Weak decays of $${\varvec{B}}_{{\varvec{c}}}$$ involving vector mesons in self-consistent covariant light-front approach

Abstract We present a comprehensive analysis of weak transition form factors, semileptonic decays, and nonleptonic decays of $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> mesons involving pseudoscalar ( P ) and vector ( V ) mesons for bottom-conserving and bottom-changing decay modes. We employ the self-consistent covariant light-front quark model (CLFQM), termed type-II correspondence, to calculate the $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> to P ( V ) transition form factors. The type-II correspondence in the CLF approach gives self-consistent results associated with the $$B^{(i)}_j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>j</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>i</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> functions, which vanish numerically after the replacement $$M^{\prime (\prime \prime )} \rightarrow M_0^{\prime (\prime \prime )}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>M</mml:mi> <mml:mrow> <mml:mo>′</mml:mo> <mml:mo>(</mml:mo> <mml:mo>″</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>′</mml:mo> <mml:mo>(</mml:mo> <mml:mo>″</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> in traditional type-I correspondence, and the covariance of the matrix elements is also restored. We investigate these effects on bottom-conserving $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> to P ( V ) form factors that have not yet been studied in CLFQM type-II correspondence. In addition, we quantify the implications of self-consistency propagating to weak decays involving both bottom-conserving and bottom-changing $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> transition form factors. We use two different parameterizations, the usual three-parameter function of $$q^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> and the model-independent z -series expansion, to establish a clear understanding of $$q^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> dependence. Using the numerical values of the form factors, we predict the branching ratios other physical observables, including forward-backward asymmetries, polarization fractions, etc. of the semileptonic $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> decays. Subsequently, we predict the branching ratios of two-body nonleptonic weak decays using the factorization hypothesis in self-consistent CLFQM. We also compare our results with those of other theoretical studies.