Quantum corrections to baryon properties in chiral soliton models

Abstract

Chiral lagrangians as effective field theories of QCD are successfully applied to meson physics at low energies in the framework of chiral perturbation theory. Because of their nonlinear structure these lagrangians allow for static soliton solutions which may be interpreted as baryons. Their semiclassical quantization, which provides the leading order in an 1/N C expansion (N C is the number of colors) turned out to be insufficient in many cases to obtain good agreement with empirical baryon observables. However with N C = 3, large corrections are expected in the next-to-leading order which is carried by pionic fluctuations around the soliton background. The calculation of these corrections requires renormalization to 1-loop of the underlying field theory. We present a procedure to calculate the 1-loop contributions for a variety of baryonic observables. In contrast to chiral perturbation theory, terms with an arbitrary number of gradients may in principle contribute and the restriction to low chiral orders can only be justified by the investigation of the scale independence of the results. The results generally give the right sign and magnitude to reduce the discrepancy between theory and experiment with one exception: the axial quantities. These suffer from the fact that the underlying current algebra mixes different N C orders, which suggests a large and positive next-to-next-to-leading order contribution, which is probably sufficient to close the gap to experiment.

Electro-magnetic nucleon form factors and their spectral functions in soliton models

“…Ideally, of course, M should coincide with the physical nucleon mass M N . However, it is known, that this difference is related to quantum corrections [23,24] which probably also affect the existence and positions of zeros in the non relativistic form factors. Therefore, M is not really well defined in the model and could be used as additional parameter to minimize the undesired terms in (2.18), (2.19) by choosing M such that G (nr)…”

Hot nucleons in chiral soliton models

“…The most simple alternative is to use an effective LEC ℓ 2 = 1/4e 2 in front of the Skyrme term. The choice e = 4.25 (instead of e = 7.24) simulates the higher chiral order terms generated by vector mesons [7]. Tree con- Table 1.…”

“…For a more detailed justification of this choice see ref. [7]. Observables other than the mass may be calculated by coupling to the corresponding external fields.…”

“…The external field has to be chosen suitably so as to give the desired quantity, for details see ref. [7]. Matrix elements of j · J are then obtained as a derivative of the soliton mass (tree + 1 loop) in the presence of the external field with respect to its strength.…”

“…3.2 and 3.3 in ref. [7]). Towards smaller values then (µ ≃ 420MeV ) the symmetric ChO(4) term (α µ α µ ) 2 in the lagrangian (3) becomes too strong and finally destroys the soliton.…”