Nuclear Physics A545 (1992) 267c270cNorth-Holland, Amsterdam

p-mesons in dense nuclear matter

R7 . Herrmanns, B.L . Frimans'6 and W. Nörenberg s,b

b Institut für Kernphysik, TH Darmstadt, D-6100 Darmstadt, Germany

s Gesellschaft für Schwerionenforschung (GSI), D-6100 Darms}wdt, Germany

Lis~

AbstractThe properties of p-mesons in dense nuclear matter are studied in a model which satisfiesunitarity and current conservation . The coupling of the p-meson to two pious as well asthe strong mixing of pious and delta-nucleon-hole states in nuclear matter are included .The p-meson self energy in nuclear matter is evaluated with in-medium pion propagatorsand the corresponding vertex corrections required by current conservation . We find thatthe p-meson width grows drastically with increasing density while its mass remains almostunchanged .

Since lepton-hadron interactions are relatively weak, the observation of lepton pairsis a promising way to probe the conditions in the hot and compressed interaction zoneproduced in nucleus-nucleus collisions [1, ~] .

Gale and I{apusta [2] pointed out that ~r+~r- annihilation into dileptons may play animportant role in intermediate energy nuclear collisions . A basic input for the calculationof this process is the pion electromagnetic form factor. In vacuum this is well described bythe tractor-Dorreinance 1Vlodel (VDM) where the photon couples to the pion only througha p-meson [3]. However, since the p-meson is a two-pion resonance, large modificationsof its properties (and thus of the pion electromagnetic form factor) are expected due tothe strong pion-nucleon coupling . In this contribution we summarize the main resultsobtained in a detailed study of such effects [4] .

The basis of our approach is a Lagrangian for the electromagnetic field, the neutralp-meson and the charged ~r-mesons that is explicitly gauge invariant and leads to vectordvmi:âu~;c [~] . i~~''e caïcuiate the seïf-energy of the p-meson to second order in the p~r~rcoupling constant . The free parameters of the model are adjusted by fitting the positionof the resonance and the magnitude of the pion form factor at the peak. Both the shapeof the form factor and the isovector p-wave phase shifts for ~~ scattering are then wellreproduced .A model for the p-meson in medium is obtained by including the coupling to in-medium

pious in the p-meson self energy. Due to the strong ~rN® coupling, pious in nuclear

0375-9474/92/$05.00 O 1992 - Elscvier Science Publishers l~.V . All rights reserved .

e~~a,tter are mixed with longitudinal ®N°1 excitations . Since the p-meson couples to thefull isospin current, it couples to all particles that carry isospin in nuclear matter, i.e ., alsoto nucleons and ~'s and in particular to the ®N°1 component of the pion-like modes.~'l~us, the requirement that the p-meson couples to a conserved current introduces vertexcorrections to both the p~~ and pp~~r vertices . All such vertex corrections, which in thecase of the p~ra~-vertex are analogous to those considered by Korpa and Pratt (6] for the~ a~-vertex, are taken into account .

~ ~~e consider the pion self energy in an approximation which contains the most impor-tae~t features of pion propagation in nuclear matter . We include the coupling to ON°1states, but neglect the width of the ®-resonance . The short-range correations are approx-imately accounted for by introducing an effective ~rN® coupling constant . Finally, the~~ion self energy is evaluatAed in the » quasi-static» approximation, where only the lowestorder term in the density is retained .

It is important to include cell vertex corrections of the same order in the p-mesoncoupling, since there are rather delicate cancellations between different diagrams ; an in-consistent calculation may be afflicted with large errors.

In fig. 1 we show the resulting p-meson spectral function in vacuum as well as ini~~aclear matter at various densities. The huge enhancement around M = 2m,~, predictedby Cale and Ilapusta (?], is completely supressed by the corrections required by currentconser "~ation and unitarity.

err

nn et cal . I p-rues®ns in dense nuclear matter

0.0

5.0

;0.(3

fmnJ

F~ ig . 1 . Spectral function of the p-meson in vacuum (solid line) and in nuclear matter atsaturation density n = n® (dotted) and at n - 2no (dashed) and 3no (dash-dotted) .

At high densities we find a new structure around M = 3rrt,~, which corresponds tothe decay of the p-meson into a pion-like and a ON-1-like made. Both longitudinal andtransverse ON-1 modes contribute to this peak.We expect that the inclusion of the large O-width will smooth the peak into a relatively

broad maximum, while an improved treatment of the short-range correlations may leadto a moderate upward shift in energy.

Our study shows that the requirements of gauge invariance, current conservation andunitarity are essential for obtaining reasonable results on medium effects for the p-meson.We find, in contrast to early expectations, that dilepton spectra most probably do

not contain direct information on the pion dispersion relation in nuclear matter . On theother hand, the properties of the p-meson in the nuclear medium are strongly influencedby changes in the pion dispersion relation . We expect this to be observable in heavy-ioncollisions, in particular in the dilepton spectra [7] . However, in a quantitative analysis ofthese effects the width of the 0-resonance must be included.

REFERENCES

M. Herrmann et al. / p-mesons in dense nuclear matter

269c

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