Parton distribution functions and transverse momentum dependence of heavy mesons

The leading Fock-state light-front wave functions of heavy quarkonia and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mrow> <mi>D</mi> </mrow> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>B</mi> </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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>x</mi> </math> as a function of the meson mass. The dependence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>x</mi> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mrow> <msubsup> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> <mrow> <mo>⊥</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </math> of the transverse distributions does not factorize into separate functions, and their falloff with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <msubsup> <mi mathvariant="bold-italic">k</mi> <mo>⊥</mo> <mn>2</mn> </msubsup> </math> is much slower than that of light mesons. Published by the American Physical Society 2024