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Quark Confinement from Different Dressed Gluon Propagators

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Abstract

The gap equation in quantum chromodynamics is solved by incorporating different gluon dressing functions, some of them derived from a quark–diquark potential that exhibits a conformal symmetry. By using the bare vertex and working in the Landau gauge, the quark mass function is found to have an infrared enhancement that smoothly transitions to an asymptotically free behavior at high momentum, which is consistent with the predictions of Schwinger–Dyson equations. Additionally, these quark propagators violate reflexion positivity, indicating that the gluon dressing provides clear evidence of quark confinement.

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Notes

  1. In our conventions, \(\{\gamma _\mu ,\gamma _\nu \}=2\delta _{\mu \nu }\), \(\gamma _\mu ^\dagger =\gamma _\mu \), and \(a\cdot b = \sum _{i=1}^4 a_i b_i\).

  2. In the chiral limit is obtained a mass of 500 MeV

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Acknowledgements

We acknowledge enlightening discussions from M. Kirchbach and the organizers of Baryons 2022 for the excellent organization.

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Author notes

    Authors and Affiliations

    1. Facultad de Ciencias en Física y Matemáticas (FCFM), Universidad Autónoma de Chiapas, Carretera Zapata Km. 8, Rancho San Francisco, 29050, Tuxtla Gutiérrez, Chiapas, México

      Marco A. Bedolla

    2. Dpto. Ciencias Integradas, Centro de Estudios Avanzados en Fis., Mat. y Comp., Fac. Ciencias Experimentales, Universidad de Huelva, 21071, Huelva, Spain

      Khépani Raya

    3. Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, Francisco J. Mújica s/n, Col. Felícitas del Río, 58040, Morelia, Michoacán, México

      Alfredo Raya

    4. Centro de Ciencias Exactas, Universidad del Bio-Bio, Avda. Andrés Bello 720, Casilla 447, Chillán, Chile

      Alfredo Raya

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    1. Marco A. Bedolla
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    Correspondence to Marco A. Bedolla.

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    Bedolla, M.A., Raya, K. & Raya, A. Quark Confinement from Different Dressed Gluon Propagators. Few-Body Syst 64, 47 (2023). https://doi.org/10.1007/s00601-023-01834-9

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