Violation of quark-hadron duality and spectral chiral moments in QCD

Abstract

We analyze the spectral moments of the V-A two-point correlation function. Using all known short-distance constraints and the most recent experimental data from tau decays, we determine the lowest spectral moments, trying to assess the uncertainties associated with the so-called violations of quark-hadron duality. We have generated a large number of "acceptable" spectral functions, satisfying all conditions, and have used them to extract the wanted hadronic parameters through a careful statistical analysis. We obtain accurate values for the χPT couplings L 10 and C 87 , and a realistic determination of the dimension six and eight contributions in the operator product expansion, O 6 = −5.4 + 3.6 − 1.6 ·10 −3 GeV 6 and O 8 = −8.9 + 12.6 − 7.4 ·10 −3 GeV 8 , showing that the duality-violation effects have been underestimated in previous literature.

Chiral sum rules and vacuum condensates from tau-lepton decay data

“…JHEP03 (2015)053 This result is in very good agreement with an early determination based on the original ALEPH data base [21],L 10 = −(6.43±0.08)×10 −3 , as well as with more recent results using more involved methods to deal with DV , e.g.L 10 = −(6.46 ± 0.15) × 10 −3 from [22,23], andL 10 = −(6.52 ± 0.14) × 10 −3 from [25]. It also agrees with lattice QCD determinations within their larger uncertainties [45,46].…”

“…The lack of evidence for DV in the separate V and A correlators at large s 0 was also demonstrated in [47], albeit with the old ALEPH data. These conclusions are in contrast with those following from specific models of DV [22,23,25]. 4) with the first two chiral condensates being O 6 and O 8 .…”

“…Instead, we interpret this good saturation as suggesting that our pinched kernels might have quenched any potential DV. However, this conclusion is not universally accepted [22,23,25]. Given the unavoidable need of specific models to account for the postulated DV, this issue remains currently an open problem.…”

“…We will demonstrate below that duality can be observed with the new ALEPH data for many sum rules. However, DV is a contentious issue relying on specific models [22,23,25], as discussed in more detail in section 3.…”

“…A key advantage of hadronic τ -decay data is that it determines both the vector and the axial-vector spectral functions. This feature allows to check the saturation of a variety of chiral sum rules [13,[19][20][21], as well as to determine the chiral correlator at zero momentum [5,[21][22][23][24][25][26][27], proportional to the counter term of the order O(p 4 ) Lagrangian of chiral perturbation theory (CHPT),L 10 . It also allows for a determination of the chiral condensates of dimension d = 6 and d = 8 [5,13,[21][22][23][24][25][26][27].…”