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

Water Consumption by Livestock Systems from 2002–2020 and Predictions for 2030–2050 under Climate Changes in the Czech Republic

The livestock system in Europe relies on a complex holistic equilibrium that is the outcome of an interplay of demand, market, crop production, livestock production, land use, water availability, and other factors. When modeling future scenarios of water consumption by livestock systems, the most suitable tools result from the interconnectivity of growth models, economic models, and climate models. We integrated the Environmental Policy Integrated Climate growth model (EPIC), animal-level model (RUMINANT), economic model (Global Biosphere Management Model, GLOBIOM), EURO-CORDEX climate models, and regression models. This study developed novel livestock production scenarios for individual regions of the Czech Republic with estimations of the categories of livestock that have been bred during the last 20 years and will be bred in the future and what their water consumption will be, both throughout the year and in particular seasons. First, the numbers of farm animals, namely, cattle, pigs, sheep, horses, goats, and poultry in 2002–2020 were evaluated, and their numbers were predicted for the following years until 2050. Second, livestock water consumption per region was determined based on the number of livestock individuals. Third, changes in the amount of water consumed by livestock per year in individual regions in 2050 compared to 2005 were estimated

On different lagrangian formalisms for vector resonances within chiral perturbation theory

We study the relation of vector Proca field formalism and antisymmetric tensor field formalism for spin-one resonances in the context of the large N_C inspired chiral resonance Lagrangian systematically up to the order O(p6) and give a transparent prescription for the transition from vector to antisymmetric tensor Lagrangian and vice versa. We also discuss the possibility to describe the spin-one resonances using an alternative "mixed" first order formalism, which includes both types of fields simultaneously, and compare this one with the former two. We also briefly comment on the compatibility of the above lagrangian formalisms with the high-energy constraints for concrete VVP correlator.Comment: 34 pages, 3 figure

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

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

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

On the background in the γp→ω(π0γ)p\gamma p \to \omega(\pi^0\gamma) p reaction and mixed event simulation

In this paper we evaluate sources of background for the $\gamma p \to \omega p$, with the $\omega$ detected through its $\pi^0 \gamma$ decay channel, to compare with the experiment carried out at ELSA. We find background from $\gamma p \to \pi^0 \pi^0 p$ followed by decay of a $\pi^0$ into two $\gamma$, recombining one $\pi^0$ and one $\gamma$, and from the $\gamma p \to \pi^0 \eta p$ reaction with subsequent decay of the $\eta$ into two photons. This background accounts for the data at $\pi^0 \gamma$ invariant masses beyond 700 MeV, but strength is missing at lower invariant masses which was attributed to photon misidentification events, which we simulate to get a good reproduction of the experimental background. Once this is done, we perform an event mixing simulation to reproduce the calculated background and we find that the method provides a good description of the background at low $\pi^0 \gamma$ invariant masses but fakes the background at high invariant masses, making background events at low invariant masses, which are due to $\gamma$ misidentification events, responsible for the background at high invariant masses which is due to the $\gamma p \to \pi^0 \pi^0 p$ and $\gamma p \to \pi^0 \eta p$ reactions.Comment: 10 pages, 5 figure

QCD in the nuclear medium and effects due to Cherenkov gluons

The equations of in-medium gluodynamics are proposed. Their classical lowest order solution is explicitly shown for a color charge moving with constant speed. For nuclear permittivity larger than 1 it describes emission of Cherenkov gluons resembling results of classical electrodynamics. The values of the real and imaginary parts of the nuclear permittivity are obtained from the fits to experimental data on the double-humped structure around the away-side jet obtained at RHIC. The dispersion of the nuclear permittivity is predicted by comparing the RHIC, SPS and cosmic ray data. This is important for LHC experiments. Cherenkov gluons may be responsible for the asymmetry of dilepton mass spectra near rho-meson, observed in the SPS experiment with excess in the low-mass wing of the resonance. This feature is predicted to be common for all resonances. The "color rainbow" quantum effect might appear according to higher order terms of in-medium QCD if the nuclear permittivity depends on color.Comment: 29 p., 4 figs; for "Phys. Atom. Nucl." volume dedicated to 80th birthday of L.B. Okun; minor corrections on pp. 11 and 13 in v

Uncovering Dangerous Cheats: How Do Avian Hosts Recognize Adult Brood Parasites?

BACKGROUND: Co-evolutionary struggles between dangerous enemies (e.g., brood parasites) and their victims (hosts) lead to the emergence of sophisticated adaptations and counter-adaptations. Salient host tricks to reduce parasitism costs include, as front line defence, adult enemy discrimination. In contrast to the well studied egg stage, investigations addressing the specific cues for adult enemy recognition are rare. Previous studies have suggested barred underparts and yellow eyes may provide cues for the recognition of cuckoos Cuculus canorus by their hosts; however, no study to date has examined the role of the two cues simultaneously under a consistent experimental paradigm. METHODOLOGY/PRINCIPAL FINDINGS: We modify and extend previous work using a novel experimental approach--custom-made dummies with various combinations of hypothesized recognition cues. The salient recognition cue turned out to be the yellow eye. Barred underparts, the only trait examined previously, had a statistically significant but small effect on host aggression highlighting the importance of effect size vs. statistical significance. CONCLUSION: Relative importance of eye vs. underpart phenotypes may reflect ecological context of host-parasite interaction: yellow eyes are conspicuous from the typical direction of host arrival (from above), whereas barred underparts are poorly visible (being visually blocked by the upper part of the cuckoo's body). This visual constraint may reduce usefulness of barred underparts as a reliable recognition cue under a typical situation near host nests. We propose a novel hypothesis that recognition cues for enemy detection can vary in a context-dependent manner (e.g., depending on whether the enemy is approached from below or from above). Further we suggest a particular cue can trigger fear reactions (escape) in some hosts/populations whereas the same cue can trigger aggression (attack) in other hosts/populations depending on presence/absence of dangerous enemies that are phenotypically similar to brood parasites and costs and benefits associated with particular host responses

Photoproduction of {\omega} Mesons off the Proton

The differential cross sections and unpolarized spin-density matrix elements for the reaction $\gamma p\to p\omega$ were measured using the CBELSA/TAPS experiment for initial photon energies ranging from the reaction threshold to 2.5 GeV. These observables were measured from the radiative decay of the $\omega$ meson, $\omega\to\pi^0\gamma$. The cross sections cover the full angular range and show the full extent of the $t$-channel forward rise. The overall shape of the angular distributions in the differential cross sections and unpolarized spin-density matrix elements are in fair agreement with previous data. In addition, for the first time, a beam of linearly-polarized tagged photons in the energy range from 1150 MeV to 1650 MeV was used to extract polarized spin-density matrix elements. These data were included in the Bonn-Gatchina partial wave analysis (PWA). The dominant contribution to $\omega$ photoproduction near threshold was found to be the $3/2^+$ partial wave, which is primarily due to the sub-threshold $N(1720)\,3/2^+$ resonance. At higher energies, pomeron-exchange was found to dominate whereas $\pi$-exchange remained small. These $t$-channel contributions as well as further contributions from nucleon resonances were necessary to describe the entire dataset: the $1/2^-$, $3/2^-$, and $5/2^+$ partial waves were also found to contribute significantly.Comment: 8 pages, 5 figures, accepted for publication in Physics Letters