corn as a source of undegradable starch is preferable to the use of other cereals to prevent conditions that promote rumen acidosis.Key words: dairy cows, fattening bulls, roughage source, starch sourceUntersuchungen zum Ersatz von Maisprodukten in Rationen für Milchkühe und MastbullenZusammenfassungAus unterschiedlichen Gründen, wie zum Beispiel dem Auftreten von Schadorganismen wie Diabrotica virgifera, könnte Mais als Rinderfutter knapp werden. Deshalb wurden verschiedene Fütterungsversuche zum Ersatz von Maiserzeugnissen in Futterrationen für Milchkühe und Mastbullen im Rahmen des „Diabrotica-Forschungsprogramms“ des Bundes und des Bundeslandes Bayern durchgeführt. Das Hauptaugenmerk lag auf Luzerne- und Grassilage als Raufutter für Milchkühe und Mastbullen. Es wurde festgestellt, dass ein teilweiser Ersatz von Silomais durch diese Erzeugnisse ein hohes Produktionsniveau bei Simmentalkühen und Mastbullen ermöglicht. Ein entscheidender Vorteil besteht darin, dass der Anteil an Proteinkonzentraten wie Soja- oder Rapsextraktionsschrot am Futter verringert werden kann. Außerdem werden weitere positive Aspekte bei der Rinderfütterung hohe Strukturwert von Luzernesilage diskutiert. Bei der Rinderfütterung wird Mais als energiereiche Nahrungsquelle verwendet. Im Rahmen eines Milchkuhfütterungsversuchs sollte festgestellt werden, ob der Ersatz von Mais durch Weizen eine aussichtsreiche Möglichkeit für die Verringerung des Maisanteils am Rinderfutter ist. Die Ergebnisse der Studie zeigen die Grenzen solcher Fütterungsstrategien, insbesondere bei maissilagebasierten Rationen mit hohem Energiegehalt und hohen Gehalten an löslichen Kohlenhydraten. In solchen Futtermitteln liegt die Konzentration abbaubarer Stärke und Zucker oft nahe an oder über den maximal empfohlenen Mengen. Aus diesem Grund wird Mais als Quelle nicht abbaubarer Stärke anderen Getreiden vorgezogen werden, um die Förderung von Azidose zu vermeiden.Stichwörter: Milchvieh, Mastbulle, Grobfutter, Stärkequelle