Phi meson spectral moments and QCD condensates in nuclear matter

Abstract

A detailed analysis of the lowest two moments of the φ meson spectral function in vacuum and nuclear matter is performed. The consistency is examined between the constraints derived from finite energy QCD sum rules and the spectra computed within an improved vector dominance model, incorporating the coupling of kaonic degrees of freedom with the bare φ meson. In the vacuum, recent accurate measurements of the e + e − → K + K − cross section allow us to determine the spectral function with high precision. In nuclear matter, the modification of the spectral function can be described by the interactions of the kaons from φ → KK with the surrounding nuclear medium. This leads primarily to a strong broadening and an asymmetric deformation of the φ meson peak structure. We confirm that, both in vacuum and nuclear matter, the zeroth and first moments of the corresponding spectral functions satisfy the requirements of the finite energy sum rules to a remarkable degree of accuracy. Limits on the strangeness sigma term of the nucleon are examined in this context. Applying our results to the second moment of the spectrum, we furthermore discuss constraints on four-quark condensates and the validity of the commonly used ground state saturation approximation.

Recent progress in QCD condensate evaluations and sum rules

“…The proposed estimates range from close to 1 [81] to 2 ∼ 3 [18] and even up to ∼ 6 [15]. For the case of s quarks, a value of ∼ 7 was reported from an analysis of finite energy sum rules in the φ meson channel [112,113]. Condensates with mass dimensions larger than 6 can play an important role in sum rules derived from interpolating fields with three or more quarks, where the convergence of the OPE is usually slower.…”

“…[243] for the ρ meson, was discussed for the φ meson spectral function in Refs. [112,113]. In these works, the importance and usefulness of spectral moments was stressed, which have been discussed in the QCDSR literature under the name of finite energy sum rules.…”

The ϕ Meson in Nuclear Matter and the Strangeness Content of the Nucleon

“…(8) and replacing the full ρ(s) by its perturbative form above a certain threshold s 0 . Leaving the details of the derivation to [38,39], we here only give the final form of the FESR in the ϕ meson channel:…”

“…In this section we describe the findings of [38,39]. In these works, we have first constructed the ϕ meson spectral function in an effective field theory approach based on hadronic degrees of freedom.…”

“…A brief account of the published works [7,38,39] will be given and the potential ramifications for the E16 experiment at J-PARC will be examined.…”