Parton distribution functions and transverse momentum dependence of heavy mesons

The leading Fock-state light-front wave functions of heavy quarkonia and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>D</a:mi></a:mrow></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>B</c:mi></c:math> mesons are obtained from the projections of their Bethe-Salpeter wave functions on the light front. We compute their leading-twist time-reversal even transverse momentum distributions and parton distribution functions. Mirroring the behavior of parton distribution amplitudes, the support of both distributions is increasingly narrower and shifted toward larger <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>x</e:mi></e:math> as a function of the meson mass. The dependence of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>x</g:mi></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:msubsup><i:mrow><i:mi mathvariant="bold-italic">k</i:mi></i:mrow><i:mrow><i:mo>⊥</i:mo></i:mrow><i:mrow><i:mn>2</i:mn></i:mrow></i:msubsup></i:mrow></i:math> of the transverse distributions does not factorize into separate functions, and their falloff with <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msubsup><l:mi mathvariant="bold-italic">k</l:mi><l:mo>⊥</l:mo><l:mn>2</l:mn></l:msubsup></l:math> is much slower than that of light mesons. Published by the American Physical Society 2024