New QCD sum rules for nucleons in nuclear matter

Abstract

Two new QCD sum rules for nucleons in nuclear matter are obtained from a mixed correlator of spin-1/2 and spin-3/2 interpolating fields. These new sum rules, which are insensitive to the poorly known four-quark condensates, provide additional information on the nucleon scalar self-energy. These new sum rules are analyzed along with previous spin-1/2 interpolator-based sum rules which are also insensitive to the poorly known four-quark condensates. The analysis indicates consistency with the expectations of relativistic nuclear phenomenology at nuclear matter saturation density. However, a weaker density dependence near saturation is suggested. Using previous estimates of in-medium condensate uncertainties, we find M * = 0.64 +0.13 −0.09 GeV and Σ v = 0.29 +0.06 −0.10 GeV at nuclear matter saturation density.

Scaling behavior in soliton models

“…With c = −0.34 we obtain m * ρ /m ρ ≈ 0.78 and g * A /g A ≈ 0.80 at x = x E = 0.35 as suggested for nuclear density by QCD sum rules [3,4] and studies of the neutron beta-decay in heavy nuclei [24], respectively. Note that c = 0 is necessary for g A to vary.…”

“…Note that c = 0 is necessary for g A to vary. The numerical calculation yields M at x = x E , which is slightly smaller than the QCD sum rules estimate of 0.67 ± 0.05 [3,4]. The scaling behavior shown in figure 1 indicates thatB is closer to an invariant than B; the variation of the former is only about 5% compared to a 17% decrease of B at x E .…”

QCD sum rules and applications to nuclear physics

“…The key here is to find new, independent sum rules for the nucleon, taking advantage of interpolating fields with both spin-1/2 and spin-3/2 parts. By considering a mixed correlator with Ioffe's current and the spin-3/2-spin-1/2 current, spin-1/2 intermediate states (including the nucleon) are still projected, but one generates additional sum rules for M * N that are independent of the problematic four-quark condensates [104,153]. This sum-rule analysis should provide a clean test of the density dependence of M * N .…”

From chiral Lagrangians to Landau-Fermi liquid theory of nuclear matter

“…In particular, the key information is available from the calculations of the masses of the ρ meson [5,6] and the nucleon [37,38] in medium. In their recent work, Jin and collaborators find (for ρ = ρ 0 ) [6,38] …”