Double-Copy Constructions and Unitarity Cuts

The duality between color and kinematics enables the construction of multiloop gravity integrands directly from corresponding gauge-theory integrands. This has led to new nontrivial insights into the structure of gravity theories, including the discovery of enhanced ultraviolet cancellations. To continue to gain deeper understandings and probe these new properties, it is crucial to further improve techniques for constructing multiloop gravity integrands. In this paper, we show by example how one can alleviate difficulties encountered at the multiloop level by relaxing the color-kinematics duality conditions to hold manifestly only on unitarity cuts instead of globally on loop integrands. As an example, we use a minimal ansatz to construct an integrand for the two-loop four-point nonsupersymmetric pure Yang-Mills amplitude in $D$ dimensions that is compatible with these relaxed color-kinematics duality constraints. We then immediately obtain a corresponding gravity integrand through the double-copy procedure. Comments on ultraviolet divergences are also included.Comment: 26 pages, 11 figures, ancillary file, RevTe

Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance

We show that at tree level, on-shell gauge invariance can be used to fully determine the first subleading soft-gluon behavior and the first two subleading soft-graviton behaviors. Our proofs of the behaviors for n-gluon and n-graviton tree amplitudes are valid in D dimensions and are similar to Low's proof of universality of the first subleading behavior of photons. In contrast to photons coupling to massive particles, in four dimensions the soft behaviors of gluons and gravitons are corrected by loop effects. We comment on how such corrections arise from this perspective. We also show that loop corrections in graviton amplitudes arising from scalar loops appear only at the second soft subleading order. This case is particularly transparent because it is not entangled with graviton infrared singularities. Our result suggests that if we set aside the issue of infrared singularities, soft-graviton Ward identities of extended BMS symmetry are not anomalous through the first subleading order.Comment: RevTeX, 5 figures, 28 pages; v3 minor corrections and clarification

Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops

We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.Comment: 35 page, 10 figures, REVTex, ancillary mathematica file containing one-loop diagram numerators, latest version includes updated references, corrected two-loop numerators and various clarification

Controlling the Au/Iron oxide interface to optimise plasmonic resonance for magneto-optic diagnostics

Sepsis is one of the biggest causes of child mortality across the globe accounting for 1 in 5 deaths. Often these deaths could have been prevented with faster diagnosis. This can be achieved by developing point of care diagnostics which can be carried out in a pharmacy or general practitioners office. One way to develop portable diagnostics such as this is the use of the unique magnetic and optical properties possessed by anisotropic nanoparticles. A possible method to identify sepsis is through the presence of bacterial endotoxins. These can be detected magneto-optically by monitoring the rotational dynamics of anisotropic nanoparticles in an external magnetic field. Nanoparticles of hematite and cerium phosphate were synthesised and evaluated for their use as sensors in magneto-optical diagnosis. The sensitivity of such a probe depends upon a combination of magnetic and plasmonic properties. These are affected by morphology, magnetic susceptibility, and surface plasmon resonance. The hydrothermal growth mechanisms of hematite nanorods were examined and the relationship between directing agent concentration, reaction temperature and time was examined. The effect of 1,2 propanediamine and alkali metal phosphates acting as directing agents were evaluated on hematite, resulting in the formation of tuneable nanorods with aspect ratios between 3-10 and 1-7 respectively. The rotational dynamics of these hematite particles was assessed in glycerol solution and shown to be sensitive to changes in viscosity at different frequencies of rotation. Cerium phosphate nanorods were prepared with a tuneable length from 78 nm to 432 nm and aspect ratios of 3-27. The magnetic susceptibility of these rods was changed through the addition of W, Fe, Ni and Mn ions. The addition of Co ions had only a minimum effect n the magnetic susceptibility. The particles were rotated in external magnetic fields and were shown to be sensitive to changes in the viscosity of a solution based on changes in phase shift. Hematite and cerium phosphate core shell particles were produced. The cores were coated in gold through the seed-mediated method and the morphology of the Au shell was shown to depend heavily upon the number of gold seeds pre-deposited on the ii surface as well as the concentration of the gold growth solution. Using this understanding of the growth mechanism, nanorods with smooth gold surfaces which would produce strong plasmonic signals were synthesised

Photo induced Force Microscopy: chemical spectroscopy beyond the diffraction limit

Over the last decade remarkable advances have been made in creating spectroscopic tools to interrogate surface properties using electromagnetic radiation in the near field, achieving lateral resolutions in the nanometre range. We review recent work involving one of the most promising of these spectroscopic tools, photo induced force microscopy (PiFM), which uses mechanical detection of dipole-dipole interactions enabling nanometre resolved mapping of surface properties ranging from vibrational modes of adsorbates to plasmon resonances. We discuss the origin of contrast in PiFM images, its applications as a local probe of chemical species and for mapping local electric fields in areas as diverse as zeolite films and biometric recognition. In comparison with related techniques such as photo thermal infrared spectroscopy (PTIR) and tip enhanced Raman spectroscopy (TERS) PiFM has many advantages but perhaps its most successful application is in combination with other surface characterisation methods which provide information averaged over much greater surface areas. We discuss the most recent developments of PiFM technology which are leading to higher resolution images and are widening the range of environments in which the technique can be applied, and we consider how the field is likely to progress in the future

PiFM and XPS Studies of Porous TiO2 Films for the Photocatalytic Decomposition of Polystyrene

The rate of photocatalytic oxidation of polystyrene over 0.1 wt% copper-doped TiO2 catalyst spin coated onto a flat substrate is investigated as a function of the catalyst deposition spin speed and, hence, film thickness. Photoinduced force microscopy and photoelectron spectroscopy show no evidence of any products of the photocatalytic oxidation remaining on the surface after reaction. The oxidation reaction shows no discernible dependence on spin speed; it is close to zero order in polystyrene concentration and exhibits a ½ life almost 50 times greater than the equivalent photocatalytic oxidation of stearic acid on the same catalysts. No difference between the rate of decay of the aliphatic and aromatic hydrogens of the polymer was observed, suggesting that once a polymer chain begins oxidising, subsequent steps are relatively rapid. This is consistent with the rate-determining step being dependent on the extent of coordination to the surface, which is much more favourable with stearic acid because of its carboxylic group

The role of growth directors in controlling the morphology of hematite nanorods

The control of the growth of hematite nanoparticles from iron chloride solutions under hydrothermal conditions in the presence of two different structure promoters has been studied using a range of both structural and spectroscopic techniques including the first report of photo induced force microscopy (PiFM) to map the topographic distribution of the structure-directing agents on the developing nanoparticles. We show that the shape of the nanoparticles can be controlled using the concentration of phosphate ions up to a limit determined to be ~6 × 10−3 mol. Akaganéite (β-FeOOH) is a major component of the nanoparticles formed in the absence of structure directors but only present in the very early stages (< 8 h) of particle growth when phosphate is present. The PiFM data suggest a correlation between the areas in which phosphate ions are adsorbed and areas where akaganéite persists on the surface. In contrast, goethite (α-FeOOH) is a directly observed precursor of the hematite nanorods when 1,2-diamino propane is present. The PiFM data shows goethite in the center of the developing particles consistent with a mechanism in which the iron hydroxide re-dissolves and precipitates at the nanorod ends as hematite