Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking

Dispersive representations of the pi-pi scattering amplitudes and pion form factors, valid at two-loop accuracy in the low-energy expansion, are constructed in the presence of isospin-breaking effects induced by the difference between the charged and neutral pion masses. Analytical expressions for the corresponding phases of the scalar and vector pion form factors are computed. It is shown that each of these phases consists of the sum of a "universal" part and a form-factor dependent contribution. The first one is entirely determined in terms of the pi-pi scattering amplitudes alone, and reduces to the phase satisfying Watson's theorem in the isospin limit. The second one can be sizeable, although it vanishes in the same limit. The dependence of these isospin corrections with respect to the parameters of the subthreshold expansion of the pi-pi amplitude is studied, and an equivalent representation in terms of the S-wave scattering lengths is also briefly presented and discussed. In addition, partially analytical expressions for the two-loop form factors and pi-pi scattering amplitudes in the presence of isospin breaking are provided.Comment: 57 pages, 12 figure

Multidimensional evaluation of managed relocation

Managed relocation (MR) has rapidly emerged as a potential intervention strategy in the toolbox of biodiversity management under climate change. Previous authors have suggested that MR (also referred to as assisted colonization, assisted migration, or assisted translocation) could be a last-alternative option after interrogating a linear decision tree. We argue that numerous interacting and value-laden considerations demand a more inclusive strategy for evaluating MR. The pace of modern climate change demands decision making with imperfect information, and tools that elucidate this uncertainty and integrate scientific information and social values are urgently needed. We present a heuristic tool that incorporates both ecological and social criteria in a multidimensional decision-making framework. For visualization purposes, we collapse these criteria into 4 classes that can be depicted in graphical 2-D space. This framework offers a pragmatic approach for summarizing key dimensions of MR: capturing uncertainty in the evaluation criteria, creating transparency in the evaluation process, and recognizing the inherent tradeoffs that different stakeholders bring to evaluation of MR and its alternatives.Articl

Multidimensional evaluation of managed relocation

Managed relocation (MR) has rapidly emerged as a potential intervention strategy in the toolbox of biodiversity management under climate change. Previous authors have suggested that MR (also referred to as assisted colonization, assisted migration, or assisted translocation) could be a last-alternative option after interrogating a linear decision tree. We argue that numerous interacting and value-laden considerations demand a more inclusive strategy for evaluating MR. The pace of modern climate change demands decision making with imperfect information, and tools that elucidate this uncertainty and integrate scientific information and social values are urgently needed. We present a heuristic tool that incorporates both ecological and social criteria in a multidimensional decision-making framework. For visualization purposes, we collapse these criteria into 4 classes that can be depicted in graphical 2-D space. This framework offers a pragmatic approach for summarizing key dimensions of MR: capturing uncertainty in the evaluation criteria, creating transparency in the evaluation process, and recognizing the inherent tradeoffs that different stakeholders bring to evaluation of MR and its alternatives.Centre of Excellence for Invasion Biolog