Efficient analytic computation of higher-order QCD amplitudes

URL: http://www-spht.cea.fr/articles/t95/026/ Le calcul analytique efficace des amplitudes aux ordres supérieurs en QCDWe review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. Particularly useful are the constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes. Certain sequences of one-loop helicity amplitudes with an arbitrary number of external gluons have been obtained using these constraints

Inherited Twistor-Space Structure of Gravity Loop Amplitudes

At tree-level, gravity amplitudes are obtainable directly from gauge theory amplitudes via the Kawai, Lewellen and Tye closed-open string relations. We explain how the unitarity method allows us to use these relations to obtain coefficients of box integrals appearing in one-loop N=8 supergravity amplitudes from the recent computation of the coefficients for N=4 super-Yang-Mills non-maximally-helicity-violating amplitudes. We argue from factorisation that these box coefficients determine the one-loop N=8 supergravity amplitudes, although this remains to be proven. We also show that twistor-space properties of the N=8 supergravity amplitudes are inherited from the corresponding properties of N=4 super-Yang-Mills theory. We give a number of examples illustrating these ideas.Comment: 32 pages, minor typos correcte

MHV-Vertices for Gravity Amplitudes

We obtain a CSW-style formalism for calculating graviton scattering amplitudes and prove its validity through the use of a special type of BCFW-like parameter shift. The procedure is illustrated with explicit examples.Comment: 21 pages, minor typos corrected, proof added in section

Effective action and interaction energy of coupled quantum dots

We obtain the effective action of tunnel-coupled quantum dots, by modeling the system as a Luttinger liquid with multiple barriers. For a double dot system, we find that the resonance conditions for perfect conductance form a hexagon in the plane of the two gate voltages controlling the density of electrons in each dot. We also explicitly obtain the functional dependence of the interaction energy and peak-splitting on the gate voltage controlling tunneling between the dots and their charging energies. Our results are in good agreement with recent experimental results, from which we obtain the Luttinger interaction parameter $K=0.74$.Comment: 5 pgs,latex,3 figs,revised version to be publshed in Phys.Rev.

One-Loop NMHV Amplitudes involving Gluinos and Scalars in N=4 Gauge Theory

We use Supersymmetric Ward Identities and quadruple cuts to generate n-pt NMHV amplitudes involving gluinos and adjoint scalars from purely gluonic amplitudes. We present a set of factors that can be used to generate one-loop NMHV amplitudes involving gluinos or adjoint scalars in N=4 Super Yang-Mills from the corresponding purely gluonic amplitude.Comment: 16 pages, JHEP versio

Quadriceps volumes are reduced in people with patellofemoral joint osteoarthritis

Objectives: This study aimed to (1) compare the volumes of vastus medialis (VM), vastus lateralis (VL), vastus intermedius and rectus femoris and the ratio of VM/VL volumes between asymptomatic controls and patellofemoral joint osteoarthritis (PFJ OA) participants; and (2) assess the relationships between cross-sectional area (CSA) and volumes of the VM and VL in individuals with and without PFJ OA. Methods: Twenty-two participants with PFJ OA and 11 controls aged ≥40 years were recruited from the community and practitioner referrals. Muscle volumes of individual quadriceps components were measured from thigh magnetic resonance (MR) images. The CSA of the VM and lateralis were measured at 10 equally distributed levels (femoral condyles to lesser femoral trochanter). Results: PFJ OA individuals had smaller normalized VM (mean difference 0.90 cm ·kg , α = 0.011), VL (1.50 cm ·kg , α = 0.012) and rectus femoris (0.71 cm ·kg , α = 0.009) volumes than controls. No differences in the VM/VL ratio were observed. The CSA at the third level (controls) and fourth level (PFJ OA) above the femoral condyles best predicted VM volume, whereas the VL volume was best predicted by the CSA at the seventh level (controls) and sixth level (PFJ OA) above the femoral condyles. Conclusion: Reduced quadriceps muscle volume was a feature of PFJ OA. Muscle volume could be predicted from CSA measurements at specific levels in PFJ OA patients and controls

On Perturbative Gravity and Gauge Theory

We review some applications of tree-level (classical) relations between gravity and gauge theory that follow from string theory. Together with $D$-dimensional unitarity, these relations can be used to perturbatively quantize gravity theories, i.e. they contain the necessary information for obtaining loop contributions. We also review recent applications of these ideas showing that N=1 D=11 supergravity diverges, and review arguments that N=8 D=4 supergravity is less divergent than previously thought, though it does appear to diverge at five loops. Finally, we describe field variables for the Einstein-Hilbert Lagrangian that help clarify the perturbative relationship between gravity and gauge theory.Comment: Talk presented at Third Meeting on Constrained Dynamics and Quantum Gravity, Villasimius (Sardinia, Italy) September 13-17, 1999 and at the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, University of Adelaide (Australia) December 13-22, 1999. Latex, 9 page

Recursive Calculation of One-Loop QCD Integral Coefficients

We present a new procedure using on-shell recursion to determine coefficients of integral functions appearing in one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including bubbles and triangles, can be determined without resorting to integration. We give criteria for avoiding spurious singularities and boundary terms that would invalidate the recursion. As an example where the criteria are satisfied, we obtain all cut-constructible contributions to the one-loop n-gluon scattering amplitude, A_n^{oneloop}(...--+++...), with split-helicity from an N=1 chiral multiplet and from a complex scalar. Using the supersymmetric decomposition, these are ingredients in the construction of QCD amplitudes with the same helicities. This method requires prior knowledge of amplitudes with sufficiently large numbers of legs as input. In many cases, these are already known in compact forms from the unitarity method.Comment: 36 pages; v2 clarification added and typos fixed, v3 typos fixe

Grand Unification with Three Generations in Free Fermionic String Models

We examine the problem of constructing three generation free fermionic string models with grand unified gauge groups. We attempt the construction of $G\times G$ models, where $G$ is a grand unified group realized at level 1. This structure allows those Higgs representations to appear which are necessary to break the symmetry down to the standard model gauge group. For $G=SO(10)$, we find only models with an even number of generations. However, for $G=SU(5)$ we find a number of 3 generation models.Comment: 22 pages, latex. References added to original versio

Electronic structure of nuclear-spin-polarization-induced quantum dots

We study a system in which electrons in a two-dimensional electron gas are confined by a nonhomogeneous nuclear spin polarization. The system consists of a heterostructure that has non-zero nuclei spins. We show that in this system electrons can be confined into a dot region through a local nuclear spin polarization. The nuclear-spin-polarization-induced quantum dot has interesting properties indicating that electron energy levels are time-dependent because of the nuclear spin relaxation and diffusion processes. Electron confining potential is a solution of diffusion equation with relaxation. Experimental investigations of the time-dependence of electron energy levels will result in more information about nuclear spin interactions in solids