$$\Lambda _b\rightarrow p$$ transition form factors in perturbative QCD
Jia-Jie Han, Ya Li, Hsiang-nan Li, Yue-Long Shen, Zhen-Jun Xiao, Fu-Sheng Yu
Abstract
Abstract We reanalyze the $$\Lambda _b\rightarrow p$$ <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:mi>p</mml:mi> </mml:mrow> </mml:math> transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a $$\Lambda _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist $$\Lambda _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> baryon and proton LCDAs gave the form factors, which are two orders of magnitude smaller than indicated by experimental data. We find that the twist-4 $$\Lambda _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> baryon LCDAs and the twist-4 and -5 proton LCDAs contribute dominantly, and the enhanced form factors become consistent with those from lattice QCD and other nonperturbative methods. The estimated branching ratios of the semileptonic decays $$\Lambda _b\rightarrow p\ell {\bar{\nu }}_\ell $$ <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:mi>p</mml:mi> <mml:mi>ℓ</mml:mi> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>ℓ</mml:mi> </mml:msub> </mml:mrow> </mml:math> and the hadronic decay $$\Lambda _b\rightarrow p\pi $$ <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:mi>p</mml:mi> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> are also close to the data. It implies that the b quark mass is not really heavy enough, and higher-power contributions play a crucial role, similar to the observation made in analyses of B meson transition form factors. With the formalism established in this work, we are ready to study various exclusive heavy baryon decays systematically in the PQCD approach.