Se p 20 00 SPECTATOR EFFECTS AND QUARK - HADRON DUALITY IN INCLUSIVE BEAUTY DECAYS

5 Quark-hadron duality 51 6 Conclusion 55 ii 0.1 Preface This Thesis is a review of the inclusive decays of heavy hadron. It is based on the author's study of two issues which are important in the description of the inclusive beauty decays given by the heavy quark expansion. • Evaluation of the expectation values of the four-quark operators in the heavy quark expansion, • Study on the validity of the quark-hadron duality in the heavy quark expansion. We evaluate the four-quark operators in two approaches: (1) in terms of the oscillator strength of the hadrons in the harmonic oscillator model, and (2) from the difference in the total decay rates of beauty hadrons under SU (3) flavour symmetry. The results obtained indicate that the lifetime difference between B meson and Λ b can be explained within heavy quark expansion by including the third order contribution. To discuss the quark-hadron duality, the power corrections to the par-tonic decays rate are obtained in terms of the gluon mass which is assumed to imitate the short distance nonperturbative effects, by the choice λ 2 ≫ Λ 2 QCD. The Thesis is organised in six Chapters, as follows: • 1 Introduction: The Standard Model is briefly discussed and then the Spin-flavour symmetry exhibited by heavy hadrons is reviewed. • 2 Four-quark operators: The author's works on the evaluation of four-quark operators are presented. • 3 Spectator effects: Presented are the calculation of ratio of lifetimes of beauty hadrons, particularly, τ (Λ b)/τ (B) and the inclusive charmless semileptonic decay rate and determination of the CKM matrix element |V ub |. • 4 Short distance nonperturbative corrections: The renormalons contribution to the heavy quark expansion is discussed based on the authors work. iii • 5 Quark-hadron duality: The validity of the assumption of quark-hadron duality is qualitatively discussed. • 6 Conclusion: Conclusion of the Thesis with outlook of the works done are given. I am glad to acknowledge that my acquaintance with heavy quark physics began with the lectures on the heavy quark symmetry by Prof. Apoorva Patel during a discussion meeting at the Centre for Theoretical Studies, Indian Institute of Science, Bangalore. I got this great opportunity due to the invitation of Prof. J. Pasupathy. My learning of QCD is due to them by the way of their invitation to the discussion meetings conducted by them. I am grateful to both of them …