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 $a_0^2$.

Ansatz zur Generierung einer konditionalen, reversiblen Wt1 k.o.-Maus

Ansatz zur Generierung einer konditionalen, reversiblen Wt1 k.o.-Maus Der Wilms-Tumor (WT, Nephroblastom) ist ein embryonaler Nierentumor, der durch die maligne Transformation von undifferenziertem Nierengewebe, sog. nephrogenen Resten, entsteht. WT treten mit einer Inzidenz von 1 in 10.000 Lebendgeburten auf. Das Hauptmanifestationsalter, der normalerweise einseitig und sporadisch auftretenden Tumore, liegt zwischen dem 3. und 4. Lebensjahr. Etwa 10 % der Patienten entwickeln jedoch bilaterale Tumore. In diesen Fällen ist eine Assoziation mit komplexen genetischen Krankheitsbildern (u. a. WAGR-, Denys-Drash-, Frasier- und Beckwith-Wiedemann-Syndrom) festzustellen. In 15 % der sporadischen WT sind Mutationen im WT1 (Wilms-Tumor 1)-Gen beschrieben. WT1 besteht aus zehn Exons und weist typische Merkmale von Transkriptionsfaktoren (z. B. vier Zinkfinger) auf. Zwei alternative Spleißereignisse betreffen Exon 5 (+/−Exon 5) und Exon 9 (Transkripte mit bzw. ohne die codierenden Sequenzen für die AS Lysin-Threonin-Serin; +/−KTS). Die Lage der drei alternativ vorhandenen AS zwischen den Zinkfingern 3 und 4 bestimmt die verschiedenen Funktionen der WT1-Proteine (4 Isoformen) als Transkriptionsfaktor (−KTS) bzw. als RNA-bindendes Protein (+KTS). Das zunächst im Zusammenhang mit WT als Tumorsuppressorgen identifizierte WT1 ist ein Entwicklungsgen mit einem sehr komplexen Expressionsmuster in der Embryonalentwicklung. Dabei ist v. a. die Bedeutung in der Urogenitalentwicklung entscheidend. Konstitutive, homozygote Wt1−/− k.o.-Mäuse sind embryonal (~ E12,5 dpc) letal und bilden u. a. keine Gonaden und keine Nieren. Aus diesem Grund existiert bisher kein Wilms-Tumormodell. Die Herstellung eines konditionalen murinen Tiermodells auf Basis des Tet on/off-Systems zur Untersuchung der Nierenentwicklung bzw. zur Analyse der Wilms-Tumorpathogenese war Ziel dieser Arbeit. Hierfür wurden drei Mauslinien generiert: Zwei transgene sog. Responder-Linien, die eine chimäre spleißbare Wt1-cDNA der Variante musWt1+Exon 5;+/−KTS unter der Kontrolle eines Tet-responsiven Promotors im Genom tragen. Dieses tTA/Dox-abhängig regulierbare Wt1-Transgen (tgWt1) sollte (exogen regulierbar) die Expression des endogenen Wt1-Lokus ausreichend nachahmen, um die kritischen Phasen der Embryogenese zu überwinden und lebensfähige Tiere zu erhalten. Parallel dazu wurde die Wt1-Effektor-Mauslinie (WE2) generiert. Diese trägt einen tetrazyklinabhängigen Transaktivator (tTA) zur Steuerung Tet-regulierbarer Transgene unter der Kontrolle des endogenen Wt1-Promotors. Die durch homologe Rekombination in ES-Zellen erreichte Integration des tTA direkt am Translationsstartpunkt des Wt1-Lokus hat in den Tieren einen heterozygoten Wt1 knock out/tTA knock in zur Folge. Die bisher vorgenommenen Verpaarungen doppelt transgener Wt1-tTA+/−/Resp-Mäuse ergaben keinen Rescue des letalen Wt1 k.o. und es konnten bislang keine Wilms-Tumore induziert werden. Alle im Verlauf der Arbeit generierten Mauslinien wurden umfassend charakterisiert. So konnte für die Tiere der Responder-Linien Wt1-Resp1 (mit zusätzlichen Isolator-Sequenzen zum Schutz des Transgens vor Positionseffekten) und Wt1-Resp2 (ohne Isolatoren) konnte die Tet-induzierbare Expression und die Spleißbarkeit des tgWt1 in MEF-Assays und mittels Effektor-Mäusen auf RNA-Ebene nachgewiesen werden. Die genomische Charakterisierung der WE2-Linie ergab eine ungeklärte etwa 120 kb große Inversion am Wt1-Lokus, die alle 5'-regulatorischen Sequenzen mitsamt des tTA vom Rest von Wt1 trennt. Tiere dieser Linie weisen aber dennoch einen funktionalen Wt1 k.o. auf: Unter den Nachkommen aus Intercross-Verpaarungen von Wt1-tTA+/−-Mäusen lassen sich auf Grund der Letalität keine Wt1−/−-Genotypen nachweisen. Die Charakterisierung der Effektor-Linie auf RNA-Ebene und mittels Reporter-Mäusen liefert ein Wt1-analoges tTA-Expressionsmuster: So findet man eine deutliche tTA-Expression u. a. in Niere (Glomeruli), Uterus, Ovar und Testis. Die hier vorgestellten Experimente ergeben darüber hinaus eindeutige Hinweise einer Beteiligung von Wt1 in der Entstehung der glatten Muskulatur bzw. in der Vaskulogenese.

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Measurement of K +- pi +- gamma gamma decays

The goal of this thesis was an experimental test of an effective theory of strong interactions at low energy, called Chiral Perturbation Theory (ChPT). Weak decays of kaon mesons provide such a test. In particular, K± → π±γγ decays are interesting because there is no tree-level O(p2) contribution in ChPT, and the leading contributions start at O(p4). At this order, these decays include one undetermined coupling constant, ĉ. Both the branching ratio and the spectrum shape of K± → π±γγ decays are sensitive to this parameter. O(p6) contributions to K± → π±γγ ChPT predict a 30-40% increase in the branching ratio. From the measurement of the branching ratio and spectrum shape of K± → π±γγ decays, it is possible to determine a model dependent value of ĉ and also to examine whether the O(p6) corrections are necessary and enough to explain the rate.About 40% of the data collected in the year 2003 by the NA48/2 experiment have been analyzed and 908 K± → π±γγ candidates with about 8% background contamination have been selected in the region with z = mγγ2/mK2 ≥ 0.2. Using 5,750,121 selected K± → π±π0 decays as normalization channel, a model independent differential branching ratio of K± → π±γγ has been measured to be:BR(K± → π±γγ, z ≥ 0.2) = (1.018 ± 0.038stat ± 0.039syst ± 0.004ext) ∙10-6. From the fit to the O(p6) ChPT prediction of the measured branching ratio and the shape of the z-spectrum, a value of ĉ = 1.54 ± 0.15stat ± 0.18syst has been extracted. Using the measured ĉ value and the O(p6) ChPT prediction, the branching ratio for z =mγγ2/mK2 <0.2 was computed and added to the measured result. The value obtained for the total branching ratio is:BR(K± → π±γγ) = (1.055 ± 0.038stat ± 0.039syst ± 0.004ext + 0.003ĉ -0.002ĉ) ∙10-6, where the last error reflects the uncertainty on ĉ.The branching ratio result presented here agrees with previous experimental results, improving the precision of the measurement by at least a factor of five. The precision on the ĉ measurement has been improved by approximately a factor of three. A slight disagreement with the O(p6) ChPT branching ratio prediction as a function of ĉ has been observed. This mightrnbe due to the possible existence of non-negligible terms not yet included in the theory. Within the scope of this thesis, η-η' mixing effects in O(p4) ChPT have also been measured.