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Register a new userOn the Chiral Quark Soliton Model with Pauli-Villars Regularization
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Masashi Wakamatsu Ohtsubo Laboratory
Publication date
1999
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English
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The Pauli-Villars regularization scheme is often used for evaluating parton distributions within the framework of the chiral quark soliton model with inclusion of the vacuum polarization effects. Its simplest version with a single subtraction term should however be taken with some caution, since it does not fully get rid of divergences contained in scalar and psuedoscalar quark densities appearing in the soliton equation of motion. To remedy this shortcoming, we propose here its natural extention, i.e. the Pauli-Villars regularization scheme with multi-subtraction terms. We also carry out a comparative analysis of the Pauli-Villars regularization scheme and more popular proper-time one. It turns out that some isovector observables like the isovector magnetic moment of the nucleon is rather sensitive to the choice of the regularization scheme. In the process of tracing the origin of this sensitivity, a noticeable difference of the two regularization scheme is revealed.
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Calculations in a (3+1)-dimensional model indicate that Pauli-Villars regularization can be combined with discrete light-cone quantization (DLCQ) to solve at least some field theories nonperturbatively. Discrete momentum states of Pauli-Villars particles are included in the Fock basis to automatically generate needed counterterms; the resultant increase in basis size is found acceptable. The Lanczos algorithm is used to extract the lowest massive eigenstate and eigenvalue of the light-cone Hamiltonian, with basis sizes ranging up to 10.5 million. Each Fock-sector wave function is computed in this way, and from these one can obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form-factor slope.
The advantage of Pauli-Villars regularization in quantum field theory quantized on the light front is explained. Simple examples of scalar $lambdavarphi^4$ field theory and Yukawa-type model are used. We give also an example of nonperturbative calculation in the theory with Pauli-Villars fields, using for that a model of anharmonic oscillator modified by inclusion of ghost variables playing the role similar to Pauli-Villars fields.
The techniques of Pauli-Villars regularization and discrete light-cone quantization are combined to analyze Yukawa theory in a single-fermion truncation. A special form of the Lanczos algorithm is constructed for diagonalization of the indefinite-metric light-cone Hamiltonian.
We calculate the axial form factor in the chiral quark soliton (semibosonized Nambu - Jona-Lasinio) model using the semiclassical quantization scheme in the next to leading order in angular velocity. The obtained axial form factor is in a good absolute (without additional scaling) agreement with the experimental data. Both the value at the origin and the $q$-dependence of the form factor as well as the axial m.s.radius are fairly well reproduced.
In this paper we present the derivation as well as the numerical results for the electromagnetic form factors of the nucleon within the chiral quark soliton model in the semiclassical quantization scheme. The model is based on semibosonized SU(2) Nambu -- Jona-Lasinio lagrangean, where the boson fields are treated as classical ones. Other observables, namely the nucleon mean squared radii, the magnetic moments, and the nucleon--$Delta$ splitting are calculated as well. The calculations have been done taking into account the quark sea polarization effects. The final results, including rotational $1/N_c$ corrections, are compared with the existing experimental data, and they are found to be in a good agreement for the constituent quark mass of about 420 MeV. The only exception is the neutron electric form factor which is overestimated.
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