Precision Tau Physics

We review the status of the coupling constants of chiral Lagrangians in the meson sector, the so-called low-energy constants (LECs). We emphasize the chiral SU(2) and SU(3) Lagrangians for the strong interactions of light mesons and discuss the theoretical and experimental input for determining the corresponding LECs. In the two-flavor sector, we review the knowledge of the LECs from both continuum fits and lattice QCD analyses. For chiral SU(3), next-to-next-to-leading-order (NNLO) effects play a much greater role. Our main new results are fits of the LECs Li at both next-to-leading order (NLO) and NNLO, making extensive use of the available knowledge of NNLO LECs. We compare our results with available lattice determinations. We then discuss resonance saturation of LECs and the convergence of chiral SU(3) to NNLO. Finally, we review the status of predictions for the LECs of chiral Lagrangians with dynamical photons and leptons.

/pdf/mesonic-low-energy-constants-m6v8v0as27.pdf

Mesonic Low-Energy Constants

With the advent of the LHC, we will be able to probe New Physics (NP) up to energy scales almost one order of magnitude larger than it has been possible with present accelerator facilities. While direct detection of new particles will be the main avenue to establish the presence of NP at the LHC, indirect searches will provide precious complementary information, since most probably it will not be possible to measure the full spectrum of new particles and their couplings through direct production. In particular, precision measurements and computations in the realm of flavour physics are expected to play a key role in constraining the unknown parameters of the Lagrangian of any NP model emerging from direct searches at the LHC. The aim of Working Group 2 was twofold: on one hand, to provide a coherent, up-to-date picture of the status of flavour physics before the start of the LHC; on the other hand, to initiate activities on the path towards integrating information on NP from high-pT and flavour data.

B, D and K decays

QCD-corrected spin analysing power of jets in decays of polarized top quarks

The next to leading order chiral corrections to the SU(2) ×SU(2) Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, δ
 π
 , the value δ
 π
 = (6.2 ± 1.6)%. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate $ \left\langle {0\left| {\bar uu} \right|0} \right\rangle \simeq \left\langle {0\left| {\bar dd} \right|0} \right\rangle \equiv {\left. {\left\langle {0\left| {\bar qq} \right|0} \right\rangle } \right|_{2\;{\text{GeV}}}} = {\left( { - 267 \pm {\text{MeV}}} \right)^3} $
 . As a byproduct, the chiral perturbation theory (unphysical) low energy constant H
 2
 r
 is predicted to be H
 2
 r
 (ν
 χ
 = M
 ρ
 ) = −(5.1 ± 1.8) × 10−3, or H
 2
 r
 (ν
 χ
 = M
 η
 ) = −(5.7 ± 2.0) × 10−3.

/pdf/chiral-corrections-to-the-su-2-su-2-gell-mann-oakes-renner-1254i4dupa.pdf

Chiral corrections to the SU(2) × SU(2) Gell-Mann-Oakes-Renner relation

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: 6(2.6 GeV2) = −(0.00226±0.00055) GeV6 , and 8(2.6 GeV2) = −(0.0054±0.0033) GeV8 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: (0) = −4 10 = 0.02579±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.

Chiral condensates from tau decay: a critical reappraisal

Using special linear combinations of finite energy sum rules which minimize the contribution of the unknown continuum spectral function, we compute the decay constants of the pseudoscalar mesons B and Bs. In the computation, we employ the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running bottom quark mass. The sum rules show remarkable stability over a wide range of the upper limit of the finite energy integration. We obtain the following results for the pseudoscalar decay constants: fB = 178±14 MeV and fBs = 200±14 MeV. The results are somewhat lower than recent predictions based on Borel transform, lattice computations or HQET. Our sum rule approach of exploiting QCD quark hadron duality differs significantly from the usual ones, and we believe that the errors due to theoretical uncertainties are smaller.

https://iopscience.iop.org/article/10.1088/1126-6708/2005/11/014/pdf

D and D(S) decay constants from QCD duality at three loops

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.

Finite energy QCD sum rules with Legendre polynomial integration kernels are used to determine the heavy meson decay constant $f_{B_c}$, and revisit $f_B$ and $f_{B_s}$. Results exhibit excellent stability in a wide range of values of the integration radius in the complex squared energy plane, and of the order of the Legendre polynomial. Results are $f_{B_c} = 528 \pm 19$ MeV, $f_B = 186 \pm 14$ MeV, and $f_{B_s} = 222 \pm 12$ MeV.

/pdf/b-meson-decay-constants-f-b-c-f-b-s-and-f-b-from-qcd-sum-15tglpmmlr.pdf

J. Peñarrocha

Papers

Chiral corrections to the SU(2) × SU(2) Gell-Mann-Oakes-Renner relation

Chiral condensates from tau decay: a critical reappraisal

D and D(S) decay constants from QCD duality at three loops

Chiral condensates from tau decay: a critical reappraisal

$B$ Meson Decay Constants $f_{B_c}$, $f_{B_s}$ and $f_B$ from QCD Sum Rules