The ππ\pi\pi interaction in nuclear matter from a study of the π+A→π+π±A′\pi^+ A \to \pi^+ \pi^{\pm} A' reactions

The pion-production reactions $\pi^+ A \to \pi^+\pi^{\pm} A'$ were studied on $^{2}H$, $^{12}C$, $^{40}Ca$, and $^{208}Pb$ nuclei at an incident pion energy of $T_{\pi^{+}}$=283 MeV. Pions were detected in coincidence using the CHAOS spectrometer. The experimental results are reduced to differential cross sections and compared to both theoretical predictions and the reaction phase space. The composite ratio $\cal C$$_{\pi\pi}^A$ between the $\pi^{+}\pi^{\pm}$ invariant masses on nuclei and on the nucleon is also presented. Near the $2m_{\pi}$ threshold pion pairs couple to $(\pi\pi)_{I=J=0}$ when produced in the $\pi^+\to \pi^+\pi^-$ reaction channel. There is a marked near-threshold enhancement of $\cal C$$_{\pi^+\pi^-}^A$ which is consistent with theoretical predictions addressing the partial restoration of chiral symmetry in nuclear matter. Furthermore, the behaviour of $\cal C$$_{\pi^+\pi^-}^A$ is well described when the restoration of chiral symmetry is combined with standard P-wave renormalization of pions in nuclear matter. On the other hand, nuclear matter only weakly influences $\cal C$$_{\pi^+\pi^+}^A$, which displays a flat behaviour throughout the energy range regardless of $A$.Comment: 30 pages, 16 figures, PS format, accepted for publication in Nucl. Phys

π→ππ\pi \to \pi\pi results in nuclei

The Crystal Ball ($CB$) collaboration at $BNL$ has recently presented results regarding a study of the $\pi^- A \to \pi^0\pi^0 A^\prime$ reaction on $H, D, C, Al$ and $Cu$, using a nearly 4$\pi$ detector. Similar results, but for the $\pi^+ A \to \pi^+\pi^{\pm} A^\prime$ reaction on $^{2}H$, $^{12}C$, $^{40}Ca$, and $^{208}Pb$, have been published earlier by the $CHAOS$ collaboration at $TRIUMF$. In this Brief Report a comparison of the results of the two measurements is made, which shows that the $CHAOS$ and $CB$ data share relevant common features. In particular, the increase in strength as a function of A seen in the near-threshold $\pi^+ \pi^-$ invariant mass spectra reported by the $CHAOS$ group, is also seen in the $\pi^0 \pi^0$ CB data, when the results from the two groups are compared in a way which accounts for the different acceptances of the two experiments.Comment: 7 pages, 1 figure, accepted for publication in Phy. Rev. C - Brief Repor

In-medium pi-pi Correlation Induced by Partial Restoration of Chiral Symmetry

We show that both the linear and the non-linear chiral models give an enhancement of the pi-pi cross section near the 2pi threshold in the scalar-iso-scalar (I=J=0) channel in nuclear matter. The reduction of the chiral condensate, i.e., the partial chiral restoration in nuclear matter, is responsible for the enhancement in both cases. We extract an effective 4pi-nucleon vertex which is responsible for the enhancement but has not been considered in the non-liear models for in-medium pi-pi interaction. Relation of this vertex and a next-to-leading order terms in the heavy-baryon chiral lagrangian, L_piN^(2), is also discussed.Comment: 5 pages, 5 eps figure, REVTe

Enhancement of πA→ππA\pi A \to \pi\pi A Threshold Cross Sections by In-Medium ππ\pi\pi Final State Interactions

We address the problem of pion production in low energy $\pi$-nucleus collisions. For the production mechanism we assume a simple model consisting of a coherent sum of single pion exchange and the excitation---followed by the decay into two pions and a nucleon---of the $N^*(1440)$ resonance. The production amplitude is modified by the final state interaction between the pions calculated using the chirally improved J\"ulich meson exchange model including the polarization of the nuclear medium by the pions. The model reproduces well the experimentally observed $\pi A \to \pi\pi A$ cross sections, especially the enhancement with increasing $A$ of the $\pi^+\pi^-$ mass distribution in the threshold region.Comment: 5 pages RevTeX, 3-eps figure

Spectral functions in the sigma-channel near the critical end point

Spectral functions in the $\sigma$-channel are investigated near the chiral critical end point (CEP), that is, the point where the chiral phase transition ceases to be first-ordered in the $(\mu,T)$-plane of the QCD phase diagram. At that point the $\sigma$ meson becomes massless in spite of explicit breaking of the chiral symmetry. It is expected that experimental signatures peculiar to CEP can be observed through spectral changes in the presence of abnormally light $\sigma$ mesons. As a candidate, the invariant-mass spectrum for diphoton emission is estimated with the chiral quark model incorporated. The results show the characteristic shape with a peak in the low energy region, which may serve as a signal for CEP. However, we find that the diphoton multiplicity is highly suppressed by infrared behaviors of the $\sigma$ meson. Experimentally, in such a low energy region below the threshold of two pions, photons from $\pi^0\to2\gamma$ are major sources of the background for the signal.Comment: 12 pages, 8 figures, 1 figure replaced, minor modification

Surface and volume effects in the photoabsorption of nuclei

Recent experimental results for meson photoproduction from nuclei obtained with TAPS at MAMI are analyzed in view of the suppression of the second nucleon resonance region in total photoabsorption. The cross sections can be split into a component from the low density surface region of nuclei and a component which scales more like the nuclear volume. The energy dependence of the surface component is similar to the deuteron cross section, it shows a clear signal for the second resonance peak assigned to the excitation of the P11(1440), D13(1520), and S11(1535). The volume component behaves differently, it is lacking the second resonance peak and shows an enhancement at intermediate photon energies.Comment: accepted for publication in Eur. J. Phys.

Recent progress on the chiral unitary approach to meson meson and meson baryon interactions

We report on recent progress on the chiral unitary approach, analogous to the effective range expansion in Quantum Mechanics, which is shown to have a much larger convergence radius than ordinary chiral perturbation theory, allowing one to reproduce data for meson meson interaction up to 1.2 GeV. Applications to physical processes so far unsuited for a standard chiral perturbative approach are presented. Results for the extension of these ideas to the meson baryon sector are discussed, together with applications to kaons in a nuclear medium and $K^-$ atoms.Comment: Contribution to the KEK Tanashi Symposium on Physics of Hadrons and Nuclei, Tokyo, December 1998, 10 pages, 3 postscript figures. To be published as a special issue of Nuclear Physics

In-medium modifications of the ππ\pi\pi interaction in photon-induced reactions

Differential cross sections of the reactions $(\gamma,\pi^\circ\pi^\circ)$ and $(\gamma,\pi^\circ\pi^++\pi^\circ\pi^-)$ have been measured for several nuclei ($^1$H,$^{12}$C, and $^{\rm nat}$Pb) at an incident-photon energy of $E_{\gamma}$=400-460 MeV at the tagged-photon facility at MAMI-B using the TAPS spectrometer. A significant nuclear-mass dependence of the $\pi\pi$ invariant-mass distribution is found in the $\pi^\circ\pi^\circ$ channel. This dependence is not observed in the $\pi^\circ\pi^{+/-}$ channel and is consistent with an in-medium modification of the $\pi\pi$ interaction in the $I$=$J$=0 channel. The data are compared to $\pi$-induced measurements and to calculations within a chiral-unitary approach

Medium Modification of The Pion-Pion Interaction at Finite Density

We discuss medium modifications of the unitarized pion-pion interaction in the nuclear medium. We incorporate both the effects of chiral symmetry restoration and the influence of collective nuclear pionic modes originating from the p-wave coupling of the pion to delta-hole configurations. We show in particular that the dropping of the sigma meson mass significantly enhances the low energy structure created by the in-medium collective pionic modes.Comment: 26 pages, 7 figures included, Latex fil

Polarization Properties of Low Energy Amplitude for πN→ππN\pi N \to \pi \pi N Reaction

The theoretical study of cross sections for polarized--target measurements of $\pi N \to \pi \pi N$ reactions gives evidence that the interplay between the strong contribution from OPE mechanism and the one from isobar exchanges, which is equally strong within isobar half--widths energy region, must result in nontrivial polarization phenomena. The Monte--Carlo simulations for asymmetries in $\pi^{-} p^{\uparrow} \to \pi^{-} \pi^{+} n$ reaction at $P_{Lab} = 360$~MeV/c with the use of theoretical amplitudes found as solutions for unpolarized data at $P_{Lab} < 500$~MeV/c provide confirmations for significant effect. The effect is capable to discriminate between the OPE and isobar exchanges and it is sensitive to the OPE parameters in question. This leads to the conclusion that the decisive $\pi N \to \pi \pi N$ analysis, aiming at determination of $\pi \pi$--scattering lengths, must combine both unpolarized data and polarization information. The appropriate measurements are shown to be feasible at the already existing CHAOS spectrometer.Comment: 24 pages, Latex, 6 Postscript figures, uses epsf.st