On global linearization of planar involutions

Let phi: a"e(2) -> a"e(2) be an orientation-preserving C (1) involution such that phi(0) = 0. Let Spc(phi) = {Eigenvalues of D phi(p) | p a a"e(2)}. We prove that if Spc(phi) aS, a"e or Spc(phi) a (c) [1, 1 + epsilon) = a... for some epsilon > 0, then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h = (I + D phi(0)phi)/2,where I: a"e(2) -> a"e(2) is the identity map. Similarly, we prove that if phi is an orientation-reversing C (1) involution such that phi(0) = 0 and Trace (D phi(0)D phi(p) > - 1 for all p a a"e(2), then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h. Finally, we show that h may fail to be a global linearization of phi if the above conditions are not fulfilled.

Search for time-integrated cp violation in $d^0 \rightarrow k^+k^-$ and $d^0 \rightarrow \pi^+\pi^-$ decays at lhcb.

The LHCb experiment at the LHC, by exploiting the high production cross section for $c\overline{c}$ quark pairs, offers the possibility to investigate $\mathcal{CP}$ violation in the charm sector with a very high precision.\\ In this thesis a measurement of time-integrated \(\mathcal{CP}\) violation using $D^0\rightarrow~K^+K^-$ and $D^0\rightarrow \pi^+\pi^-$ decays at LHCb is presented. The measured quantity is the difference ($\Delta$) of \(\mathcal{CP}\) asymmetry ($\mathcal{A}_{\mathcal{CP}}$) between the decay rates of $D^0$ and $\overline{D}^0$ mesons into $K^+K^–$ and $\pi^+\pi^-$ pairs.\\ The analysis is performed on 2011 data, collected at \(\sqrt{s}=7\) TeV and corresponding to an integrated luminosity of 1 fb\(^{-1}\), and 2012 data, collected at \(\sqrt{s}=8\) TeV and corresponding to an integrated luminosity of 2 fb\(^{-1}\).\\ A complete study of systematic uncertainties is beyond the aim of this thesis. However the most important systematic of the previous analysis has been studied. We find that this systematic uncertainty was due to a statistical fluctuation and then we demonstrate that it is no longer necessary to take into account.\\ By combining the 2011 and 2012 results, the final statistical precision is 0.08\%. When this analysis will be completed and published, this will be the most precise single measurement in the search for $\mathcal{CP}$ violation in the charm sector.

Misura di asimmetria CP nei decadimenti: $D^0 \to K^+K^-$ e $D^0 \to \pi^+ \pi^-$ ad LHCb

La fisica del sapore è uno dei settori di ricerca più promettenti per realizzare misure di altissima precisione del Modello Standard e per osservare indirettamente, attraverso i decadimenti mediati dalle interazioni deboli nuove particelle. L'esperimento LHCb \`e stato progettato per realizzare misure di altissima precisione in questo settore. Grazie all'alta luminosità integrata disponibile (3 fb \ap{-1}) ed alla elevata sezione d’urto di produzione dei quark charm, LHCb \`e in grado di realizzare misure di una precisione mai raggiunta fino ad ora da altri esperimenti. In questo lavoro di tesi \`e stata realizzata una misura preliminare della simmetria di violazione di CP, realizzata mediante i decadimenti dei mesoni neutri $D^0$ negli stati finali $K^+K^-$ e $\pi^+\pi^-$. Per realizzare la misura sono stati selezionati i decadimenti $D^{*\pm} \to D^0(K^+K^-)\pi^\pm_s$ e $D^{*\pm} \to D^0(\pi^+\pi^-)\pi^\pm_s$ utilizzando i dati raccolti da LHCb durante il RUN-1 (2010-2012) ed \`e stato sviluppato un modello di adattamento ai dati in grado di misurare la differenza di asimmetria di CP integrate nel tempo nei decadimenti $D^0 \rightarrow K^+K^-$ e $D^0 \rightarrow \pi^+\pi^-$, $\Delta A_{CP}$. Il modello \`e stato sviluppato in modo da descrivere le distribuzioni di massa invariante del $D^0$ e del $D^{*\pm}$ sia per la componente di segnale sia per quelle di fondo ed \`e stato adattato ai dati, per sottrarne i fondi e misurare le asimmetrie $A_{RAW}(K^+K^-)$ e $A_{RAW}(\pi^+\pi^-)$, corrispondenti alla differenza tra il numero di eventi di segnale $D^{*+}$ e $D^{*-}$, diviso la loro somma. La differenza di queste asimmetrie corrisponde a $\Delta A_{CP}$, la cui misura, non ufficiale, \`e stata determinata essere $\Delta A_{CP}= (-0.12\pm 0.08)\% $. Questo risultato rappresenta la miglior misura al mondo mai realizzata da un singolo esperimento.

Grain size distributions of the Bossons glacier (France)

The study presented in this PhD memory aim at better define and quantify the present timeerosion processes in glacial and proglacial domain. The Glacier des Bossons, situated in theMont-Blanc massif (Haute-Savoie, France), is a good example of a natural and nonanthropizedsystem which allows us to study this topic. This glacier lies on two mainlithologies (the Mont-Blanc granite and the metamorphic bedrock) and this peculiarity is usedto determine the origin of the glacial sediments. The sediments were sampled at the glaciersurface and at the glacier sole and also in the subglacial streams in order to understand themechanisms of mechanical erosion and particle transportation in glacial domain. The study ofthe granulometric distribution and the origin of the sediments were performed by a lithologicanalysis at macro-scale (naked-eye) and a geochemical analysis at micro-scale (U-Pb datingof zircons). These analyses allowed specifying the characteristics of glacial erosion andtransport. (1) the supraglacial sediments derived from the erosion of the rocky valley sides aremainly coarse and the glacial transport does not mix these clasts with those derived from thesub-glacial erosion, except in the lower tongue; (2) the sub-glacial erosion rates areinhomogeneous, erosion under the temperate glacier (0.4-0.8 mm/yr) is at least sixteen timesmore efficient than the erosion under the cold glacier (0.025-0.05 mm/yr); (3) the sub-glacialsediments contain a silty and sandy fraction, resulting from processes of abrasion andcrushing, which is evacuated by sub-glacial streams. The high-resolution temporal acquisitionof hydro-sedimentary data during the 2010 melt season, between the May 5th and theSeptember 17th, allowed defining the seasonal behavior of the hydrologic and sedimentaryfluxes. The sediment exportation occurs mainly during the melt season therefore, quantify thesediment fluxes in the Bossons stream and measure regularly the topographic evolution of thefluvio-glacial system allows to perform a sedimentary balance of the erosion of glacial andnon-glacial domains. During the year 2010, about 3000 tons of sediments were eroded with430 tons settled on the fluvio-glacial system. By analyzing the evolution of suspendedparticulate matter concentrations in the Bossons stream upstream and downstream the fluvioglacialsystem, the part of glacial erosion and non-glacial denudation in the sedimentarybalance could be proportioned. The erosion during the stormy events of the uncoveredmoraines, confining the fluvio-glacial system of the Bossons stream, furnishes at least 59% ofthe sediments exported by the Bossons stream and glacial erosion (41% of the flux) istherefore less efficient comparatively. The long-term evolution of the glacial systems inperiod of global warming would show a sustained erosion of proglacial environments(mountain sides and moraines) recently exposed and therefore an increasing of the detritalfluxes. The Glacier des Bossons protects the summit of the Mont-Blanc, the differentialerosion between zones under the ice and non-glacial could lead to an increase of thedifference of altitude between valleys and summits.