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Register a new userChiral condensates from tau decay: a critical reappraisal
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Jose Bordes
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The saturation of QCD chiral sum rules is reanalyzed in view of the new and complete analysis of the ALEPH experimental data on the difference between vector and axial-vector correlators (V-A). Ordinary finite energy sum rules (FESR) exhibit poor saturation up to energies below the tau-lepton mass. A remarkable improvement is achieved by introducing pinched, as well as minimizing polynomial integral kernels. Both methods are used to determine the dimension d=6 and d=8 vacuum condensates in the Operator Product Expansion, with the results: {O}_{6}=-(0.00226 pm 0.00055) GeV^6, and O_8=-(0.0053 pm 0.0033) GeV^8 from pinched FESR, and compatible values from the minimizing polynomial FESR. Some higher dimensional condensates are also determined, although we argue against extending the analysis beyond dimension d = 8. The value of the finite remainder of the (V-A) correlator at zero momentum is also redetermined: Pi (0)= -4 bar{L}_{10}=0.02579 pm 0.00023. The stability and precision of the predictions are significantly improved compared to earlier calculations using the old ALEPH data. Finally, the role and limits of applicability of the Operator Product Expansion in this channel are clarified.
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We have used the latest data from the ALEPH Collaboration to extract values for QCD condensates up to dimension d=12 in the V-A channel and up to dimension d=8 in the V, A and V+A channels. Performing 2- and 3-parameter fits, we obtain new results for the correlations of condensates. The results are consistent among themselves and agree with most of the previous results found in the literature.
The QCD vacuum condensates in the Operator Product Expansion are extracted from the final ALEPH data on vector and axial-vector spectral functions from $tau$-decay. Weighted Finite Energy Sum Rules are employed in the framework of both Fixed Order and Contour Improved Perturbation Theory. An overall consistent picture satisfying chirality constraints can be achieved only for values of the QCD scale below some critical value $Lambdasimeq350 {MeV}$. For larger values of $Lambda$, perturbation theory overwhelms the power corrections. A strong correlation is then found between $Lambda$ and the resulting values of the condensates. Reasonable accuracy is obtained up to dimension $d=8$, beyond which no meaningful extraction is possible.
We show how it is possible to define and compute the potential between $q$ and $bar q$ external sources in the singlet and octet (adjoint) representation of the colour group.
The hadronic tau decay $tau^- to u_tau eta pi^- pi^0$ occurs through V-A weak current. In this decay mode, the vector current contribution is intrinsic parity violating and the axial current contribution is G parity violating. The latter contribution is suppressed due to tiny isospin breaking. We have computed both vector and axial vector form factors using a chiral Lagrangian with vector mesons including the effect of isospin breaking and intrinsic parity violation. A numerical result of the invariant mass distribution is shown and the structure of $rho$ resonance can be seen in the distribution with respect to $M_{pi^- pi^0}$.
An intrinsic parity violating hadronic tau lepton decay is investigated. $tau to pi pi eta u$ is the process in which the dominant contribution to the amplitude is due to the intrinsic parity violation. To predict the hadronic invariant mass spectra and to compare them with experimental data, we extend the chiral Lagrangian with vector mesons so that it incorporates the intrinsic parity violating terms and $phi$ and $eta^prime$ mesons. The coefficients of the intrinsic parity violating terms will be determined by fitting the branching fractions for $V^I rightarrow P gamma$, $V^I rightarrow 3 P$ and $P to V^I gamma $ where $V^I$ denotes vector mesons $1^-$ and $P$ denotes pseudo-scalar mesons $0^-$.
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