Finite-width QCD sum rules for ρ and ω mesons

Abstract

We present a combined analysis of the in-medium behavior of ρ and ω mesons within the Borel QCD sum rule taking into account finite widths. IntroductionThe experiments at the High-Acceptance Di-Electron Spectrometer HADES [1] are aimed at verifying predictions of the behavior of light vector mesons in nuclear matter. Due to the decay channel V → e + e − a measurement of the escaping di-electrons can reveal directly the properties of the parent mesons, V = ρ, ω, · · ·, since the interaction probability of the e ± with the ambient strongly interacting medium is small.In relativistic heavy-ion collisions temperature effects play an important role, which also cause a change of the properties of vector mesons. Indeed, the experiments of the CERES collaboration at the CERN-SPS [2] can only be explained by assuming strong medium effects, in particular for the ρ meson (cf. [3,4] and further references therein). This seems to be confirmed at higher beam energies, as delivered by the Relativistic Heavy Ion Collider, since the ρ meson, as measured via the π + π − decay channel, suffers some modification [5]. In contrast, in heavy-ion collisions at typical SIS18 energies, i.e., at beam energies around 1 AGeV, the in-medium behavior of vector mesons in compressed nuclear matter can be studied, where temperature effects are small and may be neglected. Complementary to heavy-ion collisions one can seek for in-medium modifications in reactions of hadronic projectiles [6] or real and virtual photons [7] at nuclei, as already at nuclear saturation density sizeable modifications of vector mesons are predicted.There exists a vastly extended literature on the in-medium modification of hadrons. We mention here only the Brown-Rho scaling hypothesis, according to which a mass shift of a vector meson is directly interrelated to a change of the chiral condensate [8], and the vector manifestation [9], the effective Lagrangian approach [10], purely hadronic approaches [11,12], and QCD sum rules [13,14,15,16]. QCD sum rules [17] follow the idea of duality (cf. [18]) by relating quantities expressed by partonic (quark and gluon) degrees of freedom with hadronic observables. We take here the attitude to assume that the partonic quantities are given and examine the QCD sum rule to elucidate the in-medium change of the ρ and ω meson on a common footing. The corresponding current operators, expressed by the interpolating quark field operators u and d have the form J ρ µ = 1 2 (ūγ µ u−dγ µ d) and J ω µ = 1 2 (ūγ µ u+dγ µ d), * Dedicated to the memory of O.P. Pavlenko

Publisher’s Note:ρ‐ωsplitting and mixing in nuclear matter [Phys. Rev. C70, 035207 (2004)]

“…In Fig. 1 we show the results obtained with the parameter set given in Appendix D. Since in [16,17,28,37] a strong effect of the density dependence of the four-quark condensate was found we show here results for various possibilities, parameterized by κ N introduced in Appendix A, eq. (87).…”

“…These figures show that the mixing effect in the pion formfactor as well as in the di-electron production rate is washed out due to the mass shifts of the vector mesons. But one has to keep in mind that global changes of vector mesons in matter like mass shift and width broadening turn out to be correlated in nuclear matter [32,33,37]. Taking into account such broadening effects needs further investigations.…”

“…Since we are interested in medium effects, we adjust the value of κ 0 to the vacuum masses, yielding κ 0 = 3 both for ρ and ω, and study the impact of the unknown parameter κ N . As stressed in [16,37], only a comparison with experimental data can pin down κ N . For treating the ρ − ω mixing we also need…”

Medium modifications of theρmeson in nuclear photoproduction

“…medium are at most a factor of 2-3. On the contrary, for ω and φ, more than a factor of 10 broadening was extracted and/or predicted [11,[33][34][35][36][37][38], which leads to much stronger effects in the transparency ratio. For completeness, we also investigated different components in our model calculation.…”

Medium Modifications of the Rho Meson in Nuclear Photoproduction

“…Again, the reason for the apparently weaker effect for the ρ is its large vacuum width of ∼140 MeV, relative to which changes in the medium are at most a factor of 2-3. On the contrary, for the ω and φ more than a factor of 10 broadening was extracted and/or predicted [11,[33][34][35][36][37][38], which leads to much stronger effects in the transparency ratio. For completeness, we also investigated different components in our model calculation.…”