Heavy-light quark systems from the QCD instanton vacuum: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> light flavor c

We investigate heavy-light quark systems within the framework of the QCD instanton vacuum, focusing on the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>N</a:mi><a:mi>f</a:mi></a:msub><a:mo>=</a:mo><a:mn>1</a:mn></a:math> light flavor case. We derive an effective heavy-light quark interaction from the low-energy QCD partition function and construct a heavy-meson effective Lagrangian. The physical residual mass of heavy mesons, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="normal">Λ</c:mi></c:math>, is determined by employing compositeness and normalization conditions. We calculate the masses of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>D</f:mi></f:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>B</h:mi></h:math> mesons and their weak decay constants to the leading order and next-to-leading order in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mn>1</j:mn><j:mo>/</j:mo><j:msub><j:mi>m</j:mi><j:mi>Q</j:mi></j:msub></j:math> expansion. The current results for <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>f</l:mi><l:mi>D</l:mi></l:msub></l:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>f</n:mi><n:mi>B</n:mi></n:msub></n:math> are in good agreement with recent lattice QCD data and Particle Data Group (PDG) average values. Published by the American Physical Society 2024