Next-to-leading order QCD corrections to $$\Lambda _b \rightarrow p $$ form factors from light-cone sum rules

Abstract In this study, we compute the radiative corrections to 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 at next-to-leading logarithmic accuracy. With the light-cone distribution amplitudes of the $$\Lambda _b$$ <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, we employ the light-cone sum rules in the framework of soft-collinear effective theory, utilizing the method of regions to systematically extract the factorized contributions from different momentum regions . The factorization formulae of the vacuum-to- $$\Lambda _b$$ <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> correlation function, constructed from the interpolating current for the energetic proton, are derived at leading power in $$m_p / m_{\Lambda _b}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>m</mml:mi> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:msub> </mml:mrow> </mml:math> . With our specific choice of interpolating current, only the twist-4 distribution amplitude of the $$\Lambda _b$$ <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 contributes to the form factors. Numerically, we find that the next-to-leading order QCD perturbative corrections reduce the tree-level form factors to approximately 65 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> of their original value, with the next-to-leading-order jet function providing the dominant contribution. In the large-energy limit ( $$E_p \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> ), the form factors exhibit a clear $$1/E_p^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>E</mml:mi> <mml:mi>p</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> scaling, consistent with the expected power-counting behavior. By applying the z -series parameterization to perform a combined fit of the form factors from our results and available lattice QCD simulations, we further investigate the decay rate of $$\Lambda _b \rightarrow p \ell ^- \bar{\nu }_{\ell }$$ <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:msup> <mml:mi>ℓ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <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 extract the CKM matrix element $$|V_{ub}| = (3.33\pm 0.43 ) \times 10^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>ub</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3.33</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.43</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>×</mml:mo> </mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> .