Heavy quark fragmentation functions in the heavy quark effective theory.

We calculate fragmentation functions for a b-quark to fragment into color-singlet P-wave bound states c̄b in the Heavy Quark Effective Theory with the exact account of O(1/mb) corrections. We demonstrate an agreement of the obtained results with the corresponding calculations carried out in quantum chromodynamics. Introduction. The study of heavy quarkonia properties is a subject of much current interest for understanding of quark-gluon interaction dynamics. Bc-mesons, consisting of band c-quarks, hold a unique position in the heavy quarkonia physics [1]. In the first place, Bc -mesons consist of two heavy quarks, so the predictions of potential models refer to J/Ψand Υ -mesons as well as to Bc -mesons [2]. In the second place, Bc -mesons are constructed from the quarks of different flavors and masses, what essentially determine their decay characteristics [3]. Production of mesons with heavy quarks in e+e−, γγ and pp̄-interactions may be described in nonrelativistic perturbative quantum chromodynamics. At present, two mechanisms were investigated for the production of Bc-mesons: the recombination and the fragmentation. In the first case, Bc-mesons are formed from heavy quarks, produced independently in hard subprocess. The fragmentational mechanism demands the pair production of bor c-quarks in hard subprocess with their subsequent fragmentation to Bc-mesons (b̄ → Bcc̄, c → Bcb). The relative contributions of these mechanisms in the production cross-sections are different in various reactions. In e+e− -annihilation only quark fragmentation is essential [4]. In pp̄ γγ -interactions the fragmentational mechanism prevails also for Bc-mesons production with large transverse momenta [5, 6]. In the range of small transverse momenta the recombination is dominant and determines the total cross section of Bc-meson production in γγ and pp̄ interactions. But experimental conditions of Bc-meson discovery are more perspective in the large transverse momenta domain. So, the study of heavy quark fragmentation into Bc-mesons attracts considerable interest. An approach for the calculation of fragmentation functions Db̄→Bcc̄, Dc→Bcb in nonrelativistic perturbative quantum chromodynamics was suggested in [7]. At the same time, in the last years there was suggested, based on QCD, the Heavy Quark Effective Theory (HQET) [8, 9] for description of heavy hadrons properties. HQET make it possible to obtain the finite analytical result with some accuracy even for complicated processes of quarkgluon interaction. In this approach the matrix elements of