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Meson-nucleon scattering and vector mesons in nuclear matter

Meson-nucleon scattering and vector mesons in nuclear matter
Meson-nucleon scattering and vector mesons in nuclear matter

a r X i v :n u c l -t h /9808071v 1 27 A u g 1998

(1)

Meson-nucleon scattering and vector mesons

in nuclear matter ?

Bengt Friman

Gesellschaft f¨u r Schwerionenforschung (GSI)

D-64220Darmstadt,Germany

&

Institut f¨u r Kernphysik,TU Darmstadt

D-64289Darmstadt,Germany

(Received February 9,2008)

The properties of vector mesons in nuclear matter are discussed.I examine the constraints imposed by elementary processes on the widths of ρand ωmesons in nuclear matter.Furthermore,results for the ρ-and ω-nucleon scattering amplitudes obtained by ?tting meson-nucleon scattering data in a coupled-channel approach are presented.

1.Introduction

The electromagnetic decay of the vector mesons into e +e ?and μ+μ?pairs makes them particularly well suited for exploring the conditions in dense and hot matter in nuclear collisions.The lepton pairs provide virtually undistorted information on the mass distribution of the vector mesons in the medium.

The lepton-pair spectrum in nucleus-nucleus collisions at SPS energies exhibits a low-mass enhancement compared to proton-proton and proton-nucleus collisions [2].A quantitative interpretation of the lepton-pair data can be obtained within a scenario,where the e?ective vector-meson masses are reduced in a hadronic environment [3,4,5,6].On the other hand,attempts to interpret the low-mass enhancement of lepton pairs in terms of many-body e?ects also yield good agreement with the data [7,8].In these calculations the broadening of the ρmeson in nuclear matter due to the interactions of its pion cloud with the medium [9,10,11,12]and the momentum dependence of the ρ-meson self energy due to the coupling with baryon-resonance–nucleon-hole states [13,14]are taken into

account.

2proc printed on February9,2008

Through the low-density theorem hadron-nucleon scattering data can be used to determine the self-energies of hadrons in nuclear matter at low densities.In this talk I discuss the the constraints on the imaginary part of the vector-meson self energy in nuclear matter that can be derived from elementary reactions,and present results of a coupled channel calculation of meson-nucleon scattering.The latter provides a model for the vector-meson–nucleon scattering amplitude.

2.Constraints from elementary processes

The low-density theorem states that the self energy of e.g.a vector meson V in nuclear matter is given by[15]

ΣV(ρN)=?4π(1+

m V

k2πImˉf(π?p)

ωn→ωn

(θ=0),(2)

whereˉf denotes the spin-averaged scattering amplitude.Close to theωn threshold,the scattering amplitude can be expanded in powers of the rel-ative momentum in theωn channel qω.An excellent?t to the data from threshold up to q=120MeV/c2is obtained with Imˉf(π?p)

ωn→ωn=a+bq2ω+cq4ω, where a=0.013fm,b=0.10fm3and c=?0.08fm5(see Fig.1).The co-e?cient a is the imaginary part of the scattering length.

The corresponding contribution of theπ-nucleon channel to the width of theωmeson at rest in nuclear matter can now be obtained by using the

proc printed on February9,20083

Fig.1.Theπ

amplitude

low-density

ω2

4proc printed on February9,2008

Fig.2.The line shows the best ?t,while the[22]. amplitude energy of a vector-meson

Since we close to threshold,it is su?cient to consider only s-wave scattering in theρN andωN channels.This implies that in theπN andπ?channels we need only s-and d-waves.In particular,we consider the S11,S31,D13and D33 partial waves ofπN scattering.Furthermore,we consider the pion-induced production ofη,ωandρmesons o?nucleons.In order to learn something about the momentum dependence of the vector-meson self energy,vector-meson–nucleon scattering also in higher partial waves would have to be considered.

In accordance with the approach outlined above only data in the relevant kinematical range will be used in the analysis.The threshold for vector-

proc printed on February9,20085 Fig.3.The points are from

ref.[18],as

meson

with 4-point the reader is referred to ref.[21].In Fig.2our?t to theπN scattering data is illustrated by the D13channel.In the remaining channels the quality of the?t is in general better.

Furthermore,in Fig.3the cross section for the reactionπ?p→ρ0n is shown.The bumps at s1/2below1.6GeV are due to the coupling to res-onances below the threshold,like the N?(1520).This indicates that these resonances may play an important role in theρ-nucleon dynamics,in agree-ment with the results of Manley and Saleski[20].However,the strength of the coupling is uncetrain,due to the ambiguity in theρ-production cross section close to threshold mentioned above.We?nd that also theωmeson couples strongly to these resonances.

The pion-inducedη-production cross section is well described up to s1/2?1.65GeV.At higher energies presumably higher partial waves,not included in our model,become important.Similarly,the pion-induced pro-duction ofωmesons is reasonably well represented close to threshold,al-though the strong energy dependence of the amplitude shown in Fig.1is not reproduced by the model.This may be due to the coupling to channels not included at present,like the K?Σchannel.

The resultingρ-andω-nucleon scattering amplitudes are shown in Fig.4. Theρ?N andω?N scattering lengths are(-0.2+0.7i)fm and(-0.5+0.1i) fm respectively.To lowest order in the density,this corresponds to the following in-medium modi?cations of masses and widths at nuclear matter density:?mρ?20MeV,?mω?50MeV,?Γρ?140MeV and?Γω?20

6proc printed on February9,2008

Fig.4.The over spin and isospin.

MeV.resonances below of the amplitudes,will be split into a meson a resonance-hole like mode,which is pushed down in energy.The downward shift of vector-meson strength would contribute to the low-mass enhancement in the lepton-pair spectra.Thus,our results support the dynamical scenario discussed in ref.[23].

Acknowledgments

I thank M.Lutz and G.Wolf for valuable discussions.I am grateful to W.Florkowski and M.Nowak for their warm hospitality during my stay in Cracow and I acknowledge the partial support by the Polish Government

proc printed on February9,20087 Project(KBN)grant2P03B00814as well as by the Institute of Nuclear Physics in Cracow.

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