The Effective Field Theory formalism is applied to the study of problems in hadronic and nuclear physics. We develop a framework to study the exclusive two-body decays of bottomonium into two charmed mesons and apply it to study the decays of the C-even bottomonia. Using a sequence of effective field theories, we take advantage of the separation between the scales contributing to the decay processes, 2m(b) ≫ m(c) ≫∧(QCD). We prove that, at leading order in the EFT power counting, the decay rate factorizes into the convolution of two perturbative matching coefficients and three non-perturbative matrix elements, one for each hadron. We calculate the relations between the decay rate and non-perturbative bottomonium and D-meson matrix elements at leading order, with next-to-leading log resummation. The phenomenological implications of these relations are discussed. At lower energies, we use Chiral Perturbation Theory and nuclear EFTs to set up a framework for the study of time reversal (T) symmetry in one- and few-nucleon problems. We consider T violation from the QCD θ term and from all the possible dimension 6 operators, expressed in terms of light quarks, gluons and photons, that can be added to the Standard Model Lagrangian. We construct the low energy chiral Lagrangian stemming from different TV sources, and derive the implications for the nucleon Electric Dipole Form Factor and the deuteron T violating electromagnetic Form Factors. Finally, with an eye to applications to nuclei with A ≥ 2, we construct the T violating nucleon-nucleon potential from different sources of T violation.

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It is widely believed that Quantum Chromodynamics (QCD) is the theory that describes the strong interaction. In the infrared region of the theory, the perturbative expansion breaks down and so, other techniques must be used. One such technique is the study of the Schwinger-Dyson equations. In this thesis is presented such a study. It is shown that the ghost sector of QCD may be crucial to the understanding of the infrared behaviour. Conventionally, the Slavnov- Taylor identity is used to truncate the Schwinger-Dyson equations but it is found that for the ghost-gluon vertex, such an identity cannot be used in an appropriate manner. In order to extract information, a new technique is presented, based on the powerlaw behaviour of the two-point functions in the infrared. By demanding consistency in the full equations in Landau gauge and multiplicative renormalisability, it is found that in general, the gluon propagator dressing function cannot diverge and the ghost propagator function cannot vanish in the infrared. Further, it is shown that the powerlaw behaviour depends on a certain kinematical limit of only one function connected with the ghost-gluon vertex.

We present and explore a new formulation of perturbative QCD based not on the renormalised coupling but on the dimensional transmutation parameter of the theory and the property of asymptotic scaling. The approach yields a continued function, the iterated function being that involved in the solution of the two-loop β-function equation. In the so-called large-b limit the continued function reduces to a continued fraction and the successive approximants are diagonal Padé approximants. We investigate numerically the convergence of successive approximants using the leading-b approximation, motivated by renormalons, to model the all-orders result. We consider the Adler D-function of vacuum polarisation, the Polarised Bjorken and Gross-Llewellyn Smith sum rules, the (unpolarised) Bjorken sum rule, and the Minkowskian quantities R(_r) and the R-ratio of e(^+)e(^-) annihilation. In contrast to diagonal Fade approximants the truncated continued function method gives remarkably stable large-order approximants in cases where infra-red renormalon effects are important. We also use the new approach to determine the QCD fundamental parameters from the R(_r) and the R-ratio measurements, where we find Ā(^(3))(_MS)=516±48 MeV (which yields a(_s)(µ=m(_r))=0.360(^+0.021)(_=0.020)), and Ā(^(5))(_MS)=299(^+6)(_-7) MeV (which yields a(_s)(µ=m(_zo)=0.1218±0.0004), respectively. The evolution of the former value to the m(_zo) energy results in a(_s)(µ= m(_zo)) = 0.123 ± 0.002. These values are in line with other determinations available in the literature. We implement the Complete Renormalisation Group Improvement (CORGI) scheme throughout all the calculations. We report on how the mathematical concept of Stieltjes series can be used to assess the convergence of Padé approximants of perturbative series. We find that the combinations of UV renormalons which occur in perturbative QCD may or may not be Stieltjes series depending on the renormalisation scheme used.

Precise predictions of hadronic matrix elements in heavy meson decays are important to constrain the fundamental parameters in the Standard Model of particle physics. The CKM matrix element Vub can be extracted from experimental data on the decay B → πℓν if the hadronic form factor is known. In addition, loop suppressed rare decays of B-mesons, such as B → K∗γ and B → K(∗)ℓℓ, provide valuable insight into new physics models. Hadronic form factors for exclusive meson decays can be calculated in the framework of lattice QCD. As the wavelength of heavy quarks is not resolved on currently available lattices I use an effective nonrelativistic theory to discretise the heavy degrees of freedom. In addition, the discretisation errors in the final state meson are reduced by working in a moving frame. I review the phenomenology of rare B decays and describe how lattice QCD can contribute to calculating the relevant form factors. As the short distance physics in the effective theory is different from that of QCD, the Lagrangian and decay currents need to be renormalised. I show how this can be achieved in the framework of lattice perturbation theory. I calculate the perturbative renormalisation constants of the leading order operators in the heavy quark Lagrangian. Motivated by nonperturbative studies I extend this approach to higher order kinetic terms which break rotational invariance. In combination with simulations in the weak coupling regime of the theory, results from diagrammatic lattice perturbation theory are used to calculate the heavy quark selfenergy corrections and predict the fundamental parameters of QCD. I calculate the one loop correction on a finite lattice with twisted boundary conditions which is used for the extraction of higher order perturbative corrections. I renormalise the heavy-light current to one loop order in lattice mNRQCD and present results from nonperturbative studies. Finally, I discuss how the results are used in the calculation of hadronic form factors.

We demonstrate a renormalisation group improved formulation of QCD perturbation theory. At next-to-leading order (NLO) and beyond this permits a direct extraction of the QCD dimensional transmutation parameter, A(_ms) that typifies the one parameter freedom of the theory in the limit of massless quarks. We apply this to a variety of experimental data on e(^+)e" jet observables at NLO. We take into consideration data from PETRA, PEP, TRISTAN, SLC and LEP 1 and 2. In this procedure there is no need to mention, let alone to arbitrarily vary, the unphysical renormalization scale µ, and one avoids the spurious and meaningless "theoretical error" associated with standard a(_8) determinations. An attempt is made to estimate the importance of uncalculated next-to-NLO and higher order perturbative corrections, and power corrections, by studying the scatter in the values of ∆(_MS) obtained for different observables. We also consider large infrared logarithm resummations in these jet observables and present results for the particular cases of the four-jet rate to a next-to-leading logarithm approximation and the distributions for the four-jet variables, "light hemisphere mass" and "narrow jet broadening" to a next-to-next-to-leading logarithm approximation in the perturbative expansion. We apply a simple power correction to these variables and obtain remarkably good fits to the data.

Since the advent of Quantum Field Theory (QFT) in the late 1940's, perturbation theory has become one of the most successful means of extracting phenomenologically useful information from QFT. In the ever-increasing enthusiasm for new phenomenological predictions, the mechanics of perturbation theory itself have taken a back seat. It is in this light that this thesis aims to investigate some of the more fundamental properties of perturbation theory. In the first part of this thesis, we develop the idea, suggested by C.J.Maxwell, that at any given order of Feynman diagram calculation for a QCD observable all renormalization group (RG)-predictable terms should be resummed to all-orders. This "complete" RG-improvement (CORGI) serves to separate the perturbation series into infinite subsets of terms which when summed are renormalization scheme (RS)-invariant. Crucially all ultraviolet logarithms involving the dimensionful parameter, Q, on which the observable depends are resummed, thereby building the correct Q-dependence. We extend this idea, and show for moments of leptoproduction structure functions that all dependence on the renormahzation and factorization scales disappears provided that all the ultraviolet logarithms involving the physical energy scale Q are completely resummed. The approach is closely related to Grunberg's method of Effective Charges. In the second part, we perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients containing the leading power of b, the first beta-function coefficient, is resummed to all-orders. To avoid a renormalization scale dependence when we match the resummation to the exactly known next-to-leading order (NLO), and next-NLO (NNLO) results, we employ the Complete Renormalization Group Improvement (CORGI) approach , removing all dependence on the renormalization scale. We can also obtain fixed-order CORGI results. Including suitable weight-functions we can numerically integrate these results for the D-function in the complex energy plane to obtain so-called "contour-improved" results for the ratio R and its tau decay analogue Rr. We use the difference between the all-orders and fixed-order (NNLO) results to estimate the uncertainty in αs(M2/z) extracted from Rr measurements, and find αs(M2/z) = 0.120±0.002. We also estimate the corresponding uncertainty in a{Ml) arising from hadronic corrections by considering the uncertainty in R(s), in the low-energy region, and compare with other estimates. Analogous resummations are also given for the scalar correlator. As an adjunct to these studies we show how fixed-order contour-improved results can be obtained analytically in closed form at the two-loop level in terms of the Lambert W-function and hypergeometric functions.