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A bstract We consider QCD radiative corrections to Higgs boson pair production through gluon fusion in proton collisions. We combine the exact next-to-leading order (NLO) contribution, which features two-loop virtual amplitudes with the full dependence on the top quark mass M t , with the next-to-next-to-leading order (NNLO) corrections computed in the large- M t approximation. The latter are improved with different reweighting techniques in order to account for finite- M t effects beyond NLO. Our reference NNLO result is obtained by combining one-loop double-real corrections with full M t dependence with suitably reweighted real-virtual and double-virtual contributions evaluated in the large- M t approximation. We present predictions for inclusive cross sections in pp collisions at s = 13, 14, 27 and 100 TeV and we discuss their uncertainties due to missing M t effects. Our approximated NNLO corrections increase the NLO result by an amount ranging from +12% at s = 13 TeV to +7% at s = 100 TeV, and the residual uncertainty of the inclusive cross section from missing M t effects is estimated to be at the few percent level. Our calculation is fully differential in the Higgs boson pair and the associated jet activity: we also present predictions for various differential distributions at s = 14 and 100 TeV, and discuss the size of the missing M t effects, which can be larger, especially in the tails of certain observables. Our results represent the most advanced perturbative prediction available to date for this process.

A bstract We present results for Higgs boson pair production with variations of the trilinear Higgs boson self coupling at next-to-leading order (NLO) in QCD including the full top quark mass dependence. Differential results for the LHC at 14 TeV are presented and we discuss the implications of anomalous trilinear couplings as well as differences between the Pythia and Herwig parton showers in combination with POWHEG. The implementation of the NLO QCD calculation with variable Higgs boson self coupling is made publicly available in the POWHEG-BOX-V2 Monte Carlo framework. A simple method for using the new implementation to study also variations of the top quark Yukawa coupling is described.

A bstract We present the first combination of NLO QCD matrix elements for di-Higgs production, retaining the full top quark mass dependence, with a parton shower. Results are provided within both the POWHEG-BOX and MadGraph5_aMC@NLO Monte Carlo frameworks. We assess in detail the theoretical uncertainties and provide differential results. We find that, as expected, the shower effects are relatively large for observables like the transverse momentum of the Higgs boson pair, which are sensitive to extra radiation. However, these shower effects are still much smaller than the differences between the Born-improved HEFT approximation and the full NLO calculation in the tails of the distributions.

A bstract We present results for the Yukawa-enhanced and Higgs self-coupling type electroweak corrections to di-Higgs production in gluon fusion. The calculation of the corresponding four-scale, two-loop amplitude is carried out retaining the exact symbolic dependence on all masses and scales during the reduction to master integrals. The resulting integrals are then evaluated at high precision using both the series expansion of the differential equations and sector decomposition. Differential cross sections for the di-Higgs invariant mass and the transverse momentum of a Higgs boson are shown, where we find that the corrections are most pronounced at low invariant mass and transverse momentum.

A bstract We present a calculation of the NNLO QCD corrections to Z-boson pair production at hadron colliders, based on the N-jettiness method for the real radiation parts. We discuss the size and shape of the perturbative corrections along with their associated scale uncertainties and compare our results to recent LHC data at s = 13 TeV.

A bstract We present calculations of Higgs boson production via gluon-gluon fusion in association with one or two additional jets at next-to-leading order in QCD. The calculation of H +jet is exact in the treatment of the top-quark mass, whereas for the H +2 jets calculation the two-loop virtual amplitudes are approximated via a reweighting with leading-order mass effects, while keeping all top-quark mass effects in the real radiation contributions. For H +jet production, this study extends a previous calculation, revealing an error in the previous results. For total and differential cross sections, we present new results and compare the QCD corrections with the infinite top-mass limit, for which we find a strikingly good agreement if all amplitudes are rescaled by the leading-order mass dependence.

A bstract We study the effects of the exact top quark mass-dependent two-loop corrections to Higgs boson pair production by gluon fusion at the LHC and at a 100 TeV hadron collider. We perform a detailed comparison of the full next-to-leading order result to various approximations at the level of differential distributions and also analyse non-standard Higgs self-coupling scenarios. We find that the different next-to-leading order approximations differ from the full result by up to 50 percent in relevant differential distributions. This clearly stresses the importance of the full NLO result.

Despite sometimes strong codependencies of insect herbivores and plants, the responses of individual taxa to accelerating climate change are typically studied in isolation. For this reason, biotic interactions that potentially limit species in tracking their preferred climatic niches are ignored. Here, we chose butterflies as a prominent representative of herbivorous insects to investigate the impacts of temperature changes and their larval host plant distributions along a 1.4-km elevational gradient in the German Alps. Following a sampling protocol of 2009, we revisited 33 grassland plots in 2019 over an entire growing season. We quantified changes in butterfly abundance and richness by repeated transect walks on each plot and disentangled the direct and indirect effects of locally assessed temperature, site management, and larval and adult food resource availability on these patterns. Additionally, we determined elevational range shifts of butterflies and host plants at both the community and species level. Comparing the two sampled years (2009 and 2019), we found a severe decline in butterfly abundance and a clear upward shift of butterflies along the elevational gradient. We detected shifts in the peak of species richness, community composition, and at the species level, whereby mountainous species shifted particularly strongly. In contrast, host plants showed barely any change, neither in connection with species richness nor individual species shifts. Further, temperature and host plant richness were the main drivers of butterfly richness, with change in temperature best explaining the change in richness over time. We concluded that host plants were not yet hindering butterfly species and communities from shifting upwards. However, the mismatch between butterfly and host plant shifts might become a problem for this very close plant–herbivore relationship, especially toward higher elevations, if butterflies fail to adapt to new host plants. Further, our results support the value of conserving traditional extensive pasture use as a promoter of host plant and, hence, butterfly richness.

This study investigates the feasibility of microalgae cultivation with the effluent (permeate) of a decentralized anaerobic membrane bioreactor (AnMBR) treating high strength domestic wastewater. Two experiments, consisting of three and two successive batch experiments with incubation times varying between 5 and 9 days, were conducted. Nutrient removal and growth of the microalgae species Acutodesmus obliquus were studied for the following culture media: (A) permeate, (B) permeate enriched with iron (Fe), magnesium (Mg), manganese (Mn), sulfur (S) and the chelating agent EDTA, (C) commercial fertilizer as control culture. Initial nutrient concentrations in the culture media ranged from 9.3 to 16.6 mg·L−1 total phosphorus (TP) and from 85.1 to 126.2 mg·L−1 total nitrogen (TN). TP reached an average removal of 97%, 98% and 99% in (A), (B) and (C) respectively. An average TN removal of 94% and 96% was achieved in (B) and (C). Starting from the third batch of the first experiment and the second batch of the second experiment, the culture with permeate (A) showed a decrease in TN removal. Further batch experiments showed the need to add iron to ensure an optimal TN removal from the permeate.