!LABORATOIRE ATlONAl

ATURNE 91191 Gif-sur-Yvene Cedex France

VECTOR MESON MASSES IN THE NUCLEAR MEDIUM

Gerald E. BROWN State University of New-York at Stony-Brook Department of , Stony-Brook, NY 11794, USA

Mannque RHO Service de Physique Théorique, CE de Saclay F-91191 Gif-sur-Yvette Cedex, France and Madeleine SOYEUR Laboratoire National Saturne, CE de Saclay F-91191 Gif-sur-Yvette Cedex, R-ance

To be published in A, Proceedings of the International Nuclear Physics Conference (Contributed Paper), Wiesbaden, 26th July - 1st August 1992 (Edited by R. Bock)

C-t^ft - LNS/Ph/92/21

I Centre National de la Recherche Scientifique OGQ Commissariat à l'Energie Atomique Vector meson masses in the nuclear medium* G.E. Brown", M. Rho6 and M. Soyeurc "State University of New-York at Stony-Brook, Department of Physics. Stony-Brook. NY 11794, USA 'Service de Physique Théorique, CE Saclay, F-91191 Gif-sur-Yvette Cedex. France laboratoire National Saturne, CE Saclay, F-91191 Gif-sur-Yvette Cedex. France

The idea that the vector meson masses (my = mp,TTIu1) decrease with increasing baryon density like the cube root of the quark condensate,

... mV [ {o |M| O)J has been suggested by Brown and Rho [I]. Here the star means that the quantity is evaluated at finite density. Up to linear order in the change in density /i. it can be shown [2,3] that, in the dilute gas approximation,

W (Q |gg| O)* - (0 \qq\ 0) = (m^ md) P = 4P , (2)

where Zln-Jv is the - sigma term [4],

E1TiV S 45 MeV1 (3)

and mu and mj the up and down quark masses. Detailed calculations of higher order effects within the formalism of the QCD sum rules [5,6] fail to find significant corrections to eqs. (1) and (2). Taking the value of - (220 MeV)3 for the vacuum condensate in free space, we find that, for p — po,

^ S 0.8, (4) Tn y where po is nuclear matter density. The close relation between vector meson masses and the structure of the QCD vacuum expressed by eq. (1) suggests that the p- and w-meson masses could be measurable order parameters for chiral symmetry restoration at finite baryon density [I].

* supported in part by U.S. Department of Energy under Grant n0 DE-FG02-SS ER 403S Using the vector dominance model, which states that virtual photons couple to nucléons through vector mesons, we have investigated the consequences of eq. (1) for the electromagnetic form factors of nucléons embedded in the nuclear medium [7]. We have calculated longitudinal and transverse responses of bound nucléons measured in (e, e'p) reactions on nuclei where a systematic quenching of the longitudinal cross section has been observed [S-IO]. The form factors are calculated using the schematic model of refs. [11] and [12] which is based on the two-phase (quark and meson) chiral picture of the nurloon and which approximately follows the way in which isoscalar and isovector operators fraction in the chiral hyperbag [13]. In this approach, isoscalar operators couple equally to quark and meson sectors, whereas isovector operators couple only to the meson cloud. The longitudinal response measures the charge density and the operator.

OL = \ + \n, (5)

is half isoscalar, half isovector. As my —• m*, according to eq. (1), the decrease in vector meson propagator brings about a decrease in the in-medium response [T]. This is easily seen in the vector dominance model in which the 7-ray turns into a vector meson with propagator

fco being neglected. The m\ in the numerator ensures the correct nucléon charge, which is measured at k —• 0. In medium, replacing my by my < my obviously causes a decrease in D(k). The transverse response is isovector and measures the current density. The operator is O =/^4 -Ti, (7) 2m N where s is the polarization of the virtual 7-ray and fly is the isovector moment.

W = 7>(»P ~/*n) = 2.353. (S)

For nuclear matter density, m^ —> m*N = 0.8 mjv and the decreased denominator in eq. (7) builds the transverse response up, in contrast to the longitudinal case. We now compare our calculations with experiment. We show in fig. 1 the q- dependencc of the (e,e'p) transverse and longitudinal cross sections in 10Ca divided by independent particle expectations [10]. The various theoretical curves for the lon- gitudinal response are obtained with different models for partitioning the nucléon into quark core and meson cloud [7]. We see that density dependent vector meson masses in the form factors produce part of the quenching of the longitudinal response. Because of the structure of the transverse operator discussed above, our model reproduces the observed behaviour of the transverse response. We show in figs. 2 and 3 the longitudinal and transverse responses measured in the 3He(e,e'p) and 4He(e,e'p) reactions [8,9] and calculated with free [14] and in-medium form factors using the q-dependent proscription of réf. 7. We find in this case that density-dependent vector meson masses can produce a quenching of the longitudinal response in very close agreement with the data while the transverse response is very little modified.

»°Ca (e. e'p)

L

,_su

T TRANSVERSE RESPONSE TSM

———.

^s—^-= SL_

Qo q (McV,'C)

300 «00 500 1 600 700 800

O> (Im 'I

Figure 1. The g-dependence of the transverse and longitudinal cross sections for a bound proton in 40Ca, divided by independent particle expectations [10] are shown. The theoretical curves (full, dashed and dot-dashed lines) include the effects of density dependent meson masses with different nucléon models [7].

S(p=90 MeV/c) ((GeV/c)"3sr ' 150 3He(e,e'p)2H Saclay

0 0 250 500 750 1000 q(MeV/c)

Figure 2. The g-dependence of the longitudinal (circles) and transverse (triangles) responses measured in 3He(e, e'p) reaction [S] is shown. The full and dashed curves are the longitudinal and transverse responses calculated with free form factors [14]. The dot-dashed and dotted lines show the effect of including density-dependent vector meson masses in the longitudinal and tranverse responses respectively [7]. It is interesting to note the density dependence of the quenching of the longitudinal response. The effect is of the order of ~ 30 % in 40Ca [10] . It is of ~ 20 % in 1He [9] and of ~ 12 % in 3He [S] at q~ 500 MeV/c. There is no effect in 2H [15]. This density dependence of the quenching of the longitudinal response is reproduced by our model. The (e, e'p) data analyzed in the vector dominance model are therefore compatible with the in-medium vector meson masses given by eq. (1). Due to the complications related to final state interactions, it is however not possible to draw more definite conclusions from our analysis.

S(p=90 MeV/c) ((GeV/c)\sr ') 150 He(e,e'p)3H Saclay

100

* . 50 J. M. L. (L) J. M. L. (T) 0 0 250 500 750 1000 q(McV/o

Figure 3. Same as fig. 2 for the 4He(e,e'p) reaction. The data are from ref. 9 and the theoretical curves from ref. 7. REFERENCES 1 G.E. Brown and M. Rho, Phys. Rev. Lett. 66 (1991) 2720. 2 E.G. Drukarev and E.M. Levin, Nucl. Phys. A511 (1990) 679. 3 T.D. Cohen, R.J. Furnstahl and D.K. Griegel, Phys. Rev. C45 (1992) ISSl. 4 J. Gasser, H. Leutwyler and M.E. Sainio, Phys. Lett. B253 (1991) 252. 5 T. Hatsuda and S.H. Lee, Phys. Rev. D, to be published. 6 T. Hatsuda, S.H. Lee and Y. Koike, in preparation. 7 M. Soyeur, G.E. Brown and M. Rho, Nucl. Phys. A, in press. 8 L. Lakehal-Ayat et al, to be published and ref. 15. 9 A. Magnon et al., Phys. Lett. B222 (1989) 352 ; J.-E. Ducret et al., to be published and ref. 15. 10 D. Reffay-Pikcroen et al., Phys. Rev. Lett. 60 (198S) 776. 11 G.E. Brown and M. Rho, Phys. Lett. B222 (19S9) 324. 12 G.E. Brown and M. Rho, Phys. Lett. B237 (1990) 3. 13 B.-Y. Park and M. Rho. Z. Phys. A331 (19S8) 151. 14 J.-M. Laget, Phys. Lett. B151 (19S5) 325. B199 (19S7) 493, Nucl. Phys. A497 (19S9) 391C. 15 J.-E. Ducret, contribution to this Conference. Laboratoire National Saturne 91191 G if-sur-Yvette Cedex France Tel: (1)69 08 22 03 Telefax : (1)69 08 29 70 Bifnet : SATURNE @ FRCPN 11 Télex : ENERG X 604641F