Nucleon matrix elements and baryon masses in the Dirac orbital model
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ELEMENTARY PARTICLES AND FIELDS Theory
Nucleon Matrix Elements and Baryon Masses in the Dirac Orbital Model* Yu. A. Simonov** and M. A. Trusov*** Institute of Theoretical and Experimental Physics, Moscow, Russia Received December 15, 2008
Abstract—Using the expansion of the baryon wave function in a series of products of single-quark bispinors (Dirac orbitals), the nonsinglet axial and tensor charges of a nucleon are calculated. The leading term yields gA = 1.27 in good agreement with experiment. Calculation is essentially parameter-free and depends only on the strong coupling constant value αs . The importance of lower Dirac bispinor component, yielding 18% to the wave-function normalization is stressed. As a check, the baryon decuplet masses in the formalism of this model are also computed using standard values of the string tension σ and the strangequark mass ms ; the results being in a good agreement with experiment. PACS numbers: 14.20.-c, 12.40.Yx, 12.39.Kj DOI: 10.1134/S1063778809060180
Axial and tensor charges of a nucleon are important to characterize the basic structure of the nucleon as composed of strongly coupled quarks [1–4]. Whereas many baryon charateristics can be reasonably obtained in relativized quark models, where all relativistic effects are treated via Salpeter equation [5] and spin corrections, the axial and tensor charges are sensitive to the Dirac structure of quark wave functions, and, in particular, as will be shown below, to the negative energy components. The most systematic treatment of relativistic baryon system can be done in the three-body Bethe–Salpeter formalism, however, in this approach a rigorous derivation ends up in the system of more than 20 integral equations, and therefore, a drastic simplification is needed to make realistic calculations. Recently this kind of approach was developed in [6], where quark–quark interactions have been properly parametrized. However, the relativistic objects, like negative-energy-component admixture η (see below), are very sensitive to the form of interactions, and in [6] η has come out rather small. In our paper we choose another and much simpler approach, which allows to treat all Dirac components properly including lower ones, and to work out the resulting η (and axial and tensor charges) in a transparent way. ∗
The text was submitted by the authors in English. E-mail: [email protected] *** E-mail: [email protected] **
First of all, let us recall some formulas of the spin relativistic theory. Consider a polarized free fermion with spin 1/2. The fermion polarization could be described by a space-like pseudovector aµ , which reduces in the fermion rest frame to the unit 3-vector along which the fermion spin projection is equal to +1/2. The pseudovector aµ obviously meets conditions: a · a = −1, a · p = 0, where p is the the fermion 4-momentum. The corresponding Michel–Wighimann fermion density matrix is γp + m 1 − γ 5 (γa) , (1) ρ= 4m where m is the fermion mass. Note, that here and below we propose the plane wave amplitude being normalized
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