Wir präsentieren die Analyse der Daten, die in den Jahren 2002-2004 mit dem 27.56 GeV Positronenstrahl des HERA Speicherrings am DESY und dem internen transversal polarisierten Wasserstofftarget (''fixed target'') des HERMES Experiments aufgenommen wurden. Ereignisse mit einem gestreuten Positron und einem erzeugter Pion wurden selektiert. Die ausschließliche Erzeugung eines einzelnen Pions, e p -> e'' n pi+, wird durch die Anforderung gewährleistet, daß die fehlende Masse des Ereignisses der Masse des Neutrons, das nicht gemessen wird, entspricht. Der Streuquerschnitt für diesen Prozess hängt von der Bjorken-Skalenvariable, den Vierer-Impulsübertrag und den Transversalimpulsübertrag, deren durchschnittliche Werte für unsere Datensätze bei =0.12, =2.3 GeV^2, =-0.18 GeV^2 liegen, sowie zwei azimuthale Winkel: der Winkel phi zwischen den Streu- und Produktionsebene (die Schnittlinie der Ebenen enthält das virtuelle Photon), und der Winkel phi_S zwischen der Streuebene und dem Polarisationsvector des Targets. Die Asymmetrie, auch Transversal-Target-Einzelspin-Azimuthalasymmetrie genannt, wird als das Verhältnis der Differenz zur Summ der Streuquerschnitte für die positive und negative Targetpolarisation definiert. Es wird durch sechs azimuthale Sinus-Modulationen charakterisiert, deren Amplituden von -1 bis 1 varieren können. Wir messen die Asymmetrie eines Datensatzes von 2093 Ereignissen mit einem Signal-Rausch-Verhältnis von 1:1. Im Durchschnitt wurden geringe oder mit Null übereinstimmende Amplitudenwerte gefunden, abgesehen von der Amplitude von der sin(phi_S) Modulation, allerdings innerhalb der großen exprimentellen Unsicherheiten. Ein direkter und genauerer Vergleich der Daten mit der Theorie verlangt größere Statistik und verbesserte Fähigkeiten des Detektor als für die vorliegende Messung vorhanden waren. / We present the analysis of data taken in the years 2002-2004 with the 27.56 GeV positron beam of the HERA storage ring at DESY and the internal transversely polarised hydrogen fixed target of the HERMES experiment. Events with a scattered positron and a produced pion are selected. Exclusive production of single pions, e p -> e'' n pi+, is ensured by requiring the missing mass in the event to be equal to the mass of the neutron, which is not detected. The cross section for this process depends on the Bjorken scaling variable, the four-momentum transfer, and the transverse four-momentum transfer, whose average values for our sample are =0.12, =2.3 GeV^2, =-0.18 GeV^2, respectively, and two azimuthal angles: the angle phi between the scattering and production planes (their common line contains the virtual photon), and the angle phi_S between the scattering plane and the target polarisation vector. The asymmetry, also called transverse-target single-spin azimuthal asymmetry, is defined as the ratio of the difference to the sum of the cross sections for positive and negative target polarisation. It is characterised by six azimuthal sine modulations, whose amplitudes can vary from -1 to 1. We measure the asymmetry from a sample of 2093 events with a signal-to-background ratio of 1:1. At average kinematics, the values of the amplitudes are found to be small or consistent with zero, except for the amplitude of the sin(phi_S) modulation, however, within their large statistical uncertainties. A direct and more precise data-to-theory comparison requires larger statistics and improved detector capabilities than available for the present measurement.

It has been known since the 1930’s that protons and neutrons, collectively called as nucleons, are not “point-like” elementary particles, but rather have a substructure. Today, we know from Quantum Chromodynamics (QCD) that nucleons are made from quarks and gluons, with gluons being the elementary force carriers for strong interactions. Quarks and gluons are collectively called as partons. The substructure of the nucleons can be described in terms of parton correlation functions such as Form Factors, (1D) Parton Distribution Functions (PDFs) and their 3D generalizations in terms of Transverse Momentum-dependent parton Distributions (TMDs) and Generalized Parton Distributions (GPDs). All these functions can be derived from the even more general Generalized Transverse Momentum-dependent Distributions (GTMDs). This dissertation promises to provide an insight into all these functions from the point of view of their accessibility in experiments, from model calculations, and from their direct calculation within lattice formulations of QCD. In the first part of this dissertation, we identify physical processes to access GTMDs. By considering the exclusive double Drell-Yan process, we demonstrate, for the very first time, that quark GTMDs can be measured. We also show that exclusive double-quarkonium production in nucleon-nucleon collisions is a direct probe of gluon GTMDs. In the second part of this dissertation, we shift our focus to the “parton quasi-distributions”. Over the last few decades, lattice QCD extraction of the full x-dependence of the parton distributions has always been prohibited by the explicit time-dependence of the correlation functions. In 2013, there was a path-breaking proposal by X. Ji to calculate instead parton quasi-distributions (quasi-PDFs). The procedure of “matching” is a crucial ingredient in the lattice QCD extraction of parton distributions from the quasi-PDF approach. We address the matching for the twist-3 PDFs gT (x), e(x), and hL(x) for the very first time. We pay special attention to the challenges involved in the calculations due to the presence of singular zero-mode contributions. We also present the first-ever lattice QCD results for gT (x) and hL(x) and we discuss the impact of these results on the phenomenology. Next, we explore the general features of quasi-GPDs and quasi-PDFs in diquark spectator models. Furthermore, we address the Burkhardt-Cottingham-type sum rules for the relevant light-cone PDFs and quasi-PDFs in a model-independent manner and also check them explicitly in perturbative model calculations. The last part of this dissertation focuses on the extraction g1T (x,~k2⊥) TMD for the very first time from experimental data using Monte Carlo techniques. This dissertation therefore unravels different aspects of the distribution functions from varied perspectives.

The Spin Asymmetries of the Nucleon Experiment (SANE) measured the proton spin structure function g2 in a range of Bjorken x, 0.3 < x < 0.8, where extraction of the twist-3 matrix element dp2 (an integral of g2 weighted by x2) is most sensitive. The data was taken from Q2 equal to 2.5 GeV 2 up to 6.5 GeV2. In this polarized electron scattering off a polarized hydrogen target experiment, two double spin asymmetries, Ak and A⊥ were measured using the BETA (Big Electron Telescope Array) Detector. BETA consisted of a scintillator hodoscope, gas ˇCerenkov counter, lucite hodoscope and a large lead glass electromagnetic calorimeter. With a unique open geometry, a threshold gas ˇCerenkov detector allowed BETA to cleanly identify electrons for this inclusive experiment. A measurement of dp2 is compared to lattice QCD calculations. / Physics

Der H1 Detektor ist eines der komplexen Messinstrumente am HERA Beschleuniger. Er wurde gebaut, um die Wechselwirkung von Elektronen und Protonen bei höchsten Schwerpunktenergien von bis zu 320 GeV zu untersuchen. Ein Hauptthema ist die Bestimmung der Protonstruktur mit der bestmöglichen Genauigkeit über die Messung des inklusiven tiefinelastischen Wirkungsquerschnitt als Funktion der kinematischen Variablen x und Q2. In dieser Arbeit wird eine neue Messung des tiefinelastischen Wirkungsquerschnitt vorgestellt. Dazu werden Daten analysiert, welche im Jahre 2000 aufgezeichnet wurden. Die Messung ist beschränkt auf den Bereich mittlerer und niedriger Inelastizität y. In diesem Bereich ist die Messung des reduzierten Wirkungsquerschnittes fast identisch mit der Protonstrukturfunktion F2. Die Messung erstreckt sich über etwa eine Größenordnung in der Photon-Virtualität, 10 < Q2 < 180 GeV2, und drei Größenordnungen in der Bjorken Skalenvariable, 0.00013 < x < 0.15. Die Genauigkeit ist durch systematische Unsicherheiten limitiert. Im Vergleich zu den publizierten Ergebnissen mit den Daten aus den Jahren 1996/97 konnten diese Unsicherheiten signifikant reduziert werden. Die Fehler der neuen Messung liegen meist im Bereich von 1,3 - 2,0%, was eine Verbesserung um ca. 30% gegenüber früheren Resultaten darstellt. Keiner der systematischen Effekte dominiert die Unsicherheiten für die Mehrzahl der Messpunkte. Ein unerwartetes Ergebnis ist die signifikante Abweichung der neuen Messung von der publizierten. Eine neue Analyse der alten Daten zeigt, dass diese Diskrepanz nicht in den Daten selbst liegt. Es wird weiterhin gezeigt, dass Annahmen über die simulierten Ereignisdaten, welche für die Analyse der alten Daten verwendet wurden, falsch waren. Der Effekt ist eine um bis zu 3% falsche Messung. Nach einer Korrektur dieses Effektes stimmen die alte und die neue Messung unter Berücksichtigung ihrer Unsicherheiten miteinander überein. / The H1 detector at the HERA collider is a complex device to study the interactions of electrons and protons at a centre of mass energy of 320 GeV. One of the main goals is to determine the sub structure of the proton with the best possible precision by measuring the inclusive Deep Inelastic Scattering cross section as a function of the kinematic variables Q2 and x. This work presents a new measurement of the inclusive Deep Inelastic $ep$ Scattering cross section using the data taken with the H1 experiment in the year 2000. The measurement is restricted to the region of low and intermediate inelasticities y. In this domain the reduced cross section is mostly identical to the proton structure function F2. About one order of magnitude in the photon virtuality, 10 < Q2 < 180 GeV2, and three orders of magnitude in the Bjorken scaling variable, 0.00013 < x < 0.15, are covered. The accuracy in this range is limited by systematic uncertainties. Compared to the published results using the data from the years 1996/97, these uncertainties are reduced by a significant amount and a self consistent measurement is presented. The errors of the new measurement are typically in the range of 1.3 - 2.0%, which means a 30% improvement over the previously published results. None of the considered systematic error sources dominates the total uncertainty in the bulk of the measurement. An unexpected but nevertheless very important result is the observed discrepancy of the measurement to the previously published H1 results. A new analysis of the older data shows, that the data sets themselves are not responsible for this. It is also found, that assumptions made for the simulated event sample were wrong and therefore the published cross section measurement is biased by up to 3%. An approximate correction of the published data leads to a reasonable agreement of the old and the new measurement within their respective uncertainties.

In dieser Arbeit wird eine Messung des inklusiven tief-inelastischen Positron- Proton Wirkungsquerschnitts bei kleinen Impulsüberträgen Q2 vorgestellt. Die Messung wird zur Bestimmung der longitudinalen Protonstrukturfunktion FL benutzt. Es werden Daten analysiert, welche mit dem H1 Detektor in speziellen Perioden mit reduzierter Protonstrahlenergie im Jahre 2007 aufgezeichnet wurden. Die direkte Bestimmung der Strukturfunktion FL basiert auf der Messung des reduzierten tiefinelastischen Wirkungsquerschnitt bei drei verschiedenen Schwerpunktsenergien. Ein spezieller Rekonstruktionsalgorithmus für Elektronen wurde entwickelt, welcher die Informationen der zentralen Spurkammer CJC und des Siliziumdetektors BST kombiniert. Dieser wurde in die H1 Rekonstruktionssoftware H1REC integriert. Die Effizienz des Algorithmus wird untersucht. Die Arbeit präsentiert den Wirkungsquerschnitt und die FL Messung für Inelastizitäten im Bereich von 2.5 GeV2 < Q2 < 25 GeV2. / A measurement of the inclusive cross section for the deep-inelastic scattering of positrons on protons at low four-momentum transfer squared Q2 is presented. The measurement is used for the extraction of the longitudinal proton structure function FL. The analysis is based on data collected by the H1 experiment during special, low energy runs in the year 2007. The direct technique of the FL determination based on the extraction of the reduced DIS cross sections for three different centre-of-mass energies is used. For the purpose of the analysis a dedicated electron finder has been developed and integrated with the standard H1 reconstruction software H1REC. The algorithm employs information from two independent tracking detectors the Backward Silicon Tracker and the Central Jet Chamber. The performance of the finder is studied. The thesis presents the cross section and the FL measurements in the range of 2.5 GeV2 < Q2 < 25 GeV2.

<p>The Standard Model describes all elementary particles known today, but at larger energies it will have to be complemented with new particles and interactions. To be able to distinguish new physics at proton colliders such as LHC at CERN, it is essential to have an appropriate description of the colliding protons and their interactions. The study of the proton is important also in itself, to get a better understanding of the non-perturbative aspects of the strong interaction.</p><p>In paper I-IV of this thesis, a model for the non-perturbative dynamics of quarks and gluons is developed, based on quantum fluctuations in hadrons. The parton distributions of the proton are given by momentum fluctuations, with sea quark distributions generated by fluctuations into baryon-meson pairs. This model can reproduce proton structure function data, as well as measured asymmetries between up and down valence quark distributions and between the anti-up and anti-down sea. It provides an intrinsic charm quark component as indicated by data. It also predicts an asymmetry in the strange sea of the proton, which can explain the NuTeV anomaly first attributed to new physics beyond the Standard Model.</p><p>Charged Higgs bosons are predicted by several theories for new physics, including Supersymmetry. At proton colliders, the predicted dominant production mechanism is in association with top and bottom quarks. In paper V-VII, different contributions to this production are studied, and an algorithm is developed for combining the two dominant processes gb -> tH^+/- and gg -> tbH^+/-. The algorithm gives a smooth transition from small to large transverse momenta of the b-quark, which is important when the b-quark is observed. It also gives arguments for the choice of factorisation scale in the process.</p>

The Standard Model describes all elementary particles known today, but at larger energies it will have to be complemented with new particles and interactions. To be able to distinguish new physics at proton colliders such as LHC at CERN, it is essential to have an appropriate description of the colliding protons and their interactions. The study of the proton is important also in itself, to get a better understanding of the non-perturbative aspects of the strong interaction. In paper I-IV of this thesis, a model for the non-perturbative dynamics of quarks and gluons is developed, based on quantum fluctuations in hadrons. The parton distributions of the proton are given by momentum fluctuations, with sea quark distributions generated by fluctuations into baryon-meson pairs. This model can reproduce proton structure function data, as well as measured asymmetries between up and down valence quark distributions and between the anti-up and anti-down sea. It provides an intrinsic charm quark component as indicated by data. It also predicts an asymmetry in the strange sea of the proton, which can explain the NuTeV anomaly first attributed to new physics beyond the Standard Model. Charged Higgs bosons are predicted by several theories for new physics, including Supersymmetry. At proton colliders, the predicted dominant production mechanism is in association with top and bottom quarks. In paper V-VII, different contributions to this production are studied, and an algorithm is developed for combining the two dominant processes gb -&gt; tH+/- and gg -&gt; tbH+/-. The algorithm gives a smooth transition from small to large transverse momenta of the b-quark, which is important when the b-quark is observed. It also gives arguments for the choice of factorisation scale in the process.

Ce travail présente la mesure des polarisabilités généralisées (GPs) électrique αE(Q2) et magnétique βM(Q2) du proton à Q2 =0.2 GeV 2. Les GPs sont définies dans le contexte de la diffusion Compton virtuelle (VCS), γ*p → γp, où Q2 est le quadri-moment de transfert du photon virtuel. Les GPs sont la généralisation des polarisabilités mesurées en diffusion Compton réel (RCS) en considérant leur dépendance en Q2. Ce sont des propriétés dynamiques du proton définissant sa déformation lorsqu'un champ électromagnétique lui est appliqué. αE(Q2) (ou βM(Q2)) donne accès à la densité de polarisation (magnétisation) locale du proton déformé. L'effet des GPs ne contribuant qu'à 1 – 15 % de la section efficace ep → epγ une mesure de haute précision est requise. Ce travail s'inscrit dans le cadre d'une expérience conduite par la collaboration A1 de MAMI à trois valeurs inédites de Q2 : 0.1,0.2 et 0.45 GeV 2. L'analyse de premier niveau comporte une calibration détaillée des données expérimentales et l'utilisation d'une simulation de l'expérience. L'extraction des GPs requiert la mesure et la renormalisation des sections efficaces ep → epγ et la correction des effets radiatifs. Les résultats obtenus par le fit « LEX » et « DR » sont en très bon accord. / This work presents the measurement of the generalized electric αE(Q2) and magnetic βM(Q2) polarisabilities (GPs) of the proton. The GPs are defined in the Virtual Compton Scattering (VCS) context, i.e. the reaction γ*p → γp where Q2 is the four-momentum transfer of the virtual photon. The GPs are a generalization of polarizabilities measured in real Compton scattering (RCS) by taking into account the Q2-dependency. They are dynamical properties of the proton when it is deformed by an applied electromagnetic fiels. αE(Q2) (or βM(Q2)) gives access to the local polarization (or magnetization) density of the deformed proton. The studied VCS process is accessible by the photon-electroproduction reaction (ep → epγ). The GP effect is a 1 – 15 % contribution to the ep → epγ cross section, requiring a high-precision mleasurement. The present work is a part of an experiment conducted by the A1 collaboration at MAMI at three new Q2 values : 0.1,0.2 and 0.45 GeV 2. This thesis details the extraction at 0.2 GeV 2. The experiment uses the 1 GeV electron beam, the 5 cm liquid hydrogen target and spectrometers A (B) to detect the final electron (proton). The first-level analysis includes a detailed calibration of experimental data, and the use of a simulation of the experiment. The measurement of the unpolarized ep → epγ cross section is described with two of its important features : the correction of the radiative effects and the renormalization. Two differents frameworks are used to extract the GPs : the Low Energy Theorem (LET) and the dispersion relation model (DR). The two extractions lead to results in good argument. The world data still raises question about the Q2-behavior of the Gps.