The semi-leptonic form factors of $$\Lambda _{b}\rightarrow \Lambda _{c}$$ and $$\Xi _{b}\rightarrow \Xi _{c}$$ in QCD sum rules
Z. G. Zhao, Run-Hui Li, Yue-Long Shen, Yu-Ji Shi, Yansheng Yang
Abstract
Abstract In this work, the full leading order results of the form factors for $$\Xi _{b}\rightarrow \Xi _{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> and $$\Lambda _{b}\rightarrow \Lambda _{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> are obtained in QCD sum rules. Contributions from up to dimension-5 have been considered. For completeness, we also study the two-point correlation function to obtain the pole residues of $$\Xi _{Q}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> </mml:math> and $$\Lambda _{Q}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> </mml:math> , and higher accuracy is achieved. For the three-point correlation function, since stable Borel regions cannot be found, about $$20\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>20</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> uncertainties are introduced for the form factors of $$\Xi _{b}\rightarrow \Xi _{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> and $$\Lambda _{b}\rightarrow \Lambda _{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> . Our results for the form factors are consistent with those of the lattice QCD within errors.