Multiple soft pion production in nonlinear chiral sigma model

Abstract

Multiple soft pion production in the baryon scattering reactions is considered in the framework of chiral nonlinear sigma model neglecting the pion mass. Treating baryons in the eikonal approximation as classical sources, a set of analytical solutions for the pion field is found. A tree S-matrix is constructed on the basis of these solutions describing the emission (or absorption) of any number of soft pions. Then the contribution of soft virtual pions is taken into account in a closed form. It is shown that the loop corrections strongly suppress the pion radiation, and for the two limiting cases of nonrelativistic and ultra-relativistic baryon scatterings there is no pion emission from the "ends". Thus, the mechanism similar to the soft photon bremsstrahlung in the quantum electrodynamics seems to be unable to create a state with a large number of the soft pions. PACS:13.85.-t; 13.85.Hd; 11.30.Rd 1The problem of possible production of the classical pion field in the high energy hadron-hadron or ion-ion collisions has recently drawn much attention [1]. Very interesting example of the classical pion field is a disoriented chiral condensate (DCC) introduced by Bjorken and co-authors [2]. Possible experimental signatures of DCC are of special importance since one has to distinguish between this phenomenon and the effects arising due to the independent emission of a large number of soft pions. It is well-known that these effects can be described in terms of a coherent state resembling bremsstrahlung photon in the electrodynamics [3, 4] (see also [5]). Neglecting the pion interaction, such an approach leads to the predictions for the charge distribution of pions in the multiple production processes, which are really almost identical to what could be expected from DCC [6,7]. That is why it is of great interest to study how the pion interaction modifies these results.The multiple soft pion production in the hadron-hadon collisions is treated here within the nonlinear sigma-model. This model includes three isovector fields π i , i = 1, 2, 3, and an auxiliary scalar field σ obeying the constraintThe lagrangian iswhere L π is a pure pionic part,and L f describes the pion interaction with fermions,The vacuum of the model corresponds to the expectation values σ = f π , π i = 0, which result into the fermion mass M = gf π . The vacuum is degenerate, there is a set of vacuum configurations σ = f π cos θ, π i = f π n i sin θ for arbitrary parameter θ and unit vector n i . The model (1) provides a simple but qualitatively satisfactory description for soft pion-nucleon physics, g πN N and M being pion-nucleon interaction constant and nucleon mass, respectively.The sigma model can be also regarded as an effective chiral theory describing the low energy limit of QCD. It correctly reflects the important property of QCD, namely, spontaneous chiral symmetry breaking due to the quark condensate qq = 0 and the goldstone nature of pions. In this case M = M q is the mass of the constituent quark q.The pion field represents the chiral phas...