The property of a rho meson in dense nuclear matter is studied using the +CD sum rule. The spectral function appearing on the hadronic side of the sum rule is evaluated in the vector dominance model that takes into account the interaction between the rho meson and the pion. Including pion modification by the delta-hole polarization in the nuclear medium, we find that as the nuclear density increases the rho meson peak in the spectral function shifts to smaller invariant masses and its width

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... mes smaller. We discuss the possibility of studying the rho meson property in dense matter via the dilepton invariant mass spectrum from heavy-ion collisions. PACS number(s): 25.75.+r, 14.40.Cs, 12.40.Vv We have recently studied the rho meson property in nuclear medium in the vector dominance model (VDM) [1,2]. Including the coupling of the rho meson to the pion, which is further modified by the delta-hole polarization of the medium, we Bnd that with increasing nuclear density the position of the rho meson peak in the spectral function moves to larger invariant masses and its width increases [3] . Similar conclusions have also been obtained by Hermann et al. [4] . In Ref. [3], we have further found that the in-medium rho meson mass is, however, reduced if the bare rho meson mass in the model is assumed to decrease in the medium according to the scaling Ansa, tz of Brown and Rho [5] . We have thus concluded that the mean-Beld effect, parametrized by the scaling mass in Ref. [3], is more important than the loop corrections calculated by the UDM. A more consistent way to incorporate the mean-field effect is through the @CD sum rule. In the @CD sum rule [6], the spectral function appearing in the dispersion relation for the current-current correlation function is usually taken to be a delta function plus a continuum. According to Hatsuda and I ee [7], the rho meson mass in the medium determined from the @CD sum rule decreases with increasing density as a result of the partial restoration of chiral symmetry in dense matter. To include loop corrections in the hadronic side, one can use I the spectral function from the UDM but treat the bare rho meson mass as a parameter to be determined from the @CD sum rule. In terms of quarks, the current for a rho meson is given by (2) P ImII(s) ReII(Q ) =ds + subtractions. jr + 2 (3) For large Euclidean four-momenta, Q2 (=q s)~oo, the real part can be evaluated perturbatively by the operator product expansion [8]. Including operators up to dimension 6 and twist 2, we have 7p 7p (1) 2 Its correlation function in the medium n~(q) = i f e*' (rJ"(z) J (0))pd'T, where (. . ) z denotes the expectation value in the medium, can be expressed in terms of the transverse and longitudinal parts. At zero momentum, g = 0, the two are, however, related and only the longitudinal correlation function II is needed. The real and imaginary parts of the correlation function are related by the dispersion relation, 2 ;((q~, »A q)(q~"»A q))~-) ((qp"A q) (q'p" A q')) p q'=u, d 2I0 Q~&~~2 + /Z I W1D~2~( +~&~2 0~3~4 X /P I~1D~2D~3D~4 8ja a o a q'=n, d q =tt)8 (4) In the above, n is the @CD coupling constant, Qo is an arbitrary scale parameter, and D"= o)"-igA"A /2 with A the SU(3)-color matrices and A the gluon field. Both the light quark masses and their condensates are taken to be the same, i.e. , mq -m = mg and (qq)~= (uu)~= (dd)~. The last two terms in the above equation are the derivative condensates from the nonscalar operators as a result of the breaking of I orentz invariance in the medium [7, 9] . The symmetrization and traceless operator is denoted by S.