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We report on progress in the calculation of corrections to positronium energy levels of order $$m \alpha^7$$. Corrections at this level will be needed for the interpretation of the results of upcoming measurements. A procedure for the calculation of high order corrections has been developed based on the Bethe-Salpeter equation of dimensionally regularized NRQED and the method of regions. We demonstrate the effectiveness of this approach by using it to obtain all pure recoil corrections to positronium energies at $$O(m \alpha^6)$$ in a unified manner. 

Abstract The karrikin (KAR) receptor and several related signaling components have been identified by forward genetic screening, but only a few studies have reported on upstream and downstream KAR signaling components and their roles in drought tolerance. Here, we characterized the functions of KAR UPREGULATED F-BOX 1 (KUF1) in drought tolerance using a reverse genetics approach in Arabidopsis (Arabidopsis thaliana). We observed that kuf1 mutant plants were more tolerant to drought stress than wild-type (WT) plants. To clarify the mechanisms by which KUF1 negatively regulates drought tolerance, we performed physiological, transcriptome, and morphological analyses. We found that kuf1 plants limited leaf water loss by reducing stomatal aperture and cuticular permeability. In addition, kuf1 plants showed increased sensitivity of stomatal closure, seed germination, primary root growth, and leaf senescence to abscisic acid (ABA). Genome-wide transcriptome comparisons of kuf1 and WT rosette leaves before and after dehydration showed that the differences in various drought tolerance-related traits were accompanied by differences in the expression of genes associated with stomatal closure (e.g. OPEN STOMATA 1), lipid and fatty acid metabolism (e.g. WAX ESTER SYNTHASE), and ABA responsiveness (e.g. ABA-RESPONSIVE ELEMENT 3). The kuf1 mutant plants had higher root/shoot ratios and root hair densities than WT plants, suggesting that they could absorb more water than WT plants. Together, these results demonstrate that KUF1 negatively regulates drought tolerance by modulating various physiological traits, morphological adjustments, and ABA responses and that the genetic manipulation of KUF1 in crops is a potential means of enhancing their drought tolerance.