Power corrections in the determination of heavy meson light-cone distribution amplitudes: A renormalon-based estimation

At leading power accuracy, the QCD light-cone distribution amplitudes (LCDAs) for a heavy meson can be matched onto the LCDAs in the framework of heavy-quark effective theory (HQET) through a factorization formula. We examine the power corrections to this factorization in the renormalon model, which can associate the power corrections originating from high-twist contributions to the divergent series in a matching kernel. Our analysis indicates that the dominant power corrections originate from the virtual part of the vertex bubble chain diagrams, which generate poles at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>w</a:mi><a:mo>=</a:mo><a:mi>n</a:mi><a:mo>+</a:mo><a:mfrac><a:mn>1</a:mn><a:mn>2</a:mn></a:mfrac><a:mo>,</a:mo><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mo stretchy="false">∀</a:mo><a:mi>n</a:mi><a:mo>∈</a:mo><a:mi mathvariant="double-struck">N</a:mi></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>w</e:mi><e:mo>=</e:mo><e:mn>1</e:mn></e:math> in the Borel plane. Employing phenomenological models for both HQET and QCD LCDA, we present a numerical estimate. The results indicate that the power corrections in the peak region are approximately 22% for the D meson and 7% for the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mover accent="true"><g:mi mathvariant="normal">B</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math> meson. These findings showcase the magnitude and potential importance of power corrections in achieving high-precision phenomenological predictions for heavy mesons.