Factorization formula connecting the Λb LCDA in QCD and boosted HQET

A bstract Light-cone distribution amplitudes (LCDAs) are essential to precision phenomenology in heavy baryon decays. In this work, we derive a factorization formula connecting the leading-twist QCD LCDA to the boosted HQET LCDA of the Λ b baryon in the peak region. We demonstrate a significant simplification of the matching procedure by applying the method-of-regions to perturbative calculations. With this simplification, we calculate the required one-loop perturbative corrections to the QCD and boosted HQET LCDAs in the $$ \overline{\textrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> scheme, and thereby obtain the one-loop jet function that serves as the matching kernel in the factorization formula. We have also performed the matching of the Λ b decay constants in QCD and boosted HQET, leading to the final factorization formula connecting the LCDAs in these two theories. A detailed discussion of the Λ b QCD LCDA in the tail region is provided. This work provides an essential step toward lattice QCD calculation of heavy baryon LCDAs in the future.