Abstract
We predict the masses of the lowlying $B_c$ mesons with $J^P = 0^-,\,1^-,\,0^+,\,1^+,\,2^+$, using a flavor dependent interaction pattern which gives an unified successful description of the light, heavy-light and heavy mesons and is also appliable to the radial excited heavy mesons. The errors are controlled carefully. With the errors from the RL approximation subduced, our predictions are consistent with the lQCD and quark model results, which supports strongly that the flavor dependent interaction pattern is reasonable. Our predictions provide significant guides to the experiment search of the $B_c$ mesons.
Highlights
The Bc mesons are the only heavy mesons containing two different flavor valence quarks, one charm quark and one bottom quark
A meson corresponds to a pole in the quark-antiquark scattering kernel [20], and the amplitude is solved by the BetheSalpeter equation (BSE) [21]
We extend our study to Bc mesons with JP 1⁄4 0−; 1−; 0þ; 1þ and 2þ
Summary
The Bc mesons are the only heavy mesons containing two different flavor valence quarks, one charm quark and one bottom quark. The quark flavor difference forbids their annihilation into gluons or photons, so that the ground state pseudoscalar Bcð1SÞ can only decay weakly, which makes it interesting for the study of weak interaction. Basic degree of freedom, i.e., the quarks and the gluons, is complementary to lQCD In this approach, a meson corresponds to a pole in the quark-antiquark scattering kernel [20], and the amplitude is solved by the BetheSalpeter equation (BSE) [21]. While the forms of the quark-gluon-vertex and the scattering kernel have been investigated [24], the most widely used and technically simple one is the rainbow ladder (RL) approximation This scheme has gained many phenomenological successes in the hadron spectrum, the form factors, the distribution functions, etc.
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