The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM

We give an explicit recursive formula for the all L-loop integrand for scattering amplitudes in N=4 SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This generalizes the BCFW recursion relation for tree amplitudes to all loop orders, and extends the Grassmannian duality for leading singularities to the full amplitude. It also provides a new physical picture for the meaning of loops, associated with canonical operations for removing particles in a Yangian-invariant way. Loop amplitudes arise from the "entangled" removal of pairs of particles, and are naturally presented as an integral over lines in momentum-twistor space. As expected from manifest Yangian-invariance, the integrand is given as a sum over non-local terms, rather than the familiar decomposition in terms of local scalar integrals with rational coefficients. Knowing the integrands explicitly, it is straightforward to express them in local forms if desired; this turns out to be done most naturally using a novel basis of chiral, tensor integrals written in momentum-twistor space, each of which has unit leading singularities. As simple illustrative examples, we present a number of new multi-loop results written in local form, including the 6- and 7-point 2-loop NMHV amplitudes. Very concise expressions are presented for all 2-loop MHV amplitudes, as well as the 5-point 3-loop MHV amplitude. The structure of the loop integrand strongly suggests that the integrals yielding the physical amplitudes are "simple", and determined by IR-anomalies. We briefly comment on extending these ideas to more general planar theories.Comment: 46 pages; v2: minor changes, references adde

Spectroscopic, Morphological and Mechanistic Investigation of the Solvent.Promoted Aggregation of Porphyrins Modified in meso-positions by Glucosylated steroids

Solvent-driven aggregation of a series of porphyrin derivatives was studied by UV/Vis and circular dichroism spectroscopy. The porphyrins are characterised by the presence in the meso positions of steroidal moieties further conjugated with glucosyl groups. The presence of these groups makes the investigated macrocycles amphiphilic and soluble in aqueous solvent, namely, dimethyl acetamide/ water. Aggregation of the macrocycles is triggered by a change in bulk solvent composition leading to formation of large architectures that express supramolecular chirality, steered by the presence of the stereogenic centres on the periphery of the macrocycles. The aggregation behaviour and chiroptical features of the aggregates are strongly dependent on the number of moieties decorating the periphery of the porphyrin framework. In particular, experimental evidence indicates that the structure of the steroid linker dictates the overall chirality of the supramolecular architectures. Moreover, the porphyrin concentration strongly affects the aggregation mechanism and the CD intensities of the spectra. Notably, AFM investigations reveal strong differences in aggregate morphology that are dependent on the nature of the appended functional groups, and closely in line with the changes in aggregation mechanism. The suprastructures formed at lower concentration show a network of long fibrous structures spanning over tens of micrometres, whereas the aggregates formed at higher concentration have smaller rodshaped structures that can be recognised as the result of coalescence of smaller globular structures. The fully steroid substituted derivative forms globular structures over the whole concentration range explored. Finally, a rationale for the aggregation phenomena was given by semiempirical calculations at the PM6 level

New differential equations for on-shell loop integrals

We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N=4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar N=4 super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.Comment: 39 pages, 8 figures; v2: typos corrected, definition of harmonic polylogarithms adde

Future agroclimatic conditions and implications for European grasslands.

Grasslands play a significant role in livestock fodder production and thus, contribute to food security worldwide while providing numerous additional ecosystem services. However, how agroclimatic conditions and adverse weather events relevant for grasslands will change across the European grassland areas has not been examined to date. Using a single reference setup for soil and management over 476 European sites defined by climate stations, we show the probability of eight selected adverse weather events with the potential to significantly affect grassland productivity under climate change and how these events vary regionally across Europe. Changes in these eight key agroclimatic indicators create markedly specific spatial patterns. We found that by 2050, the exposure of the south and west European grasslands to heat and drought may double in comparison with today and that the area with frequent occurrences of heat and drought will expand northwards. However, across Ukraine, Belarus, and the Baltic countries to southern Finland and Sweden, the likelihood of these events is likely to decrease. While changing cultivars and management strategies are unavoidable, shifting grassland production to other regions to reduce the risk may not be possible as the risk of adverse events beyond the key grassland-growing areas increases even further. Moreover, we found marked changes in the overall thermal and water regimes across European regions. The effect of adverse weather events in the future could be different in other regions of the world compared to regions in Europe, emphasizing the importance of conducting similar analyses for other major grassland producing regions. To mitigate the impact of climate change, new ways of maintaining grassland productivity need to be developed. These methods include more efficient selection of species mixtures for specific regions, including increased use of legumes and forbs; incorporation of new genetic resources, including the development of hybrid cultivars, such as Festulolium hybrids; and incorporation of state-of-the-art technologies in breeding programs and new grazing management

Generic multiloop methods and application to N=4 super-Yang-Mills

We review some recent additions to the tool-chest of techniques for finding compact integrand representations of multiloop gauge-theory amplitudes - including non-planar contributions - applicable for N=4 super-Yang-Mills in four and higher dimensions, as well as for theories with less supersymmetry. We discuss a general organization of amplitudes in terms of purely cubic graphs, review the method of maximal cuts, as well as some special D-dimensional recursive cuts, and conclude by describing the efficient organization of amplitudes resulting from the conjectured duality between color and kinematic structures on constituent graphs.Comment: 42 pages, 18 figures, invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", v2 minor corrections, v3 added reference

Recent growth coherence in long-term oak (Quercus spp.) ring width chronologies in the Czech Republic

Oak ring width measurements compiled from 44 sampling sites throughout the territory of the Czech Republic are analysed for the 1655-2013 period. Measurements taken at all these sites are sorted into 10 sub-chronologies on the basis of 5 environmental factors: soil moisture (dry/wet), elevation (low/high), age (young/old), species (Quercus robur or Q. petraea), and geographical position (east/west). Several statistical tests are applied to investigate existing significant differences between chronologies during 1920-2013. Further, the sensitivities of individual sub-chronologies to precipitation are compared. Three tests indicate 5 pairs of very similar sub-chronologies. Moreover, the growth-response to May-July precipitation totals is very much the same in these sub-chronologies. This analysis demonstrates that, even in the absence of certainty about age structure, species composition and some environmental factors in the earlier parts of oak ring width chronologies, the internal homogeneity of the chronology remains essentially unaffected, and the lack of such information does not preclude their use in dendroclimatology

Basics of Generalized Unitarity

We review generalized unitarity as a means for obtaining loop amplitudes from on-shell tree amplitudes. The method is generally applicable to both supersymmetric and non-supersymmetric amplitudes, including non-planar contributions. Here we focus mainly on N=4 Yang-Mills theory, in the context of on-shell superspaces. Given the need for regularization at loop level, we also review a six-dimensional helicity-based superspace formalism and its application to dimensional and massive regularizations. An important feature of the unitarity method is that it offers a means for carrying over any identified tree-level property of on-shell amplitudes to loop level, though sometimes in a modified form. We illustrate this with examples of dual conformal symmetry and a recently discovered duality between color and kinematics.Comment: 37 pages, 10 figures. Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich(ed

Climate-induced severe water scarcity events as harbinger of global grain price

The severe water scarcity (SWS) concept allows for consistent analysis of the supply and demand for water sourced grain production worldwide. Thus, the primary advantage of using SWS is its ability to simultaneously accommodate the spatial extent and temporal persistence of droughts using climatic data. The SWS concept was extended here to drivers of global grain prices using past SWS events and prices of three dominant grain crops: wheat, rice and maize. A significant relation between the SWS affected area and the prices of wheat was confirmed. The past price–SWS association was then used to project future wheat prices considering likely climate change scenarios until 2050 and expected SWS extent. The projected wheat prices increase with increasing SWS area that is in turn a function of greenhouse gas emissions. The need to act to reduce greenhouse gas emissions is again reinforced assuming the SWS-price relation for wheat is unaltered