Factorization and non-local 1/m b corrections in the decay B X s gamma

In this thesis, a systematic analysis of the bar B to X_sgamma photon spectrum in the endpoint region is presented. The endpoint region refers to a kinematic configuration of the final state, in which the photon has a large energy m_b-2E_gamma = O(Lambda_QCD), while the jet has a large energy but small invariant mass. Using methods of soft-collinear effective theory and heavy-quark effective theory, it is shown that the spectrum can be factorized into hard, jet, and soft functions, each encoding the dynamics at a certain scale. The relevant scales in the endpoint region are the heavy-quark mass m_b, the hadronic energy scale Lambda_QCD and an intermediate scale sqrt{Lambda_QCD m_b} associated with the invariant mass of the jet. It is found that the factorization formula contains two different types of contributions, distinguishable by the space-time structure of the underlying diagrams. On the one hand, there are the direct photon contributions which correspond to diagrams with the photon emitted directly from the weak vertex. The resolved photon contributions on the other hand arise at O(1/m_b) whenever the photon couples to light partons. In this work, these contributions will be explicitly defined in terms of convolutions of jet functions with subleading shape functions. While the direct photon contributions can be expressed in terms of a local operator product expansion, when the photon spectrum is integrated over a range larger than the endpoint region, the resolved photon contributions always remain non-local. Thus, they are responsible for a non-perturbative uncertainty on the partonic predictions. In this thesis, the effect of these uncertainties is estimated in two different phenomenological contexts. First, the hadronic uncertainties in the bar B to X_sgamma branching fraction, defined with a cut E_gamma > 1.6 GeV are discussed. It is found, that the resolved photon contributions give rise to an irreducible theory uncertainty of approximately 5 %. As a second application of the formalism, the influence of the long-distance effects on the direct CP asymmetry will be considered. It will be shown that these effects are dominant in the Standard Model and that a range of -0.6 < A_CP^SM < 2.8 % is possible for the asymmetry, if resolved photon contributions are taken into account.

Chiral properties of two-flavour QCD at zero and non-zero temperature

Lattice Quantum Chromodynamics (LQCD) is the preferred tool for obtaining non-perturbative results from QCD in the low-energy regime. It has by nowrnentered the era in which high precision calculations for a number of phenomenologically relevant observables at the physical point, with dynamical quark degrees of freedom and controlled systematics, become feasible. Despite these successes there are still quantities where control of systematic effects is insufficient. The subject of this thesis is the exploration of the potential of todays state-of-the-art simulation algorithms for non-perturbativelyrn$\mathcal{O}(a)$-improved Wilson fermions to produce reliable results in thernchiral regime and at the physical point both for zero and non-zero temperature. Important in this context is the control over the chiral extrapolation. Thisrnthesis is concerned with two particular topics, namely the computation of hadronic form factors at zero temperature, and the properties of the phaserntransition in the chiral limit of two-flavour QCD.rnrnThe electromagnetic iso-vector form factor of the pion provides a platform to study systematic effects and the chiral extrapolation for observables connected to the structure of mesons (and baryons). Mesonic form factors are computationally simpler than their baryonic counterparts but share most of the systematic effects. This thesis contains a comprehensive study of the form factor in the regime of low momentum transfer $q^2$, where the form factor is connected to the charge radius of the pion. A particular emphasis is on the region very close to $q^2=0$ which has not been explored so far, neither in experiment nor in LQCD. The results for the form factor close the gap between the smallest spacelike $q^2$-value available so far and $q^2=0$, and reach an unprecedented accuracy at full control over the main systematic effects. This enables the model-independent extraction of the pion charge radius. The results for the form factor and the charge radius are used to test chiral perturbation theory ($\chi$PT) and are thereby extrapolated to the physical point and the continuum. The final result in units of the hadronic radius $r_0$ is rn$$ \left\langle r_\pi^2 \right\rangle^{\rm phys}/r_0^2 = 1.87 \: \left(^{+12}_{-10}\right)\left(^{+\:4}_{-15}\right) \quad \textnormal{or} \quad \left\langle r_\pi^2 \right\rangle^{\rm phys} = 0.473 \: \left(^{+30}_{-26}\right)\left(^{+10}_{-38}\right)(10) \: \textnormal{fm} \;, $$rn which agrees well with the results from other measurements in LQCD and experiment. Note, that this is the first continuum extrapolated result for the charge radius from LQCD which has been extracted from measurements of the form factor in the region of small $q^2$.rnrnThe order of the phase transition in the chiral limit of two-flavour QCD and the associated transition temperature are the last unkown features of the phase diagram at zero chemical potential. The two possible scenarios are a second order transition in the $O(4)$-universality class or a first order transition. Since direct simulations in the chiral limit are not possible the transition can only be investigated by simulating at non-zero quark mass with a subsequent chiral extrapolation, guided by the universal scaling in the vicinity of the critical point. The thesis presents the setup and first results from a study on this topic. The study provides the ideal platform to test the potential and limits of todays simulation algorithms at finite temperature. The results from a first scan at a constant zero-temperature pion mass of about 290~MeV are promising, and it appears that simulations down to physical quark masses are feasible. Of particular relevance for the order of the chiral transition is the strength of the anomalous breaking of the $U_A(1)$ symmetry at the transition point. It can be studied by looking at the degeneracies of the correlation functions in scalar and pseudoscalar channels. For the temperature scan reported in this thesis the breaking is still pronounced in the transition region and the symmetry becomes effectively restored only above $1.16\:T_C$. The thesis also provides an extensive outline of research perspectives and includes a generalisation of the standard multi-histogram method to explicitly $\beta$-dependent fermion actions.

Laboratory and field measurements of enantiomeric and non-enantiomeric biogenic VOCs and anthropogenic BTEX compounds

This doctoral thesis was focused on the investigation of enantiomeric and non-enantiomeric biogenic organic compound (BVOC) emissions from both leaf and canopy scales in different environments. In addition, the anthropogenic compounds benzene, toluene, ethylbenzene, and xylenes (BTEX) were studied. BVOCs are emitted into the lower troposphere in large quantities (ca. 1150 Tg C ·yr-1), approximately an order of magnitude greater than the anthropogenic VOCs. BVOCs are particularly important in tropospheric chemistry because of their impact on ozone production and secondary organic aerosol formation or growth. The BVOCs examined in this study were: isoprene, (-)/ (+)-α-pinene, (-)/ (+)-ß-pinene, Δ-3-carene, (-)/ (+)-limonene, myrcene, eucalyptol and camphor, as these were the most abundant BVOCs observed both in the leaf cuvette study and the ambient measurements. In the laboratory cuvette studies, the sensitivity of enantiomeric enrichment change from the leaf emission has been examined as a function of light (0-1600 PAR) and temperature (20-45°C). Three typical Mediterranean plant species (Quercus ilex L., Rosmarinus officinalis L., Pinus halepensis Mill.) with more than three individuals of each have been investigated using a dynamic enclosure cuvette. The terpenoid compound emission rates were found to be directly linked to either light and temperature (e.g. Quercus ilex L.) or mainly to temperature (e.g. Rosmarinus officinalis L., Pinus halepensis Mill.). However, the enantiomeric signature showed no clear trend in response to either the light or temperature; moreover a large variation of enantiomeric enrichment was found during the experiment. This enantiomeric signature was also used to distinguish chemotypes beyond the normal achiral chemical composition method. The results of nineteen Quercus ilex L. individuals, screened under standard conditions (30°C and 1000 PAR) showed four different chemotypes, whereas the traditional classification showed only two. An enclosure branch cuvette set-up was applied in the natural boreal forest environment from four chemotypes of Scots pine (Pinus sylvestris) and one chemotype of Norway spruce (Picea abies) and the direct emissions compared with ambient air measurements above the canopy during the HUMPPA-COPEC 2010 summer campaign. The chirality of a-pinene was dominated by (+)-enantiomers from Scots pine while for Norway spruce the chirality was found to be opposite (i.e. Abstract II (-)-enantiomer enriched) becoming increasingly enriched in the (-)-enantiomer with light. Field measurements over a Spanish stone pine forest were performed to examine the extent of seasonal changes in enantiomeric enrichment (DOMINO 2008). These showed clear differences in chirality of monoterpene emissions. In wintertime the monoterpene (-)-a-pinene was found to be in slight enantiomeric excess over (+)-a-pinene at night but by day the measured ratio was closer to one i.e. racemic. Samples taken the following summer in the same location showed much higher monoterpene mixing ratios and revealed a strong enantiomeric excess of (-)-a-pinene. This indicated a strong seasonal variance in the enantiomeric emission ratio which was not manifested in the day/night temperature cycles in wintertime. A clear diurnal cycle of enantiomeric enrichment in a-pinene was also found over a French oak forest and the boreal forest. However, while in the boreal forest (-)-a-pinene enrichment increased around the time of maximum light and temperature, the French forest showed the opposite tendency with (+)-a-pinene being favored. For the two field campaigns (DOMINO 2008 and HUMPPA-COPEC 2010), the BTEX were also investigated. For the DOMINO campaign, mixing ratios of the xylene isomers (meta- and para-) and ethylbenzene, which are all well resolved on the ß-cyclodextrin column, were exploited to estimate average OH radical exposures to VOCs from the Huelva industrial area. These were compared to empirical estimates of OH based on JNO2 measured at the site. The deficiencies of each estimation method are discussed. For HUMPPA-COPEC campaign, benzene and toluene mixing ratios can clearly define the air mass influenced by the biomass burning pollution plume from Russia.