Measurement of the K + - pi + pi - e + - (-) v e form factors and of the pi pi scattering length a 0 0

The quark condensate is a fundamental free parameter of Chiral Perturbation Theory ($chi PT$), since it determines the relative size of the mass and momentum terms in the power expansion. In order to confirm or contradict the assumption of a large quark condensate, on which $chi PT$ is based, experimental tests are needed. In particular, the $S$-wave $pipi$ scattering lengths $a_0^0$ and $a_0^2$ can be predicted precisely within $chi PT$ as a function of this parameter and can be measured very cleanly in the decay $K^{pm} to pi^{+} pi^{-} e^{pm} stackrel{mbox{tiny(---)}}{nu_e}$ ($K_{e4}$). About one third of the data collected in 2003 and 2004 by the NA48/2 experiment were analysed and 342,859 $K_{e4}$ candidates were selected. The background contamination in the sample could be reduced down to 0.3% and it could be estimated directly from the data, by selecting events with the same signature as $K_{e4}$, but requiring for the electron the opposite charge with respect to the kaon, the so-called ``wrong sign'' events. This is a clean background sample, since the kaon decay with $Delta S=-Delta Q$, that would be the only source of signal, can only take place through two weak decays and is therefore strongly suppressed. The Cabibbo-Maksymowicz variables, used to describe the kinematics of the decay, were computed under the assumption of a fixed kaon momentum of 60 GeV/$c$ along the $z$ axis, so that the neutrino momentum could be obtained without ambiguity. The measurement of the form factors and of the $pipi$ scattering length $a_0^0$ was performed in a single step by comparing the five-dimensional distributions of data and MC in the kinematic variables. The MC distributions were corrected in order to properly take into account the trigger and selection efficiencies of the data and the background contamination. The following parameter values were obtained from a binned maximum likelihood fit, where $a_0^2$ was expressed as a function of $a_0^0$ according to the prediction of chiral perturbation theory: f'_s/f_s = 0.133+- 0.013(stat)+- 0.026(syst) f''_s/f_s = -0.041+- 0.013(stat)+- 0.020(syst) f_e/f_s = 0.221+- 0.051(stat)+- 0.105(syst) f'_e/f_s = -0.459+- 0.170(stat)+- 0.316(syst) tilde{f_p}/f_s = -0.112+- 0.013(stat)+- 0.023(syst) g_p/f_s = 0.892+- 0.012(stat)+- 0.025(syst) g'_p/f_s = 0.114+- 0.015(stat)+- 0.022(syst) h_p/f_s = -0.380+- 0.028(stat)+- 0.050(syst) a_0^0 = 0.246+- 0.009(stat)+- 0.012(syst)}+- 0.002(theor), where the statistical uncertainty only includes the effect of the data statistics and the theoretical uncertainty is due to the width of the allowed band for $a_0^2$.

Genetic dynamics across early life stages in the tropical tree Prunus africana (Rosaceae)

In many plant species, the genetic template of early life-stages is formed by animal-mediated pollination and seed dispersal and has profound impact on further recruitment and population dynamics. Understanding the impact of pollination and seed dispersal on genetic patterns is a central issue in plant population biology. In my thesis, I investigated (i) contemporary dispersal and gene flow distances as well as (ii) genetic diversity and spatial genetic structure (SGS) across subsequent recruitment stages in a population of the animal-pollinated and dispersed tree Prunus africana in Kakamega Forest, West Kenya. Using microsatellite markers and parentage analyses, I inferred distances of pollen dispersal (father-to-mother), seed dispersal/maternal gene flow (mother-to-offspring) as well as paternal gene flow (father-to-offspring) for four early life stages of the species (seeds and fruits, current year seedlings, seedlings ≤ 3yr, seedlings > 3yr). Distances of pollen and seed dispersal as well as paternal gene flow were significantly shorter than expected from the spatial arrangement of trees and sampling plots. They were not affected by the density of conspecific trees in the surrounding. At the propagule stage, mean pollen dispersal distances were considerably (23-fold) longer than seed dispersal distances, and paternal gene flow distances exceeded maternal gene flow by a factor of 25. Seed dispersal distances were remarkably restricted, potentially leading to a strong initial SGS. The initial genetic template created by pollination and seed dispersal was extensively altered during later recruitment stages. Potential Janzen-Connell effects led to markedly increasing distances between offspring and both parental trees in older life stages. This showed that distance and density-dependent mortality factors are not exclusively related to the mother tree, but also to the father. Across subsequent recruitment stages, the pollen to seed dispersal ratio and the paternal to maternal gene flow ratio dropped to 2.1 and 3.4, respectively, in seedlings > 3yr. The relative changes in effective pollen dispersal, seed dispersal, and paternal gene flow distances across recruitment stages elucidate the mechanisms affecting the contribution of the two processes pollen and seed dispersal to overall gene flow. Using the same six microsatellite loci, I analyzed genetic diversity and SGS across five life stages, from seed rain to adults. Levels of genetic diversity within the studied P. africana population were comparable to other Prunus species and did not vary across life stages. In congruence with the short seed dispersal distances, I found significant SGS in all life stages. SGS decreased from seed and early seedling stages to older juvenile stages, and it was higher in adults than in late juveniles of the next generation. A comparison of the data with direct assessments of contemporary gene flow patterns indicate that distance- or density-dependent mortality, potentially due to Janzen-Connell effects, led to the initial decrease in SGS. Intergeneration variation in SGS could have been driven by variation in demographic processes, the effect of overlapping generations, and local selection processes. Overall, my study showed that complex sequential processes during recruitment contribute to the spatial genetic structure of tree populations. It highlights the importance of a multistage perspective for a comprehensive understanding of the impact of animal-mediated pollen and seed dispersal on spatial population dynamics and genetic patterns of trees.