First radial excitations of mesons and diquarks in a contact interaction

We present a calculation for the masses of the first radially excited states of 40 mesons and diquarks made up of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>u</a:mi></a:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>d</c:mi></c:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>s</e:mi></e:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>c</g:mi></g:math>, and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>b</i:mi></i:math> quarks, including states that contain one or both heavy quarks. To this end, we employ a combined analysis of the Bethe-Salpeter and Schwinger-Dyson equations within a self-consistent and symmetry-preserving vector-vector contact interaction. The same set of parameters describes ground and excited states of mesons and their diquark partners. The wave function of the first radial excitation contains a zero whose location is correlated with an additional parameter <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>d</k:mi><k:mi>F</k:mi></k:msub></k:math> which is a function of dressed quark masses. Our results satisfy the equal spacing rules given by the Gell-Mann Okubo mass relations. Wherever possible, we make comparisons of our findings with known experimental observations as well as theoretical predictions of several other models and approaches including lattice quantum chromodynamics, finding a very good agreement. We report predictions for a multitude of radial excitations not yet observed in experiments. Published by the American Physical Society 2024