QCD Sum Rules for Skeptics

Abstract

A new Monte-Carlo based uncertainty analysis is introduced to quantitatively determine the predictive ability of QCD sum rules. A comprehensive analysis of ground state rho-meson and nucleon spectral properties is performed. Many of the findings contradict the conventional wisdom of both practitioners and skeptics alike. Associations between the phenomenological fit parameters are particularly interesting as they reveal how the sum rules resolve the spectral properties. The use of derivative sum rules for the determination of rho-meson spectral properties is shown to be a very unfavorable approach. Most prior nucleon sum rule analyses are based on a sum rule which is found to be invalid; the results are suspect, and should be reevaluated. The ``Ioffe formula'', argued by many to qualitatively encapsulate a description of the nucleon mass in terms of the chiral symmetry breaking order parameter is misleading at best. QCD Sum Rules are found to be self-consistent without contributions from direct instantons. This implies that instanton effects are adequately accounted for in the nonperturbative vacuum condensates. This in-depth examination of QCD sum rule self consistency paints a favorable picture for further quantitative refinements of the QCD sum rule approach.Comment: 70 page RevTeX Manuscript with 40 embedded figures. Revised manuscript accepted for publication. Recent estimates of QCD vacuum condensates are used in the analysis. This and related papers may also be obtained from http://www.phys.washington.edu/~derek/Publications.htm

Pion form factor and quark mass evolution in a light-front quark model

“…The Ball-Chiu ansatz was used for the dressed quarkphoton vertex. We were also able to calculate the quark condensate as − qq =(0.3 GeV) 3 [6], which is quite compariable with the value employed in contemporary phenomenological studies: (0.236 GeV) 3 [9]. This shows the PCAC relation is reasonably well satisfied in LFQM with our mass evolution function.…”

The impact of chirally odd condensates on the rho meson

“…One still seems to have at least a connection between chiral restoration -drop of two-and fourquark condensates -and in-medium changes, no matter whether it is a mass shift or a broadening or a more complicated in-medium modification [13,34]. However, also point 2 and as its consequence point 4 are questionable: Whether the four-quark condensates factorize at least in vacuum is discussed since the invention of QCD sum rules, see, e.g., [23,24,[35][36][37][38][39][40][41] and for in-medium situations also [27,[42][43][44][45][46]. Raising doubts on point 2 immediately questions point 4 and in that way the seemingly clear connection between chiral restoration and in-medium changes gets lost.…”

New QCD sum rules for nucleons in nuclear matter

“…The three vacuum sum rules obtained from the correlator Π 12 µν (q) at ρ N = 0 have been studied extensively in Refs. [15,16]. To obtain the finite-density sum rules from this mixed correlator, we follow the procedures established in Ref.…”

“…This behavior arises naturally in the factorized form where the density dependence of the gluon condensate is estimated to be a 7% effect. There are many other dimension-seven operators; their contributions are assumed to be relatively small [16] and are neglected. To analyze the sum rules, we follow the techniques introduced in Ref.…”