1/m_Q Corrections to the Bethe-Salpeter Equation for Λ_{Q} in the Diquark Picture

Abstract

Corrections of order 1/m_Q (Q=b or c) to the Bethe-Salpeter (B-S) equation for Λ_Q are analyzed on the assumption that the heavy baryon Λ_Q is composed of a heavy quark and a scalar, light diquark. It is found that in addition to the one B-S scalar function in the limit m_Q -> \infty, two more scalar functions are needed at the order 1/m_Q. These can be related to the B-S scalar function in the leading order. The six form factors for the weak transition Λ_b -> Λ_c are expressed in terms of these wave functions and the results are consistent with heavy quark effective theory to order 1/m_Q. Assuming the kernel for the B-S equation in the limit m_Q -> \infty to consist of a scalar confinement term and a one-gluon-exchange term we obtain numerical solutions for the B-S wave functions, and hence for the ${\Lambda }_b\to {\Lambda }_c$ form factors to order 1/m_Q. Predictions are given for the differential and total decay widths for Λ_b -> Λ_c l \barν, and also for the nonleptonic decay widths for Λ_b -> Λ_c plus a pseudoscalar or vector meson, with QCD corrections being also included.

Latex, 24 pages, two figures

References in corpus (4)

• Isgur-Wise Function for ${\Lambda }_b\to {\Lambda }_c$ in B-S Approach
• Bethe-Salpeter Equation for Heavy Baryons ω_{Q}^{(*)} in the Diquark Picture
• Measurements of the B^0_s and Λ_b Lifetimes
• Λ_b \to Λ_c P(V) Nonleptonic Weak Decays

Cited by in corpus (11)

• Some mass relations for mesons and baryons in Regge phenomenology
• Revisiting semileptonic decays of ${\Lambda }_{b(c)}$ supported by baryon spectroscopy
• Strong decays of heavy baryons in Bethe-Salpeter formalism
• Investigation of the possible $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ molecule states
• Charm Physics - A Field Full with Challenges and Opportunities
• The Average Kinetic Energy of the Heavy Quark in ${\Lambda }_b$ in the Bethe-Salpeter Equation Approach
• X(3872) as a molecular $D{\bar{D}}^{\ast }$ state in the Bethe-Salpeter equation approach
• Calculation of 1/m^{2}_{b} corrections to <Λ_{b}(v,s)|\bar{b}γ^λγ_{5}b|Λ_{b}(v,s)> for polarized Λ_{b} in the Bethe-Salpeter equation approach
• Heavy quark distribution functions in heavy baryons
• Study on the Form Factors at Effective Vertices of Diqarks Interacting with Gauge Bosons
• Residues of ${\Lambda }_Q$-type and ${\Sigma }_Q$-type Baryons in the Bethe-Salpeter Equation Approach