SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints arising solely from group theory. We derive these constraints for n=5 at all loop orders using an iterative approach. These constraints generalize well-known tree-level and one-loop group theory relations.Comment: 16 pages, no figures; v2: minor corrections and clarifications, published versio

Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory

Using the novel diagrammatic rules recently proposed by Cachazo, Svrcek, and Witten, I give a compact, manifestly Lorentz-invariant form for tree-level gauge-theory amplitudes with three opposite helicities.Comment: 12 pages, 1 figur

Calculation of 1-loop Hexagon Amplitudes in the Yukawa Model

We calculate a class of one-loop six-point amplitudes in the Yukawa model. The construction of multi-particle amplitudes is done in the string inspired formalism and compared to the Feynman diagrammatic approach. We show that there exists a surprisingly efficient way of calculating such amplitudes by using cyclic identities of kinematic coefficients and discuss in detail cancellation mechanisms of spurious terms. A collection of formulas which are useful for the calculation of massless hexagon amplitudes is given.Comment: 15 pages Late

Recursive Approach to One-loop QCD Matrix Elements

We describe the recursive Approach to One-loop QCD Matrix Elements.Comment: 6 pages, to appear in the proceedings of the 7th International Symposium on Radiative Corrections: Application of Quantum Field Theory to Phenomenology (RADCOR 2005), Japan, 2-7 Oct 200

Exploiting Twistor Techniques for One-loop QCD Amplitudes

In this talk we describe the recursive Approach to One-loop QCD Matrix Elements.Comment: Talk presented by David C. Dunbar at Loop and Legs 2006, 5 page

An Integrand Reconstruction Method for Three-Loop Amplitudes

We consider the maximal cut of a three-loop four point function with massless kinematics. By applying Groebner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.Comment: 15 pages, 1 figur

Multiple Singular Emission in Gauge Theories

I derive a class of functions unifying all singular limits for the emission of a given number of soft or collinear gluons in tree-level gauge-theory amplitudes. Each function is a generalization of the single-emission antenna function of ref. [1]. The helicity-summed squares of these functions are thus also generalizations to multiple singular emission of the Catani--Seymour dipole factorization function.Comment: Corrections for final journal version (sign in eqn. (6.11), equation references, typos in indices) & removal of comment about FD

Reduction method for dimensionally regulated one-loop N-point Feynman integrals

We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral in D=4, and a general two-point integral in D space time dimensions. All the divergences present in the original integral are contained in the general two-point integral and associated coefficients. The problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner. Being derived with no restrictions regarding the external momenta, the method is completely general and applicable for arbitrary kinematics. In particular, it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta, which are unavoidable when calculating one-loop contributions to the hard-scattering amplitude for exclusive hadronic processes at large momentum transfer in PQCD. The iterative structure makes it easy to implement the formalism in an algebraic computer program.Comment: 22 pages, 2 figures; one appendix added, discussions clarified, version to appear in Eur. Phys. J.

Timescales of carbon turnover in soils with mixed crystalline mineralogies

Organic matter–mineral associations stabilize much of the carbon (C) stored globally in soils. Metastable short-range-order (SRO) minerals such as allophane and ferrihydrite provide one mechanism for long-term stabilization of organic matter in young soil. However, in soils with few SRO minerals and a predominance of crystalline aluminosilicate or Fe (and Al) oxyhydroxide, C turnover should be governed by chemisorption with those minerals. Here, we correlate mineral composition from soils containing small amounts of SRO minerals with mean turnover time (TT) of C estimated from radiocarbon (¹⁴C) in bulk soil, free light fraction and mineral-associated organic matter. We varied the mineral amount and composition by sampling ancient soils formed on different lithologies in arid to subhumid climates in Kruger National Park (KNP), South Africa. Mineral contents in bulk soils were assessed using chemical extractions to quantify Fe oxyhydroxides and SRO minerals. Because of our interest in the role of silicate clay mineralogy, particularly smectite (2 : 1) and kaolinite (1 : 1), we separately quantified the mineralogy of the clay-sized fraction using X-ray diffraction (XRD) and measured ¹⁴C on the same fraction. <br><br> Density separation demonstrated that mineral associated C accounted for 40–70 % of bulk soil organic C in A and B1 horizons for granite, nephelinite and arid-zone gabbro soils, and &gt; 80 % in other soils. Organic matter strongly associated with the isolated clay-sized fraction represented only 9–47 % of the bulk soil C. The mean TT of C strongly associated with the clay-sized fraction increased with the amount of smectite (2 : 1 clays); in samples with &gt; 40 % smectite it averaged 1020 ± 460 years. The C not strongly associated with clay-sized minerals, including a combination of low-density C, the C associated with minerals of sizes between 2 µm and 2 cm (including Fe oxyhydroxides as coatings), and C removed from clay-sized material by 2 % hydrogen peroxide had TTs averaging 190 ± 190 years in surface horizons. Summed over the bulk soil profile, we found that smectite content correlated with the mean TT of bulk soil C across varied lithologies. The SRO mineral content in KNP soils was generally very low, except for the soils developed on gabbros under more humid climate that also had very high Fe and C contents with a surprisingly short, mean C TTs. In younger landscapes, SRO minerals are metastable and sequester C for long timescales. We hypothesize that in the KNP, SRO minerals represent a transient stage of mineral evolution and therefore lock up C for a shorter time. <br><br> Overall, we found crystalline Fe-oxyhydroxides (determined as the difference between Fe in dithionate citrate and oxalate extractions) to be the strongest predictor for soil C content, while the mean TT of soil C was best predicted from the amount of smectite, which was also related to more easily measured bulk properties such as cation exchange capacity or pH. Combined with previous research on C turnover times in 2 : 1 vs. 1 : 1 clays, our results hold promise for predicting C inventory and persistence based on intrinsic timescales of specific carbon–mineral interactions

Calculation of Graviton Scattering Amplitudes using String-Based Methods

Techniques based upon the string organisation of amplitudes may be used to simplify field theory calculations. We apply these techniques to perturbative gravity and calculate all one-loop amplitudes for four-graviton scattering with arbitrary internal particle content. Decomposing the amplitudes into contributions arising from supersymmetric multiplets greatly simplifies these calculations. We also discuss how unitarity may be used to constrain the amplitudes.Comment: 25 pages +5 figs. , SWAT-94-37 UCLA/TEP/94/30, Plain TeX. (Typos in eqns. fixed