Structure of the nucleon in chiral effective theory on the light front
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ESSION “QUANTUM FIELD THEORY AND THEORY OF ELEMENTARY PARTICLES”
Structure of the Nucleon in Chiral Effective Theory on the Light Front1, 2 N. A. Tsirovaa, V. A. Karmanovb, and J.F. Mathiotb a
Laboratoire de Physique Corpusculaire, F63177 Aubière Cedex, France b Lebedev Physical Insitute, 119991 Moscow, Russia
Abstract—We propose a new approach to treat the nucleon structure in terms of an effective chiral Lagrangian. The state vector of the nucleon is defined on the light front plane and is decomposed in Fock components. An adequate Fock sector dependent renormalization scheme is applied. We present our first results of the calculation of nucleon properties in a twobody Fock truncation. DOI: 10.1134/S1063779610060390 21
1. INTRODUCTION
For the last 40 years pionnucleon systems and their theoretical investigation within the general framework of chiral perturbation theory have been of great interest. Since the nucleon mass is not zero in the chiral limit, all momentum scales are involved in the calculation of baryon properties (like masses or elec troweak observables) beyond tree level. This is at vari ance with the meson sector for which a meaningful power expansion in characteristic momenta of any physical amplitude can be done. While there is not much freedom, thanks to chiral symmetry, for the construction of the effective Lagrangian in Chiral Per turbation Theory (ChPT), ᏸChPT, in terms of the pion field – or more precisely in terms of the U field defined by U = exp ( iτ ⋅ ϕ/f π ) where fπ is the pion decay con stant – one should settle an appropriate approxima tion scheme in order to calculate the baryon proper ties. Up to now, two main strategies have been adopted. The first one is to force the bare (and hence the physical) nucleon mass to be infinite, in Heavy Baryon Chiral Perturbation Theory [1]. In this case, by construction, an expansion in characteristic momenta can be developed. The second one is to use a specific regularization scheme [2] in order to sepa rate contributions which exhibit a meaningful expan sion in momenta, and hide the other parts in appropri ate counterterms. In both cases however, the explicit calculation of baryon properties relies on an extra approximation in the sense that physical amplitudes are further calculated by expanding ᏸChPT in a finite number of pion fields.
Following [3], we propose to calculate nucleon properties using the general eigenvalue equation for the state vector projected on the light front. This non perturbative equation is then solved in a truncated Fock space. This enables to consider irreducible con tributions arising from ππNN contact interactions in a systematic way, as shown in Fig. 1. It was calculated in perturbation theory in [4]. This decomposition of the state vector in a finite number of Fock components implies to consider an effective Lagrangian which enables all possible elementary couplings between the pion and the nucleon fields to the same order. This is indeed easy to achieve in chiral perturbation theory since each deri
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