QCD sum rule analysis of the mixed-isospin vector current correlator reexamined

Abstract

The mixed-isospin vector current correlator, 0|T (V ρ µ V ω ν )|0 is evaluated using both QCD sum rules and Chiral Perturbation Theory (ChPT) to one-loop order. The sum rule treatment is a modification of previous analyses necessitated by the observation that those analyses produce forms of the correlator that fail to be dominated, near q 2 = 0, by the most nearby singularities.Inclusion of contributions associated with the φ meson rectify this problem.The resulting sum rule fit provides evidence for a significant direct ω → ππ coupling contribution in e + e − → π + π − . It is also pointed out that results for the q 2 -dependence of the correlator cannot be used to provide information about the (off-shell) q 2 -dependence of the off-diagonal element of the vector meson propagator unless a very specific choice of interpolating fields for the vector mesons is made. The results for the value of the correlator near q 2 = 0 in ChPT are shown to be more than an order of magnitude smaller than those extracted from the sum rule analysis and the reasons why this suggests slow 1 convergence of the chiral series for the correlator given.

Vector meson dominance and ρ-ω mixing

“…It has recently been asserted [16] that a direct ω → 2π coupling is not only necessary on general principles, but that a significant coupling is supported by a theoretical QCD sum rule analysis of a isospinbreaking correlator of vector currents. This assertion has prompted reanalyses of the data on e + e − → π + π − [17,18], and the modeling of this putative contact ω → 2π term in two quark based models of ρ • − ω mixing [19,20].…”

“…We re-examine, in the light of current particle data [13], the numerical accuracy of vector meson dominance (VMD) [14], and then use VMD to link measured decays of the I = 1 scalar meson a 0 to the universality of ∆I = 1 meson transitions recently established [15]. We close with a discussion of the implications of our results for recent conjectures about a direct ω → 2π coupling [16][17][18][19][20]; ie. a decay not based on ω → ρ → 2π, which is a G parity-violating ∆I = 1 transition.…”

Isospin-breaking effects in the extraction of isoscalar and isovector spectral functions frome+e−→hadrons

“…[22]) is necessarily incorrect, since off-shell Green functions are well-known to be altered by redefinitions of the hadronic fields and, as such, are not capable of being related to physical objects such as the mixed-isospin vector current correlator (an earlier claim by the present author, contained in Ref. [23], that the rescaled versions of the vector fields represented a possible field choice for the vector mesons is also incorrect). The only questions relevant to the use of the spectral function solution of Ref.…”

“…Based on this observation, it was realized, in Ref. [23], that, although f φ could be expected to be significantly smaller than f ρ or f ω (of order 6-7% if one makes an estimate based on the Particle Data Group evaluation of the deviation of vector meson mixing from ideal mixing [23]), the contribution of the φ to the actual sum rule need not be negligible. The sum rule was then re-analyzed, including the φ contribution, though still in the narrow width approximation.…”

“…We will, in fact, use the results of existing analyses [21][22][23][24] of the related correlator, Π ρω (q 2 ), defined by…”