Study of σ(750) andρ0(770) production in measurements of πN↑

Abstract

We present a new and improved model-independent amplitude analysis of the reactions ϩ n ↑ → ϩ Ϫ p at 5.98 and 11.85 GeV/c and Ϫ p ↑ → Ϫ ϩ n at 17.2 GeV/c measured with transversely polarized targets at the CERN Proton Synchrotron. For dipion masses below 1000 MeV the pion production process is described by two S-wave and six P-wave production amplitudes. Previous analyses suffered from the presence of unphysical solutions for moduli of amplitudes or cosines of their relative phases, causing uncertainties regarding the signal for the scalar state Iϭ0 0 ϩϩ (750). To remove the unphysical solutions we use a Monte Carlo approach to amplitude analysis. In each (m,t) bin we randomly varied the input spin-density-matrix elements 30 000 times within their experimental errors and performed an amplitude analysis for each selection. Unphysical solutions were rejected and the physical solutions produced a continuous range of values for moduli, cosines of relative phases, and for partial wave intensities. A clear signal for (750) resonance emerges in all four solutions for an S-wave intensity I S at 5.98 and 11.85 GeV/c and in both solutions for an S-wave amplitude ͉S ͉ 2 ⌺ at 17.2 GeV/c. Its ϩ Ϫ decay width is estimated to be in the range 200-300 MeV. We find a significant suppression of 0 production in the amplitudes ͉U͉ 2 ⌺, ͉N ͉ 2 ⌺ and at 17.2 GeV/c in ͉L͉ 2 ⌺. The mass dependence of the amplitudes ͉L ͉ 2 ⌺ and ͉L͉ 2 ⌺ shows unexpected structures within the 0 mass region which correlate the mass spectra corresponding to opposite nucleon spins. These features of the P-wave moduli reveal the essential role of nucleon spin in the pion production process and contradict the factorization hypothesis. Our results emphasize the need for a systematic study of pion production on the level of amplitudes in a new generation of dedicated experiments with spin at the recently proposed high-intensity hadron facilities.

Screening effects on the elastic nucleon-nucleon cross section in relativistic nuclear matter

“…The p+ 9 Be collision probes low densities in the surface, while the p+ 12 C, p+ 27 Al, p+ 40 Ca, which all give similar results, are thought to probe the nuclear density n = n sat . The result of Tanaka Fig.…”

“…(35) to (38) by excluding the last term in Eqs. (40). This last term corresponds to the quasi-nucleon distribution in the Dirac sea (vacuum distribution) and leads to divergences in the calculation of the real parts of the polarization tensors which must be renormalized.…”

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

“…But in the late nineties, further support for the existence of a broad and light sigma around 500 MeV, forming a nonet with the f 0 (980), a 0 (980) and κ, was also obtained from models where the scalar resonances are included explicitly either as poles in the amplitudes [85] or in the Lagrangian in a linear representation of a chiral multiplet [86,87,88,89]. Nevertheless, the confusion lingered on, since there were some analyses that produced a narrow sigma around 700 [90], although the phase-shifts would differ substantially from other analyses like those in Fig.2. 15…”

“…In addition, Forward Dispersion Relations [173] and Roy equations [49] seemed to imply that only the "down" solution was consistent with dispersion theory. However, the "up-down" controversy was briefly resurrected and killed again in the 90's [90] when a narrow σ was suggested around 750 MeV in a reanalysis of the CERN-Krakow-Munich polarized data. The key point was the observation that the a 1 resonance exchange, ignored in most previous analyses, was important to extract ππ scattering from πN → ππN .…”

Broad sub-continuum resonances and the case for finite-energy sum-rules

“…Even if the first pion excitation state is identified with the Π(1300) resonance, whose mass pole is still likely to be below the continuum threshold, the width of this resonance may be as large as 600 MeV [5]. Moreover, the lowest isoscalar 0 + meson, if it exists at all [6], may have a width even larger than its mass [7], though arguments for a σ(550)-resonance with a somewhat more moderate width have also been recently advanced [8].…”