Effective field theory (EFT) provides a framework to exploit separation of scales in the physical system in order to perform systematic model-independent calculations. There has been significant interest in applying the methods of EFT to halo nuclei. Using halo effective field theory, I provide a model-independent calculation of the radiative neutron capture on lithium-7 over an energy range where the contribution from the 3+ resonance becomes important. This reaction initiate the sequence in the carbon-nitrogen-oxygen (CNO) cycle in the inhomogeneous BBN models, and determine the amount of heavy element production from its reaction rate. One finds that a satisfactory description of the capture reaction, in the present single-particle approximation, suggests the use of a resonance width about three times larger than the experimental value. Power counting arguments that establish a hierarchy for the electromagnetic one- and two-body currents is also presented. The neutron capture of Lithium7 calculation has direct impact on the proton capture on beryllium7 which plays an important role in the neutrino experiments studying physics beyond the Standard Model of particle physics. As a further study of halo nuclei interactions, the cross section of radiative capture of a neutron by carbon-14 is calculated by considering the dominant contribution from electric dipole transition. This is also a part of the CNO cycle and as the slowest reaction in the chain it limits the flow of the production of heavier nuclei A > 14. The cross section is expressed in terms of the elastic scattering parameters of an effective range expansion. Contributions from both the resonant and non-resonant interactions are calculated. Significant interferences between these leads to a capture contribution that deviates from a simple Breit-Wigner resonance form. Using EFT, I present electromagnetic form factors of several halo nuclei. The magnetic dipole moment and the charge radii of carbon-15, beryllium-11, and carbon-19 halo systems are considered. Prediction is made for the magnetic moment in the leading order. I can only provide some estimates for the form factors in next-to-leading order where two-body currents appear. The estimates are based on power counting unless the effective range and the magnetic moment are known. Charge radii for three systems have also been estimated at LO and NLO.

The proton is described by the electric G_E and magnetic G_M form factors which characterise its internal structure. The way to measure the proton form factors consists in measuring the angular distribution of the e-p elastic scattering accessing the so-called Space-Like region where q^2<0. Using the crossed channel pbar p<-->e+e-, one accesses another kinematical region, the so-called Time-Like region where q^2>0. However, due to the pbar p<-->e+e- threshold q^2_{th}, only the kinematical domain q^2>q^2_{th}>0 is available. To access the unphysical region, one may use the pbar p --> pi0e+e- reaction where the pi0 takes away a part of the system energy allowing q^2 to be varied between q^2_{th} and almost 0. This thesis aims to show the feasibility of such measurements with the PANDA detector which will be installed on the antiproton ring at the FAIR facility at Darmstadt. To describe the pbar p --> pi0e+e- reaction, a Lagrangian based approach is developed. The 5-fold differential cross section is determined and related to linear combinations of hadronic tensors. Under the assumption of one nucleon exchange, the hadronic tensors are expressed in terms of the 2 complex proton electromagnetic form factors. An extraction method which provides an access to the proton electromagnetic form factor ratio R=|G_E|/|G_M| and for the first time in an unpolarized experiment to the cosine of the phase difference is developed. Such measurements have never been performed in the unphysical region. Extended simulations were performed to show how the ratio R and the cosine can be extracted from the positron angular distribution. Furthermore, a model is developed for the pbar p-->pi0pi+pi- background reaction considered as the most dangerous one. The background contribution can be reduced to the percent level or even less. The corresponding signal efficiency ranges from a few % to 30%. The precision on the determination of the ratio R and of the cosine is determined using the expected counting rates via Monte Carlo method. A part of this thesis is also dedicated to more technical work with the study of the prototype of the electromagnetic calorimeter and the determination of its resolution.

A central objective of the field of nuclear physics is understanding the fundamental properties of hadrons and nuclei in terms of QCD. In the last decade, a large range of experimental and theoretical methods have been developed to study the nature of quark confinement and the structure of hadrons which are composites of quarks and gluons. One important way to address some questions of hadron physics is studying the electromagnetic form factors of hadrons. The electric and magnetic form factors are related to the distribution of charge and magnetization in hadrons.The internal structure of hyperons, which are a subgroup of hadrons, is a topic of interest of particle physicists. The BES III experiment is one of the few current facilities for studying hadron structure.The Uppsala Hadron Physics group, which is a part of the BES III collaboration, is preparing a proposal for data taking for ΛΣ̄ 0 transition form factors and Σ 0 direct form factors at 2.5 GeV.Aiming the electromagnetic form factors of Σ hyperons, this work contributes to this proposal by simulation study of the e+ e− → ΛΣ̄ 0 and e + e − → Σ 0 Σ̄ 0 reactions. The efficiency and resolution of the electromagnetic calorimeter sub-detector of BES III and kinematic properties of the detected particles are studied in this work. Our final goal is to provide input for the beam time proposal and optimize the future measurement.In the first chapter, the theoretical background including the Standard Model, strong interaction, QCD, and hadrons are studied. In the second chapter, some concepts like the formalism of cross section, relativistic kinematics, and electromagnetic form factors are briefly presented. The third chapter is dedicated to introducing the e + e − → ΛΣ̄ 0 and e + e − → Σ 0 Σ̄ 0 reactions. The BES experiment at BEPC-II is introduced in chapter 4. In chapter 5, the software tools which have been used for this work are introduced. In the sixth chapter, the result of a toy-Monte Carlo study for parameter estimation is presented. The last chapter is dedicated to the results of a full BES software simulation.

In this thesis, we study low energy capture reactions and neutron-deuteron elastic scattering using halo effective field theory (EFT). At low energy, EFT provides a general framework to analyze physical systems regarding as an expansion of short-distance over large distance scales. We provide a model-independent calculation for neutron capture on carbon-14, radiative capture of 3He-4He, radiative capture of 3H-4He, and neutrondeuteron (n-d) doublet channel elastic scattering using halo EFT. These reactions play a significant role in the carbon-nitrogen-oxygen (CNO) cycle, solar neutrino flux measurement, lithium production, and big bang nucleosynthesis (BBN) in the early universe. The cross section is calculated for radiative neutron capture in carbon-14 using halo EFT. This reaction is slowest in the CNO cycle, and it acts as a bottleneck in the production of heavier nuclei A greater than 14. The capture contribution is different from Brett-Wigner resonance because of interference between resonant and non-resonant contribution. Also, we calculated, electromagnetic form factors for one-neutron halo nuclei such as carbon-15, beryllium-11, and carbon-19 using EFT. The electromagnetic form factors depend on the nucleon separation energy, effective range, and the two-body current. The EFT expressions are presented to leading order (LO) for 15C and next-to-leading order (NLO) for 11Be and 19C. We also calculated astronomical Sactor for 3He-4He and 3H-4He radiative capture reactions. The low energy Sactor for these reactions are important to understand the Li problem and neutrino physics. At the LO, the capture amplitude contains the initial state swave strong and Coulomb interactions summed to all orders. The NLO contribution comes from non-perturbative Coulomb interaction. Our calculated astrophysical Sactor for 3He- 4He is slightly above the average compared to the other measurement and prediction but consistent within current error bars. The Sactor for 3H-4He is also compatible with the experimental extrapolation. Finally, we studied doublet channel n-d scattering using halo EFT. A two dimer halo EFT is developed to describe the virtual state and three-body bound state in n-d scattering. We show the connection between virtual state and three-body bound state using S-matrix analysis and phase shift analysis which is supported by the Efimov plots.

Le proton est décrit par les facteurs de forme électrique et magnétique qui caractérisent sa structure interne. Le moyen de mesurer les facteurs de forme consiste à mesurer la distribution angulaire de la diffusion élastique e-p: dans cette région dite espace q^2 est négatif. En utilisant la réaction croisée pbar p<--> e+ e-, on atteint une autre région cinématique appelée région temps où q^2>0. Cependant, à cause du seuil q^2_{th} de les réactions pbar p <--> e+e-, seul le domaine cinématique q^2>q^2_{th}>0 est autorisé. Pour atteindre la région non physique, on utilise la réaction pbar p --> pi0e+e- où le pi0 emporte une partie de l'énergie autorisant ainsi q^2 à varier entre q^2_{th} et presque 0. Cette thèse vise à démontrer la faisabilité de ces mesures avec le détecteur PANDA qui sera installé sur l'anneau d'antiprotons du futur complexe FAIR à Darmstadt. Pour décrire la réaction pbar p --> pi0e+e- une approche basée sur des lagrangiens est développée. La section efficace 5 fois différentielle est determinée et reliée à des combinaisons linéaires de tenseurs hadroniques. Sous l'hypothèse de l'échange d'un nucléon, les tenseurs hadroniques sont exprimés en fonctions des 2 facteurs de forme électromagnétiques complexes du proton. Une méthode est développée, qui donne accès au rapport des facteurs de forme électromagnétiques du proton R=|G_E|/|G_M| et pour la première fois avec une expérience non polarisée au cosinus de la différence de phase. A ce jour, de telles mesures n'ont jamais été faites dans la région non physique. Des simulations détaillées ont été effectuées pour montrer comment le rapport R et le cosinus peuvent être extraits de la distribution angulaire du positron. De plus, un modèle est développé pour la réaction parasite pbar p-->pi0pi+pi- considérée comme la plus dangereuse. La contribution du bruit de fond peut être réduite à quelques pour-cent voire moins. L'efficacité typique de détection du signal correspondante varie de l'ordre de 5 pour-cent à 30 pour-cent. La précision sur la détermination du rapport R et du cosinus est determinée pour le nombre de coups attendu via la méthode Monte Carlo. Une partie de cette thèse est aussi dédiée à un travail plus technique avec l'étude du prototype du calorimètre électromagnétique et la détermination de sa résolution. / The proton is described by the electric G_E and magnetic G_M form factors which characterise its internal structure. The way to measure the proton form factors consists in measuring the angular distribution of the e-p elastic scattering accessing the so-called Space-Like region where q^2<0. Using the crossed channel pbar p<-->e+e-, one accesses another kinematical region, the so-called Time-Like region where q^2>0. However, due to the pbar p<-->e+e- threshold q^2_{th}, only the kinematical domain q^2>q^2_{th}>0 is available. To access the unphysical region, one may use the pbar p --> pi0e+e- reaction where the pi0 takes away a part of the system energy allowing q^2 to be varied between q^2_{th} and almost 0. This thesis aims to show the feasibility of such measurements with the PANDA detector which will be installed on the antiproton ring at the FAIR facility at Darmstadt. To describe the pbar p --> pi0e+e- reaction, a Lagrangian based approach is developed. The 5-fold differential cross section is determined and related to linear combinations of hadronic tensors. Under the assumption of one nucleon exchange, the hadronic tensors are expressed in terms of the 2 complex proton electromagnetic form factors. An extraction method which provides an access to the proton electromagnetic form factor ratio R=|G_E|/|G_M| and for the first time in an unpolarized experiment to the cosine of the phase difference is developed. Such measurements have never been performed in the unphysical region. Extended simulations were performed to show how the ratio R and the cosine can be extracted from the positron angular distribution. Furthermore, a model is developed for the pbar p-->pi0pi+pi- background reaction considered as the most dangerous one. The background contribution can be reduced to the percent level or even less. The corresponding signal efficiency ranges from a few % to 30%. The precision on the determination of the ratio R and of the cosine is determined using the expected counting rates via Monte Carlo method. A part of this thesis is also dedicated to more technical work with the study of the prototype of the electromagnetic calorimeter and the determination of its resolution.