Parton distribution functions of ground state mesons composed of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml

The valence quark parton distribution functions (PDFs) of all ground state heavy mesons composed of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>b</a:mi></a:math> or <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>c</c:mi></c:math> quarks, are discussed; namely, the pseudoscalar <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>η</e:mi><e:mi>c</e:mi></e:msub><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:mi>S</e:mi><e:mo stretchy="false">)</e:mo></e:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>η</i:mi><i:mi>b</i:mi></i:msub><i:mo stretchy="false">(</i:mo><i:mn>1</i:mn><i:mi>S</i:mi><i:mo stretchy="false">)</i:mo></i:math>, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>B</m:mi><m:mi>c</m:mi></m:msub></m:math>, together with the corresponding vector ones, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>J</o:mi><o:mo>/</o:mo><o:mi>ψ</o:mi></o:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi mathvariant="normal">ϒ</q:mi><q:mo stretchy="false">(</q:mo><q:mn>1</q:mn><q:mi>S</q:mi><q:mo stretchy="false">)</q:mo></q:math>, and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msubsup><v:mi>B</v:mi><v:mi>c</v:mi><v:mo>*</v:mo></v:msubsup></v:math>. We use a quantum chromodynamics (QCD)-inspired constituent quark model, which has been applied with success to conventional heavy mesons, so that one advantage here is that all parameters have already been fixed by previous studies. The wave functions of the heavy mesons in the rest frame are obtained by solving the Schrödinger equation, then boosted to its light-front, based on Susskind’s Lorentz transformation. The PDFs at the hadron scale, are then obtained by integrating out the transverse momenta of the modulus square of the light-front wave function. Our study shows how the valence quark distributions differ between pseudoscalar and vector mesons, as well as among charmonia, bottomonia and bottom-charmed mesons. Comparisons with other theoretical calculations demonstrate that the PDFs obtained herein are in general narrower but align well with the expected patterns. Moreover, each PDF’s pointwise behavior is squeezed with respect to the scale-free partonlike PDF.