Abstract
We present first results for the quark mass function in Minkowski space in both the spacelike and timelike regions calculated from the same quark-antiquark interaction kernel used in the latest meson calculations using the Gross equation. This kernel consists of a Lorentz vector effective one-gluon-exchange-type interaction, a vector constant, and a mixed scalar-pseudoscalar covariant linear confining interaction that does not contribute to the mass function. We analyze the gauge dependence of our results, prove the gauge independence of the constituent quark mass and mass gap equation, and identify the Yennie gauge as the appropriate gauge to be used in CST calculations. We compare our results in the spacelike region to lattice QCD data and find good agreement.
Highlights
The highly nonperturbative nature of QCD in the low-energy regime makes the theoretical description of strong-interaction phenomena, such as confinement and dynamical chiral symmetry breaking (DχSB), very difficult
We present first results for the quark mass function in Minkowski space in both the spacelike and timelike regions calculated from the same quark-antiquark interaction kernel used in the latest meson calculations using the Gross equation
Many different approaches have been used to calculate the properties of QCD bound states and their reactions, such as lattice QCD [1,2,3,4,5,6,7,8,9,10], Bethe-Salpeter/ Dyson-Schwinger (BSDS) equations [11,12,13,14,15,16,17,18,19,20,21], effective field theories [22,23], Hamiltonian approaches [24,25,26,27,28,29,30,31], and various kinds of effective phenomenological quark models, which are often based on quark-quark interactions similar to the Cornell potential [32]
Summary
The highly nonperturbative nature of QCD in the low-energy regime makes the theoretical description of strong-interaction phenomena, such as confinement and dynamical chiral symmetry breaking (DχSB), very difficult. The calculation of the quark self-energy makes it feasible to implement an important constraint of QCD, namely the dynamical breaking of chiral symmetry This is a key ingredient for a realistic description of the properties of light mesons, in particular the pion. It shows in detail the calculation of the self-energy for the gluon-exchange kernel in a general linear covariant gauge, with special attention to the dependence of the results on the gauge parameter.
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