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Register a new userSymmetry Tests in Photo-Pion Production
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A.M.Bernstein
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Small angle electron scattering with intense electron beams opens up the possibility of performing almost real photon induced reactions with thin, polarized hydrogen and few body targets, allowing for the detection of low energy charged particles.This promises to be much more effective than conventional photon tagging techniques. For photo-pion reactions some fundamental new possibilities include: tests of charge symmetry in the N-N system by measurement of the neutron-neutron scattering length $a_{nn}$ in the $gamma D rightarrow pi^{+} nn$ reaction; tests of isospin breaking due to the mass difference of the up and down quarks; measurements with polarized targets are sensitive to $pi$N phase shifts and will test the validity of the Fermi-Watson (final state interaction) theorem. All of these experiments will test the accuracy and energy region of validity of chiral effective theories.
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In the past two decades, pions created in the high density regions of heavy ion collisions have been predicted to be sensitive at high densities to the symmetry energy term in the nuclear equation of state, a property that is key to our understanding of neutron stars. In a new experiment designed to study the symmetry energy, the multiplicities of negatively and positively charged pions have been measured with high accuracy for central $^{132}$Sn+$^{124}$Sn, $^{112}$Sn+$^{124}$Sn, and $^{108}$Sn+$^{112}$Sn collisions at $E/A=270~mathrm{MeV}$ with the S$pi$RIT Time Projection Chamber. While the uncertainties of individual pion multiplicities are measured to 4%, those of the charged pion multiplicity ratios are measured to 2%. We compare these data to predictions from seven major transport models. The calculations reproduce qualitatively the dependence of the multiplicities and their ratios on the total neutron to proton number in the colliding systems. However, the predictions of the transport models from different codes differ too much to allow extraction of reliable constraints on the symmetry energy from the data. This finding may explain previous contradictory conclusions on symmetry energy constraints obtained from pion data in Au+Au system. These new results call for better understanding of the differences among transport codes, and new observables that are more sensitive to the density dependence of the symmetry energy.
We summarize the pertinent experimental and theoretical developments in the field of pion photo- and electroproduction in the threshold region. We discuss which experiments and which calculations should be done/performed in the future.
New data on the production of single neutral pions in the $pdrightarrow{}^3textrm{He},pi^0$ reaction are presented. For fifteen proton beam momenta between $p_p=1.60;textrm{GeV}/c$ and $p_p=1.74;textrm{GeV}/c$, differential cross sections are determined over a large fraction of the backward hemisphere. Since the only previous systematic measurements of single-pion production at these energies were made in collinear kinematics, the present work constitutes a significant extension of the current knowledge on this reaction. Even this far above the production threshold, significant changes are found in the behaviour of the angular distributions over small intervals in beam momentum.
The $NDeltato NN$ cross sections, which take into account the $Delta$-mass dependence of M-matrix and momentum $p_{NDelta}$, are applied on the calculation of pion production within the framework of the UrQMD model. Our study shows that UrQMD calculations with the $Delta$-mass dependent $NDeltato NN$ cross sections enhance the pion multiplicities and decrease the $pi^-/pi^+$ ratios. By analyzing the time evolution of the pion production rate and the density in the overlapped region for Au+Au at the beam energy of 0.4A GeV, we find that the pion multiplicity probes the symmetry energy in the region of 1-2 times normal density. The process of pion production in the reaction is tracked including the loops of $NNleftrightarrow NDelta$ and $Deltaleftrightarrow Npi$, our calculations show that the sensitivity of $pi^-/pi^+$ to symmetry energy is weakened after 4-5 N-$Delta$-$pi$ loops in the pion production path, while the $pi^{-}/pi^{+}$ ratio in reactions at near threshold energies remains its sensitivity to the symmetry energy. By comparing the calculations to the FOPI data, we obtain a model dependent conclusion on the symmetry energy and the symmetry energy at two times normal density is $S(2rho_0)$=38-73 MeV within $1sigma$ uncertainties. Under the constraints of tidal deformability and maximum mass of neutron star, the symmetry energy at two times normal density is reduced to $48-58$ MeV and slope of symmetry energy $L=54-81$ MeV, and it is consistent with the constraints from ASY-EOS flow data.
Exclusive $pi^+pi^-p$ photo- and electroproduction data from CLAS have considerably extended the information on the spectrum and structure of nucleon resonances. The data from the $pi^+pi^-p$ and $Npi$ channels have provided results on the electrocouplings of most resonances in the mass region up to 1.8 GeV and at photon virtualities up to 5.0 GeV$^2$. The recent CLAS data on $pi^+pi^-p$ photoproduction have improved knowledge on the photocouplings of nucleon resonances in the mass range of 1.6 GeV $<$ $M_{N^*}$ $<$ 2.0 GeV and on their decays to the $pi Delta$ and $rho p$ final hadron states. For the first time, the electrocouplings of the $N(1440)1/2^+$ and $N(1520)3/2^-$ excited states have become available from $pi^+pi^-p$ data at 2.0 GeV$^2$ $<$ $Q^2$ $<$ 5.0 GeV$^2$. Analyses of the combined $pi^+pi^-p$ photo- and electroproduction data have revealed evidence for the candidate-state $N(1720)3/2^+$. The new results on the nucleon resonance spectrum, electroexcitation amplitudes from analysis of the CLAS $pi^+pi^-p$ photo- and electroproduction data, and their impact on the exploration of strong QCD are presented.
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