Semileptonic Decay of B-Meson into D and the Bjorken Sum Rule

We study the semileptonic branching fraction of B-meson into higher resonance of charmed meson D by using the Bjorken sum rule and the heavy quark effective theory(HQET). This sum rule and the current experiment of B-meson semileptonic decay into D and D predict that the branching ratio into Dlνl is about 1.7%. This predicted value is larger than the value obtained by the various theoretical hadron models based on the HQET. It is well known that the heavy quark effective theory (HQET) is a very useful method to study physics of hadrons containing a heavy quark[1]. For example, the HQET is used to determine Kobayashi-Mskawa matrix element |Vcb|, from experiment of semileptonic decay B → Dlν[2]. The attractive features of the HQET are generally verified in phenomena where both of initial and final states include ground states of heavy hadron. However, the phenomena between a ground state and an excited one, for example branching ratio of B meson semileptonic decay into the excited charmed meson state B → Dlν, where D means a higher resonance state of charmed meson, are not interpreted in various models of hadrons based on the HQET[3, 4, 5, 6, 7, 8, 9]. This incoincidence could be reduced to the models of hadrons as a composite system. It is expected that the models which interpret the B-meson branching fractions of the semileptonic decays into D, D and Ds. At present we have no such a model. So it is meaningful to study these processes by a model-independent approach. The purpose of this short note is a test of the HQET applicability to an excited state by dealing with charmed hadron excited states D without model dependence. In the heavy quark limit mQ → ∞, heavy quark spin and velocity are free from low energy QCD[1]. So hadron state is factorized into heavy quark |Q〉 and light degrees of freedom (l.d.f.) |ldf〉 as |hadron〉 = |Q〉 ⊗ |ldf〉. (1) These hadrons are classified by l.d.f. as following (0, 1) = |Q( 1 2 + )〉 ⊗ |ldf( 1 2 − )〉, (0, 1) = |Q( 1 2 + )〉 ⊗ |ldf( 1 2 + )〉, (2) (1, 2) = |Q( 1 2 + )〉 ⊗ |ldf( 3 2 + )〉, (1, 2) = |Q( 1 2 + )〉 ⊗ |ldf( 3 2 − )〉,