Date of Award


Degree Type


Degree Name

Doctor of Philosophy


We study the production of colourless clusters (CC) in high energy {dollar}e\sp{lcub}+{rcub}e\sp{lcub}-{rcub}{dollar} collisions in the framework of perturbative QCD. We adopt a jet calculus approach, which enables us to treat the cascade of successively generated partons initiated by the virtual photon in the above process in terms of quantum mechanical probabilities rather than amplitudes. Special attention is given to the presence of soft gluons in the cascade, which produce non-negligible quantum mechanical interference contributions thus causing a serious obstacle to the probabilistic view inherent in jet calculus and its subsequent refinements; among these the Crespi-Jones (CJ) approach is ideally suited for studying the gluons in a colourless cluster, and hence is used throughout this work. Mueller's criterion of angle-ordered gluon emission is invoked to redefine the evolution variable in the conventional CJ equations in order to account for these soft gluon (coherence) effects. A careful examination of the kinematics forces us to invoke an "averaging procedure", without which a comparison between conventional and coherent approaches would be meaningless. The method of moments is used for solving the CJ equations, and results are presented in both moment space and longitudinal momentum (x) space (for {dollar}x\geq{dollar} 0.2). Subsequently, the zeroth moment of the CC distribution in gluon jets is evaluated under certain asymptotic approximations and the results for low x are shown to be in fair agreement with Mueller's prediction and the Monte Carlo simulation by Marchesini and Webber.;Part II of this work is devoted to the numerical inversion of moments (and Laplace transforms), which have played a vital role in our solution of the CJ equations. In addition to reviewing previous work in the field, we present several new inversion algorithms including some based on Chebyshev polynomials and one based on generalized Laguerre polynomials, which has proved to be particularly relevant to the aforementioned study of the low x region in QCD. Lastly, a method based on Gaussian quadrature and Singular Value Decomposition is discussed. The methods are tested on a wide variety of trial functions, and the inverted solutions are compared with the exact values.



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