Majorana Neutrino Masses Can Save One Family Technicolour

We make non perturbative estimates of the electroweak radiative correction parameter $S$ in dynamical symmetry breaking models with Majorana neutrino masses. The Majorana masses are treated as perturbations to a Non Local Chiral Model of the strong interactions. We argue that parameter ranges exist that would allow realistic values of $S$ and $T$ in one family Technicolour models.Comment: 15 pages plus appended diagrams (ps), Latex, SHEP 92/93--2

Classically integrable boundary conditions for symmetric-space sigma models

We investigate boundary conditions for the nonlinear sigma model on the compact symmetric space $G/H$, where $H \subset G$ is the subgroup fixed by an involution $\sigma$ of $G$. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions in correspondence with involutions which commute with $\sigma$. Applied to $SO(3)/SO(2)$, the nonlinear sigma model on $S^2$, these yield the great circles as boundary submanifolds. Applied to $G \times G/G$, they reproduce known results for the principal chiral model.Comment: 8 pages. v2 has an introduction added and a few minor correction

Conserved charges and supersymmetry in principal chiral and WZW models

Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess-Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of the underlying algebra, and the construction of infinitely many commuting charges, with spins equal to the exponents of the algebra modulo its Coxeter number, can be carried out irrespective of the coefficient of the Wess-Zumino term. In the supersymmetric models, a different pattern of conserved quantities emerges, based on antisymmetric invariant tensors. The current algebra is much more complicated than in the bosonic case, and it is analysed in some detail. Two families of commuting charges can be constructed, each with finitely many members whose spins are exactly the exponents of the algebra (with no repetition modulo the Coxeter number). The conserved quantities in the bosonic and supersymmetric theories are only indirectly related, except for the special case of the WZW model and its supersymmetric extension.Comment: LaTeX; 49 pages; v2: minor changes and additions to text and ref

Efficiency in sequential testing: Comparing the sequential probability ratio test and the sequential Bayes factor test

In a sequential hypothesis test, the analyst checks at multiple steps during data collection whether sufficient evidence has accrued to make a decision about the tested hypotheses. As soon as sufficient information has been obtained, data collection is terminated. Here, we compare two sequential hypothesis testing procedures that have recently been proposed for use in psychological research: Sequential Probability Ratio Test (SPRT; Psychological Methods, 25(2), 206–226, 2020) and the Sequential Bayes Factor Test (SBFT; Psychological Methods, 22(2), 322–339, 2017). We show that although the two methods have different philosophical roots, they share many similarities and can even be mathematically regarded as two instances of an overarching hypothesis testing framework. We demonstrate that the two methods use the same mechanisms for evidence monitoring and error control, and that differences in efficiency between the methods depend on the exact specification of the statistical models involved, as well as on the population truth. Our simulations indicate that when deciding on a sequential design within a unified sequential testing framework, researchers need to balance the needs of test efficiency, robustness against model misspecification, and appropriate uncertainty quantification. We provide guidance for navigating these design decisions based on individual preferences and simulation-based design analyses

Strategies towards robust interpretations of in situ zircon Lu–Hf isotope analyses

The combination of U–Pb and Lu–Hf compositions measured in zircon crystals is a remarkably powerful isotopic couplet that provides measures on both the timing of mineral growth and the radiogenic enrichment of the source from which the zircon grew. The U–Pb age documents the timing of zircon crystallization/recrystallization and Hf isotopes inform on the degree to which the host melt was derived from a radiogenic reservoir (e.g. depleted mantle) versus an unradiogenic reservoir (e.g. ancient continental crust), or some mixture of these sources. The ease of generating large quantities of zircon U–Pb and Lu–Hf data has been in large part facilitated by instrument advances. However, the dramatic increase in time constrained zircon Lu–Hf analyses in the Earth science community has brought to the fore the importance of careful data collection and reduction workflows, onto which robust geological interpretations may be based. In this work, we discuss the fundamentals of Lu–Hf isotopes in zircon, which then allows us to provide a robust, accessible, methodology for the assessment of data quality. Additionally, we discuss some novel techniques for: data visualization — that facilitates better transparency of data interpretation; integration of geographic information — that may reveal spatial trends where temporal trends were only apparent before; and some novel statistical evaluation tools — that may provide more rigorous inter- and intra-sample comparisons