Heavy baryon excitations with functional calculations + Diquark correlations of the baryon spectrum

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Recent years have witnessed significant progress in heavy baryon spectroscopy, with almost 30 new heavy baryon states discovered at the LHC. On the theoretical front, many methods have been employed to study baryon spectroscopy, such as quark models, effective field theories and lattice QCD. All have with their own advantages and drawbacks, such as the challenges posed by excited states in lattice QCD, the limited range available in effective field theories or the non-relativistic approaches from quark model implementations. In this work, we employ functional methods within QCD, which contains the toolset of Dyson-Schwinger and Bethe-Salpeter equations.

The aim is to extend its successful application beyond the light and strange baryon spectrum, to charmed and bottom baryons. Additionally, we study baryons formed from any flavor combination, from three equally flavored quarks to three different flavored quarks.The work builds upon the quark-diquark Bethe-Salpeter equation (BSE), where the interaction consists of quark exchange between quarks and diquarks, with all components determined from the quark level.

This approach simplifies the Faddeev equation, which describes the baryon as a three-body system, to a two-body equation that is numerically solvable. Its solution scheme involves a deeper exploration of the Dirac and flavor terms of the quark-diquark amplitude, and a transformation of its BSE into an eigenvalue problem that can yield, through statistical intrapolation and extrapolation techniques, desirable properties from the ground and excited states of a given baryon.

The approach reveals interesting insights into the internal structure of baryons, including non-negligible relativistic components in terms of p-waves, which are typically suppressed in non-relativistic treatments, as well as unequal diquark contributions for a given baryon with different flavored quarks. Current results focus on the 1/2+ and 3/2+ baryon channels as well as 0+ and 1+ diquark channels, meaning that future work is focused on expanding the obtained results beyond these channels.