QCD sum rules for Σ hyperons in nuclear matter

Abstract

Within the finite-density +CD sum-rule approach we investigate the self-energies of Z hyperons propagating in nuclear matter from a correlator of Z interpolating fields evaluated in the nuclear matter ground state. We find that the Lorentz vector self-energy of the Z is similar to the nucleon vector self-energy. The magnitude of Lorentz scalar self-energy of the Z is also close to the corresponding value for nucleon; however, this prediction is sensitive to the strangeness content of the nucleon and to the assumed density dependence of certain four-quark condensate. The scalar and vector self-energies tend to cancel, but not completely. The implications for the couplings of Z to the scalar and vector mesons in nuclear matter and for the Z spin-orbit force in a finite nucleus are discussed.PACS number(s): 24.85. +p, 21.65.+f, 21.80.+a, 11.55.Hx

QCD sum rules for Δ isobar in nuclear matter

“…The sum-rule calculations indicate that the self-energies of the Σ are close to the corresponding nucleon self-energies while the self-energies of the Λ are only about 1 3 of the nucleon self-energies. The sum-rule predictions for the baryon scalar self-energies are, however, sensitive to assumptions made about the density dependence of certain four-quark condensates [2,4,16,17]. In this brief report, we study the self-energies of the ∆ isobar in an infinite nuclear matter within finite-density QCD sum-rule approach.…”

“…In Refs. [16,17], the self-energies of the Λ and Σ hyperons are investigated within the same framework. The sum-rule calculations indicate that the self-energies of the Σ are close to the corresponding nucleon self-energies while the self-energies of the Λ are only about 1 3 of the nucleon self-energies.…”

“…[2,4,16,17]. To get a prediction for the ∆ mass, we apply the same procedure to the sum rules evaluated in the zero-density limit.…”

“…We follow Refs. [2,4,16,17] and assume a pole ansatz for the quasibaryon (higher-energy states are included in a continuum contribution), which, in the Rarita-Schwinger formalism [26], can be expressed as [20,25] …”

“…Since we want to focus on the positive-energy quasiparticle pole, we follow Refs. [2,4,16,17] and construct the sum rules that suppress the contributions from the region of the negative energy excitations:…”