In this thesis we study non-relativistic, low-energy, s-wave scattering in a four-body spin-1/2 fermion system. The scattering is caused by an attractive twoermion contact interaction which is capable of producing a weakly bound state known as a dimer. This fourermion system is used to study the scattering of a two-dimer system. Using Hybrid Monte Carlo methods we compute the ground state energies of the system on a lattice. Luscher’s finite-volume formula and the Effective Range Expansion are used to calculate the dimer-dimer scattering length add and effective range rdd in terms of the fermionermion scattering length aff. Using these techniques we obtain the values add=aff = 0:60 +/- 0:04 and rdd=aff = 3:2 +/- 0:5. This scattering length shows excellent agreement with the numerous values in the literature. We also compare this effective range with the only currently known value in the literature.

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.

No description available.

In this work, the radiative capture reactions 7Li(n, γ)8Li, 7Be(p, γ)8B, 3He(α, γ)7Be, and 3H(α, γ)7Li are studied using halo effective field theory (EFT). These capture reac- tions are some of the key nuclear reactions for the solar neutrino production and heavy element production in stellar and primordial nucleosyntheses. At low energy, halo EFT provides a model independent framework to describe physical observable as an expansion of a low momentum scale over a high momentum scale with well-defined error estimates. In this dissertation, electric dipole (E1) capture cross section of 7Li(n, γ)8Li reaction is calculated as a coupled channel using EFT with excited 7Li⋆ core and is compared with EFT without the excited 7Li⋆ core. Then we extend our coupled channel treatment to 7Be(p, γ)8B reaction which is the iso-spin mirror of 7Li(n, γ)8Li by adding the Coulomb force in the calculation. Similar to 7Li(n,γ)8Li calculation, we calculate the astrophys- ical Sactor for 7Be(p,γ)8B reaction using the two halo EFTs, one halo EFT without excited 7Be⋆ core and the other halo EFT with the excited 7Be⋆ core as an explicit degree of freedom. We present a formalism to compare different EFT power countings using Bayesian analysis. This is useful when the EFT couplings are poorly known, and one has competing power counting proposals. The Sactor for 3He(α,γ)7Be reaction was calculated for two competing power countings in halo EFT approach. The two power countings defer in the contribution of the two body currents. In one power counting, the two body currents contribute at the leading order and in the other power counting, the two body currents contribute at higher orders. Bayesian inference is drawn to estimate EFT parameters and calculate the posterior odds in order to do the model comparison. The posterior odds is used to propose the best power counting. We extend our calculation to the iso-spin mirror 3H(α,γ)7Li reaction using the same expressions by making the appropriate changes in masses, charges, and binding momenta. We estimate the EFT parameters and calculate the posterior odds using Bayesian analysis. The best power counting is proposed using the posterior odds.

This work details how to use the Point-Particle Effective Field Theory (PPEFT) framework to make predictions for the nuclear-size contributions to spectroscopic transitions of atoms without the overbearing large uncertainties generally associated with such effects. After a lightning review of Quantum Field Theories, Effective Field Theories and their model-building algorithms, the backbones of the PPEFT formalism are laid down by considering the low-energy effective theories of lumps. Then, by drawing an analogy between a certain type of lumps and a freely propagating point-particle we build a PPEFT for nuclei, which we gradually couple to gauge and fermionic fields. We find that the consequences of having a nucleus in our theory are captured by a set of new near-nucleus boundary conditions its action implies for the surrounding fields, set up on a Gaussian spherical boundary with arbitrary radius, $\epsilon$. Afterwards, we use this formalism to derive the effects of the finite size of the nucleus on bound-state energies in terms of Renormalization Group (RG)-invariant parameters that characterize the running of the PPEFT couplings in $\epsilon$, implied by these new boundary conditions in order to keep physical quantities independent of this fictitious scale. Surprisingly, when comparing to formulae from the literature that express these same energy shifts in terms of nuclear moments there always appear to be fewer RG-invariants than moments. By fitting these handful of parameters using experimental data we then reduce the errors in nuclear-size effect predictions for other transitions by writing them in terms of differences between spectroscopic measurements and their corresponding energy differences predicted by those bound-state Quantum Electrodynamics calculations that assume nuclei to be point-like. Finally, we apply this algorithm to the systems: ${}^4_2 {\rm He}^+$, $\mu \, {}^4_2 {\rm He}^+$, H, and $\mu$H, where we make such predictions. / Thesis / Doctor of Philosophy (PhD) / The finite size of the nucleus shifts the bound-state energy of electrons (or muons) in atoms. Although these effects had been captured through a large number of nuclear-model independent ``nuclear moments'' closely related to the extent of the nucleus in the past, they introduce large uncertainties into theoretical predictions, which hinders testing fundamental subatomic processes in spectroscopic measurements. In this work it is shown that there is a more manageable number of parameters that control these effects because the above moments always appear in specific combinations. This allows for trading these combinations for differences between experimental values and their theoretically expected ones that assume the nucleus to have no size, which is the key in making predictions for atomic transitions that do not suffer from the large nuclear errors. A large set of such predictions are made for Hydrogen and the principles are applied to its muonic cousin as well.

Effective field theories (EFTs) provide frameworks to systematically improve perturbation expansions in quantum field theory. This improvement is essential in quantum chromodynamics (QCD) predictions, both at low energy in the description of low momentum hadron-hadron scattering and at high energy in the description of electron-positron, proton-proton, proton-electron collisions. It is also important in quantum electrodynamics (QED), when electrons interact with a high-intensity, long-wavelength classical field. I introduce the principles and methods of effective field theory and describe my work in three EFTs: First, in the perturbative QCD region, I use soft collinear effective theory (SCET) to prove that strong interaction soft radiation is universal and to increase the QCD accuracy to next-to-next-to-next-to leading logarithm order for new particle searches in hadron colliders. I also compute a new class of non-perturbative, large logarithmic enhancement arising near the elastic limits of deep inelastic scattering and Drell-Yan processes. Second, in the QCD confinement region, I use heavy hadron chiral perturbation theory to study near-threshold enhancements in the scattering of 𝐷 and 𝜋 mesons near the threshold for the excited 𝐷-meson state, 𝐷*, as well as in the scattering of 𝐷 and 𝐷* mesons near the threshold for the exotic hadron X(3872). This work provides a clear picture of the hadronic molecule X(3872) and more profound understanding of the nuclear force between hadrons. Finally, inspired by SCET, I construct a new electron-laser effective field theory to describe highly-relativistic electrons traveling in strong laser fields, extract the universal distribution of electrons in strong electromagnetic backgrounds and its evolution in energy from the separated momentum scales of emitted photons and classical radiation, and predict the rate of wide angle photon emission. I conclude with limitations of EFT methods and some perspectives on what new work may be achieved with these EFTs.

Effective field theories can be used to describe measurements at e⁺e⁻ colliders over a wide kinematic range while allowing reliable error predictions and systematic extensions. We show this in two physical situations. First, we give a factorization formula for the e⁺e⁻ thrust distribution dσ/dτ with thrust T and τ = 1 − T based on soft collinear effective theory. The result is applicable for all τ, i.e. in the peak, tail, and far-tail regions. We present a global analysis of all available thrust distribution data measured at center-of-mass energies Q = 35 to 207 GeV in the tail region, where a two parameter fit to the strong coupling constant α(s)(m(Z)) and the leading power correction parameter Ω₁ suffices. We find α(s)(m(Z)) = 0.1135 ± (0.0002)expt ± (0.0005)hadr ± (0.0009)pert, with x²/dof = 0.91, where the displayed 1-sigma errors are the total experimental error, the hadronization uncertainty, and the perturbative theory uncertainty, respectively. In addition, we consider cumulants of the thrust distribution using predictions of the full spectrum for thrust. From a global fit to the first thrust moment we extract α(s)(m(Z)) and Ω₁. We obtain α(s)(m(Z)) = 0.1140 ± (0.0004)exp ± (0.0013)hadr ± (0.0007)pert which is compatible with the value from our tail region fit. The n-th thrust cumulants for n ≥ 2 are completely insensitive to Ω₁, and therefore a good instrument for extracting information on higher order power corrections, Ω'(n)/Qⁿ, from moment data. We find (˜Ω₂)^1/2 = 0.74 ± (0.11)exp ± (0.09)pert GeV. Second, we study the differential cross section dσ/dx of e⁺e⁻-collisions producing a heavy hadron with energy fraction x of the beam energy in the center-of-mass frame. Using a sequence of effective field theories we give a definition of the heavy quark fragmentation function in the endpoint region x → 1. From the perspective of our effective field theory approach we revisit the heavy quark fragmentation function away from the endpoint and outline how to develop a description of the heavy quark fragmentation function valid for all x. Our analysis is focused on Z-boson decays producing one B-meson. Finally, we will give a short outlook of how we want to apply our approach to determine the leading nonperturbative power corrections of the b-quark fragmentation function from LEP experiments.

<p>In this thesis, we study effective field theories for doubly heavy baryons and lattice QCD. We construct a chiral Lagrangian for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading O(1/m_Q ) symmetry violating operators. The theory is used to predict the electromagnetic decay width of the J = 3/2 member of the ground state doubly heavy baryon doublet. Numerical estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons. We derive the couplings of heavy diquarks to weak currents in the limit of heavy quark-diquark symmetry, and construct the chiral Lagrangian for doubly heavy baryons coupled to weak currents. Chiral corrections to doubly heavy baryon zero-recoil semileptonic decay for both unquenched and partially quenched QCD are calculated. This theory is used to derive chiral extrapolation formulae for measurements of the doubly heavy baryon zero-recoil semileptonic decay form factors in lattice QCD simulations. Additionally, we study the pion physics on lattice using chiral perturbation theory. For finite volume field theories with discrete translational invariance, conserved currents can obtain additional corrections from infrared effects. We demonstrate this for pions using chiral perturbation theory coupled to electromagnetism in a periodic box. Gauge invariant single particle effective theories are constructed to explain these results. We use chiral perturbation theory to study the extraction of pion electromagnetic polarizabilities from lattice QCD. Chiral extrapolation formulae are derived for partially quenched and quenched QCD simulations. We determine finite volume corrections to the Compton scattering tensor of pions.</p> / Dissertation

The 7σ discrepancy between the charge radius of the proton as extracted from electronic hydrogen to the determination from muonic hydrogen, coined the proton ``radius puzzle", challenges our understanding of physics based on the standard model. High-precision measurements have been conducted on muonic deuterium to study whether the discrepancy with ordinary atoms persists or varies with mass number. For the success of this experimental campaign accurate theoretical calculations of the nuclear structure corrections in muonic deuterium (μD) are required. In this work we contributed by accurately and precisely calculating them using state-of-the-art nuclear potentials derived from chiral effective field theory. We performed a multipole expansion of the electromagnetic operator and accounted for Coulomb, relativistic and finite-nucleon-size corrections. Our determinations will impact the accuracy of the experimental program. / October 2015

We describe work on the construction of an effective field theory on a spherical light shell. The motivation arises from classical electromagnetism: If a collision produces charged particles with zero net charge emerging simultaneously from a point and instantaneously accelerating to the speed of light, then the electromagnetic fields due to these charges lie entirely on a spherical shell expanding at the speed of light. We show that this also applies to classical color radiation from high-energy collisions that produce colored particles. Specifically, the color fields produced in such a process are associated with a non-linear &sigma;-model on the 2D light shell with specific symmetry-breaking terms. The quantum version of such a picture exhibits asymptotic freedom and should therefore be a useful starting point for a light-shell effective theory for QCD. We start in the simplified context of zero-flavor scalar quantum electrodynamics. Our effective theory has 3 major ingredients: breaking down the fields into soft and hard sectors with the large energy of the hard fields in the radial direction scaled out, a special gauge called light-shell gauge in which the picture simplifies, and a gauge-invariant source defined on a spherical light shell having infinitesimal radius. We match the fields between the effective theory and the full theory, meaning zero-flavor scalar QED. This allows us to compute the amplitude for the production of any number of scalars from the gauge-invariant source. We then find the tree-level amplitude for the emission of a photon using our effective theory and show that our result agrees with the full theory. To calculate loop effects in our effective theory, we need the photon propagator in light-shell gauge. We derive this propagator and use it to calculate the 1-loop correction to the amplitude for the production of a scalar and anti-scalar pair arising from virtual photon effects. This reduces to a pair of purely angular integrals in the effective theory and reproduces the familiar double logs of the full theory subject to an appropriate interpretation of an angular cutoff. / Physics