Decay of high-density matter in the electroweak theory

High-density fermion matter is meta-stable due to the anomalous non-conservation of baryon and lepton numbers in the electroweak theory. The meta-stable state decays by penetrating the sphaleron barrier separating topologically different vacua. The decay happens locally, and results in an annihilation of twelve fermions, accompanied by a production of gauge and Higgs bosons. We find numerically local bounce solutions determining the decay rate, which are classical paths in imaginary time, connecting two adjacent topological sectors. We also follow the real-time evolution of the bosonic fields after the tunneling and analyze the spectrum of the created bosons.Comment: 13 pages, 4 Postscript figure

Spontaneous annihilation of high-density matter in the electroweak theory

In the presence of fermionic matter the topologically distinct vacua of the standard model are metastable and can decay by tunneling through the sphaleron barrier. This process annihilates one fermion per doublet due to the anomalous non-conservation of baryon and lepton currents and is accompanied by a production of gauge and Higgs bosons. We present a numerical method to obtain local bounce solutions which minimize the Euclidean action in the space of all configurations connecting two adjacent topological sectors. These solutions determine the decay rate and the configuration of the fields after the tunneling. We also follow the real time evolution of this configuration and analyze the spectrum of the created bosons. If the matter density exceeds some critical value, the exponentially suppressed tunneling triggers off an avalanche producing an enormous amount of bosons.Comment: 38 pages, 6 Postscript figure

Loop corrections to the sphaleron transition rate in the minimal standard model

The baryon number dissipation rate due to sphaleron transitions at high temperatures in the minimal standard model is evaluated. We find that this rate can be considerably suppressed by one loop contributions of bosonic and fermionic fluctuations which are particularly important for a small mass of the Higgs boson and a large top quark mass. Fixing the latter to its recently stated value of 174 GeV the complete erasure of the baryon asymmetry is prevented within the framework of the minimal standard model if the Higgs mass is less than about 66 GeV.Comment: 11 pages (LaTex) plus 2 figures (uuencoded postscript files); RUB-TPII-05/9

A protocol to develop Shared Socio-economic Pathways for European agriculture

Moving towards a more sustainable future requires concerted actions, particularly in the context of global climate change. Integrated assessments of agricultural systems (IAAS) are considered valuable tools to provide sound information for policy and decision-making. IAAS use storylines to define socio-economic and environmental framework assumptions. While a set of qualitative global storylines, known as the Shared Socio-economic Pathways (SSPs), is available to inform integrated assessments at large scales, their spatial resolution and scope is insufficient for regional studies in agriculture. We present a protocol to operationalize the development of Shared Socio-economic Pathways for European agriculture – Eur-Agri-SSPs – to support IAAS. The proposed design of the storyline development process is based on six quality criteria: plausibility, vertical and horizontal consistency, salience, legitimacy, richness and creativity. Trade-offs between these criteria may occur. The process is science-driven and iterative to enhance plausibility and horizontal consistency. A nested approach is suggested to link storylines across scales while maintaining vertical consistency. Plausibility, legitimacy, salience, richness and creativity shall be stimulated in a participatory and interdisciplinary storyline development process. The quality criteria and process design requirements are combined in the protocol to increase conceptual and methodological transparency. The protocol specifies nine working steps. For each step, suitable methods are proposed and the intended level and format of stakeholder engagement are discussed. A key methodological challenge is to link global SSPs with regional perspectives provided by the stakeholders, while maintaining vertical consistency and stakeholder buy-in. We conclude that the protocol facilitates systematic development and evaluation of storylines, which can be transferred to other regions, sectors and scales and supports inter-comparisons of IAAS. © 2019 Elsevier Lt

A protocol to develop shared socio-economic pathways for European agriculture

Moving towards a more sustainable future requires concerted actions, particularly in the context of global climate change. Integrated assessments of agricultural systems (IAAS) are considered valuable tools to provide sound information for policy and decision-making. IAAS use storylines to define socio-economic and environmental framework assumptions. While a set of qualitative global storylines, known as the Shared Socio-economic Pathways (SSPs), is available to inform integrated assessments at large scales, their spatial resolution and scope is insufficient for regional studies in agriculture. We present a protocol to operationalize the development of Shared Socio-economic Pathways for European agriculture – Eur-Agri-SSPs – to support IAAS. The proposed design of the storyline development process is based on six quality criteria: plausibility, vertical and horizontal consistency, salience, legitimacy, richness and creativity. Trade-offs between these criteria may occur. The process is science-driven and iterative to enhance plausibility and horizontal consistency. A nested approach is suggested to link storylines across scales while maintaining vertical consistency. Plausibility, legitimacy, salience, richness and creativity shall be stimulated in a participatory and interdisciplinary storyline development process. The quality criteria and process design requirements are combined in the protocol to increase conceptual and methodological transparency. The protocol specifies nine working steps. For each step, suitable methods are proposed and the intended level and format of stakeholder engagement are discussed. A key methodological challenge is to link global SSPs with regional perspectives provided by the stakeholders, while maintaining vertical consistency and stakeholder buy-in. We conclude that the protocol facilitates systematic development and evaluation of storylines, which can be transferred to other regions, sectors and scales and supports inter-comparisons of IAAS

Fermion sea along the sphaleron barrier

In this revised version we have improved the treatment of the top and bottom quark mass. This leads to slight changes of the numerical results, especially of those presented in Fig.4. The discussion of the numerical procedure and accuracy has been extended.Comment: 39 pages (LaTex) plus 5 figures (uuencoded postscript files); RUB-TPII-62/93, to appear in Phys.Rev.

Shared Socio-economic Pathways for European agriculture and food systems: the Eur-Agri-SSPs

Scenarios describe plausible and internally consistent views of the future. They can be used by scientists, policymakers and entrepreneurs to explore the challenges of global environmental change given an appropriate level of spatial and sectoral detail and systematic development. We followed a nine-step protocol to extend and enrich a set of global scenarios – the Shared Socio-economic Pathways (SSPs) – providing regional and sectoral detail for European agriculture and food systems using a one-to-one nesting participatory approach. The resulting five Eur-Agri-SSPs are titled (1) Agriculture on sustainable paths, (2) Agriculture on established paths, (3) Agriculture on separated paths, (4) Agriculture on unequal paths, and (5) Agriculture on high-tech paths. They describe alternative plausible qualitative evolutions of multiple drivers of particular importance and high uncertainty for European agriculture and food systems. The added value of the protocol-based storyline development process lies in the conceptual and methodological transparency and rigor; the stakeholder driven selection of the storyline elements; and consistency checks within and between the storylines. Compared to the global SSPs, the five Eur-Agri-SSPs provide rich thematic and regional details and are thus a solid basis for integrated assessments of agriculture and food systems and their response to future socio-economic and environmental change

Sphaleron transitions in the Minimal Standard Model and the upper bound for the Higgs Mass

We calculate the dissipation of the baryon number after the electroweak phase transition due to thermal fluctuations above the sphaleron barrier. We consider not only the classical Boltzmann factor but also fermionic and bosonic one-loop contributions. We find that both bosonic and especially fermionic fluctuations can considerably suppress the transition rate. Assuming the Langer--Affleck formalism for this rate, the condition that an initial baryon asymmetry must not be washed out by sphaleron transitions leads, in the Minimal Standard Model ($\sin\theta_W=0$), to an upper bound for the Higgs mass in the range 60 to 75 GeV.Comment: 49 pages, 5 figures (uuencoded PostScript); fixing of the renormalization scale has been improved, numerics has been extende

The sphaleron rate in the electroweak theory

Die Sphaleronen-Rate in der elektroschwachen Theorie: Die Vakuumkonfigurationen der elektroschwachen Eichfelder lassen sich durch den ganzzahligen Chern-Simons-Index klassifizieren. Übergänge zwischen verschiedenen Vakua bewirken eine Verletzung der Baryonenzahl, werden jedoch normalerweise durch die Sphaleronen-Barriere sehr effektiv verhindert. Wir berechnen einerseits die Tunnelwahrscheinlichkeit für sehr hohe Fermiondichten, andererseits die thermische Übergangsrate für beliebige Temperaturen unterhalb des elekroschwachen Phasenübergangs, bei dem die Sphaleronen-Barriere verschwindet. Im Rahmen des Minimalen Standardmodells ergibt sich eine völlige Auswaschung sämtlicher Baryonen durch thermische Sphaleronen-Übergänge nach dem Phasenübergang, welche aber nicht stattgefunden hat. Für eine kosmologisch konsistente Beschreibung der Epoche des elekroschwachen Phasenübergangs sind also Erweiterungen des Minimalen Standardmodells notwendig