Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1993-11-23
Physics
High Energy Physics
High Energy Physics - Phenomenology
12 pages, 2 figures (available upon request), LaTeX (no macros required), minor typos corrected MZ-TH/93-33
Scientific paper
We point out that there exist two different formulations of the Heavy Quark Effective Theory (HQET). One formulation of HQET was mostly developed at Harvard and involves the use of the equation of motion to eliminate the small components of the heavy quark field. The second formulation, developed in Mainz, involves a series of Foldy-Wouthuysen-type field transformations which diagonalizes the heavy quark Lagrangian. Starting at O($1/m_Q^2$) the two formulations are different in that their effective Lagrangians, their effective currents, and their fields differ. However, when these three differences are properly taken into account, the two alternative formulations lead to identical S-matrix elements. This is demonstrated in an explicit example at O($1/m_Q^2$). We point to an essential difficulty of the Harvard HQET in that the Harvard effective fields are not properly normalized starting at order $O(1/m_Q^2)$.
Balk S.
Ilakovac Amon
Körner Juergen G.
Pirjol Dan
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