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Definition of Local Spatial Densities in Hadrons.

E Epelbaum1, J Gegelia1,2, N Lange1

  • 1Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany.

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This study defines spatial density using matrix elements of local operators in hadronic states. It clarifies the relationship between charge density and electric form factors for spinless particles.

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Area of Science:

  • Quantum Chromodynamics
  • Hadronic Physics
  • Particle Physics

Background:

  • The spatial distribution of particles within hadrons is crucial for understanding their structure.
  • Defining spatial densities from theoretical constructs like matrix elements presents challenges.
  • Existing methods may lack unambiguous definitions for these densities.

Purpose of the Study:

  • To establish an unambiguous method for defining spatial density from the matrix element of a local operator.
  • To explore the connection between hadronic spatial densities and electromagnetic properties.
  • To provide a novel interpretation of spatial densities and their moments.

Main Methods:

  • Utilizing the matrix element of a local operator between hadronic states.
  • Applying the formalism to calculate the charge density of a spinless particle.
  • Analyzing the relationship between the derived charge density and the electric form factor.

Main Results:

  • An unambiguous definition for spatial density associated with local operators is demonstrated.
  • The charge density of a spinless particle is explicitly calculated.
  • A clear relationship between spatial charge density and the electric form factor is established.

Conclusions:

  • The matrix element of a local operator provides a rigorous definition of spatial density.
  • This approach offers an unconventional but consistent interpretation of spatial densities.
  • The findings have implications for the study of hadron structure and form factors.