Confronting electron-positron annihilation into hadrons with QCD: an operator product expansion analysis

Abstract

Experimental data on the total cross section of e + e − annihilation into hadrons are confronted with QCD and the operator product expansion using finite energy sum rules. Specifically, the power corrections in the operator product expansion, i.e. the vacuum condensates, of dimension d = 2, 4 and 6 are determined using recent isospin I = 0 + 1 data sets. Reasonably stable results are obtained which are compatible within errors with values from τ -decay. However, the rather large data uncertainties, together with the current value of the strong coupling constant, lead to very large errors in the condensates. It also appears that the separation into isovector and isoscalar pieces introduces additional uncertainties and errors. In contrast, the high precision τ -decay data of the ALEPH collaboration in the vector channel allows for a more precise determination of the condensates. This is in spite of QCD asymptotics not quite been reached at the end of the τ spectrum. We point out that isospin violation is negligible in the integrated cross sections, unlike the case of individual channels.

Search for short strings ine+e−-annihilation

“…C 2 has negative sign and is compatible with zero only at 3 σ-level. At 1 σ-level: C 2 = −0.086 ± 0.050 GeV 2 , α s /π GG = 0.025 ± 0.012 GeV 4 .…”

“…The problem of the existence of the operator with dimension 2, whose contribution to QCD sum rules [1] is proportional to 1/Q 2 , and search for relevant OPE corrections are performed already for quite a long time [2][3][4].…”

“…In Cornell potential [5] V(r) ≈ − 4α s (r) 3r + kr the term kr describes string potential (connected to the phenomenon of confinement) at short distances, leading 3 to the correction ∼ k/Q 2 . In paper [3] the correlation between short strings and perturbation theory order was established 4 . The contribution of the operator with dimension 2 to the e + e − data was studied later [4,7] and it was found to be compatible to zero with large errors.…”

“…In paper [3] the correlation between short strings and perturbation theory order was established 4 . The contribution of the operator with dimension 2 to the e + e − data was studied later [4,7] and it was found to be compatible to zero with large errors.…”

Strange quark mass from sum rules with improved perturbative QCD convergence

“…Information on the the gluon condensate, and the higher dimensional condensates has been obtained from analyses of τ -decay [12] and e − e + annihilation into hadrons [13]. The quark condensates have been determined from the Gell-Mann-Oakes-Renner relation, including its corrections [14].…”