Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the b-quark fragmentation function from electron-positron annihilation data at the Z-boson peak at next-to-next-to leading order with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to next -to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the b-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Using an approach based on effective field theory allows us to systematically control theoretical errors. While the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the b-quark fragmentation function at smaller values of momentum fraction.

Exploiting the substructure of jets observed at the LHC to better understand and interpret the experimental data has recently been a very active area of research. In this thesis we study the substructure of high-pt QCD jets, which form a background to many new physics searches. In particular, we explore in detail the perturbative distributions of a certain class of observables known as non-global jet shapes. More specifically, we identify and present state-of-the-art calculations, both at fixed-order and to all-orders in the perturbative expansion, of a set of large logarithms known as non-global logarithms. Hitherto, these logarithms have been largely mis-treated, and in many cases ignored, in the literature despite being first pointed out more than a decade ago. Our work has triggered the interest of many groups, particularly Soft and Collinear Effective Theory (SCET) groups, and led to a flurry of papers on non-global logarithms and related issues. Although our primary aim is to provide analytical results for hadron-hadron scattering environments, it is theoretically instructive to consider the simpler case of e+e- annihilation. We thus examine, in chapters 4, 5 and 6, the the said jet shapes in the latter environment and compute the full next-to-leading logarithmic resummation of the large logarithms present in the distribution for various jet definitions. We exploit the gained experience to extend our calculations to the more complex hadronic environment in chapter 7. We provide state-of-the-art resummation of the jet mass observable in vector boson + jet and dijet QCD processes at the LHC up to next-to-leading logarithmic accuracy. The resultant distribution of the former (vector boson + jet) process agrees well, after accounting for hadronisation corrections, with standard Monte Carlo event generators and potential comparisons to data from the LHC will be made soon.

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