A. A. Almasy, K. Schilcher, H. Spiesberger
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.
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The possibility of detecting the S-wave of the decays tau -> 3 pi + nu(tau) in the threshold region is explored, with emphasis on the sensitivity to the size of the quark antiquark condensate <qq>.
We study a functional method to extract the V-A condensate of dimension 6 from a comparison of tau-decay data with the asymptotic space-like QCD prediction. Our result is in agreement within errors with that from conventional analyses based on finite energy sum rules.
The difference of tau partial decay widths into even and odd number of pions may be considered as another important constraint on the hadronic spectral function, in addition to four classic sum rules of current algebra. Within certain reasonable assumptions its value may be used to test the factorization hypothesis and estimate the contribution of dimension 6 condensates into the tau hadronic decay width.
The high-precision data from hadronic tau decays allows one to extract information on QCD condensates. Using the finalized ALEPH data, we obtain a more rigorous determination of the dimension 6 and 8 condensates for the V-A correlator. In particular, we find that the recent data fix a certain linear combination of these QCD condensates to a precision at the level of O(2%). Our approach relies on more general assumptions than alternative approaches based on finite energy sum rules.
The problem of determination of $α_{s}$ and the condensates from the moments of invariant mass distribution in the semileptonic tau decays is considered. It is investigated how the extracted values of alpha_s(m^{2}_{tau}) and the condensates are affected by the the renormalization scheme dependence of the next-to-next-to-leading order perturbative corrections to the spectral moments. A simplified approach is used, in which the nonperturbative contributions are approximated by the terms of dimension six in the SVZ expansion, which arise from the four-quark condensates. \\
The spectral function $ρ_{V-A}(s)$ is determined from ALEPH and OPAL data on hadronic tau decays using a neural network parametrization trained to retain the full experimental information on errors, their correlations and chiral sum rules: the DMO sum rule, the first and second Weinberg sum rules and the electromagnetic mass splitting of the pion sum rule. Nonperturbative QCD vacuum condensates can then be determined from finite energy sum rules. Our method minimizes all sources of theoretical uncertainty and bias producing an estimate of the condensates which is independent of the specific fi…
The possibility of detecting a Higgs boson through several production and decay channels is instrumental to the measurement of its couplings. In this paper we study the pp-> ttH(H-> tau tau) channel at the LHC, for the case of a scalar Higgs boson, and use the obtained results to improve on existing strategies toward a model independent determination of the Higgs boson couplings. The case of a scalar Higgs boson with mass below 140 GeV looks particularly promising.
The total tau hadronic width can be accurately calculated using analyticity and the operator product expansion. The result turns out to be very sensitive to the value of alpha_s(m_tau^2), providing a precise determination of the strong coupling constant. The theoretical description of this observable is updated, including the recently computed O(alpha_s^4) contributions. The experimental determination of alpha_s(m_tau^2) and its actual uncertainties are discussed.
We update the hadronic tau determination of |V_{us}|, showing that current strange branching fractions produce results 2-3 sigma lower than 3-family unitarity expectations. Issues related to the size of theoretical uncertainties and results from an alternate, mixed tau-electroproduction sum rule determination (which, by construction, produces a much smaller theoretical uncertainty), are also considered.
The tau anomalous magnetic moment (a_tau) and electric dipole moment (d_tau) have not yet been observed. The present bounds on their values are of order 10^-2 and 10^-17 e*cm, respectively. We propose to measure a_tau with a precision of O(10^-3) or better and improve the existing limits on d_tau using precise tau- -> l- nu_tau \bar{nu}_l gamma (l=e or mu) data from high-luminosity B factories. A detailed feasibility study of this method is underway.
We analyze the lowest spectral moments of the left-right two-point correlation function, using all known short-distance constraints and the recently updated ALEPH V-A spectral function from tau decays. This information is used to determine the low-energy couplings L10 and C87 of chiral perturbation theory and the lowest-dimensional contributions to the Operator Product Expansion of the left-right correlator. A detailed statistical analysis is implemented to assess the theoretical uncertainties, including violations of quark-hadron duality.
The QCD corrections to the moments of the invariant mass distribution in the semileptonic $τ$ decays are considered. The effect of the renormalization scheme dependence on the fitted values of alpha_s(m^2_tau) and the condensates is discussed, using a simplified approach where the nonperturbative contributions are approximated by the dimension six condensates. The fits in the vector and the axial-vector channel are investigated in the next-to-leading and the next-to-next-to-leading order. The next-to-next-to-leading order results are found to be relatively stable with respect to change of the …
The two highest precision determinations of alpha_s(M_Z^2), that based on the analysis of short-distance-sensitive lattice observables, and that based on an analysis of hadronic tau decay data, have, until very recently, given results which are not in good agreement. I review new versions of these analyses which bring the two determinations into excellent agreement, and discuss prospects for additional future improvements.
The QCD vacuum condensates in the Operator Product Expansion are extracted from the final ALEPH data on vector and axial-vector spectral functions from $τ$-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 $Λ\simeq350 {MeV}$. For larger values of $Λ$, perturbation theory overwhelms the power corrections. A strong correlation is then found between $Λ$ and the resulting values of…
In order to determine the fundamental MSSM parameters M_1, M_2, μand \tanβthe tau polarization from stau decays can be explored as a `bridge' between the gaugino/higgsino and the stau sector in particular in the high \tanβrange. Even in the case of high \tanβan accuracy of δ(\tanβ)\approx 5% with an simultanous determination of A_τ is possible without assuming a specific SUSY breaking scheme.
The determination of the numerical value for the strong coupling constant from tau decays in perturbative QCD is briefly described. Main emphasis is made on the use of the renormalization scheme invariance of the theory for reducing uncertainties related to truncation of the series in the strong coupling constant. The analysis of the convergence of the series is presented and the possibility of the asymptotic growth at the NNNLO is discussed.
The total $τ$ hadronic width can be accurately calculated using analyticity and the operator product expansion. The theoretical analysis of this observable is updated to include all available perturbative and non-perturbative corrections. The experimental determination of $α_s(M_τ^2)$ and its actual uncertainties are discussed.
We present a general analysis of SU(3) breaking effects in the semi-inclusive tau hadronic width. The recent ALEPH measurements of the inclusive Cabibbo--suppressed decay width of the tau and several moments of its invariant mass distribution are used to determine the value of the strange quark mass. We obtain, in the MS scheme, m_s(M_τ^2) = (119\pm 24) MeV to O(α_s^3), which corresponds to m_s (1 GeV^2) = (164 \pm 33) MeV, m_s(4 GeV^2) = (114\pm 23) MeV .
I review sum rule determinations of |V_us| employing hadronic tau decay data, taking into account recent HFAG updates of exclusive tau branching fractions and paying special attention to the impact of the slow convergence of the relevant integrated D=2 OPE series and the potential role of contributions of as-yet-unmeasured higher multiplicity modes to the strange inclusive spectral distribution. In addition to conventional flavor-breaking sum rule determinations, information obtainable from mixed tau-electroproduction sum rules having much reduced OPE uncertainties, and from sum rules based on…
The recent update of the strange spectral function and the moments of the invariant mass distribution by the OPAL collaboration from hadronic tau decay data are employed to determine |V_us| as well as m_s. Our result, |V_us|=0.2208\pm0.0034, is competitive to the standard extraction of |V_us| from K_e3 decays and to the new proposals to determine it. Furthermore, the error associated to our determination of |V_us| can be reduced in the future since it is dominated by the experimental uncertainty that will be eventually much improved by the B-factories hadronic tau data. Another improvement tha…
The decays tau -> 3 pi + nu(tau) are analyzed at one loop order in the framework of Generalized Chiral Perturbation Theory, in order to test the sensitivity to the size of spontaneous chiral symmetry breaking parameters, contained in the S-wave. The latter, due to a kinematical suppression, at threshold, of the P-wave, is relatively large enough to be detectable at high energy machines, through azimuthal left-right asymmetries. This quantity (for the pi- pi- pi+ mode), integrated from threshold to Q^2 = 0.35 GeV^2, varies from (17 +- 3) % in the standard case of large condensate up to (40 +- 5…
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 …
We revisit the determination of alpha_s(m_tau) using a fit to inclusive tau hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K_4 in the expansion of the Adler function, (2) new precision measurements from BABAR of e+e- annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on tau branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced…
The recent ALEPH measurements of the inclusive Cabibbo--suppressed decay width of the $τ$ and several moments of its invariant mass distribution are used to determine the value of the strange quark mass. We obtain, in the $\bar{\rm MS}$ scheme, $m_s(M_τ^2) = (119\pm 24)$ MeV, which corresponds to $ m_s(1 {\rm GeV}^2) = (164 \pm 33) {\rm MeV}, m_s(4 {\rm GeV}^2) = (114\pm 23) {\rm MeV} $.
The accurate determination of the strong coupling from tau decay data is briefly reviewed. The present phenomenological status is summarized.
The tau hadronic width provides a determination of the strong coupling constant alpha_s at low energies, since it can be related to a weighted integral of the Adler function in the complex energy plane. Using Operator Product Expansion, one sees that the sensitivity to alpha_s comes from the perturbative contribution, which can be obtained by integrating the perturbative expansion of the Adler function. Two different prescriptions proposed to perform this integral, called Fixed-Order Perturbation Theory and Contour-Improved Perturbation Theory (FOPT and CIPT), yield different results for the s…
We show a general form of neutrino mass matrix (M), whose matrix elements are denoted by M_{ij} (i.j=e, mu, tau) as flavor neutrino masses, that induces maximal CP violation as well as maximal atmospheric neutrino mixing. The masses of M_{mu mu}, M_{tau tau} and M_{mu tau}+sigma M_{ee} (sigma =\pm 1) turn out to be completely determined by M_{e mu} and M_{e tau} for given mixing angles. The appearance of CP violation is found to originate from the interference between the mu-tau symmetric part of M and its breaking part. If |M_{e mu}|=|M_{e tau}|, giving either M_{e mu}=-sigma e^{i theta} M_{e…
The paper presents the short review of our to-day knowledge of vacuum condensates in QCD. The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determination of physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of quark condensate, connected with the existence of baryon masses is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic tau-decay. In the theoretical an…
The bounds on the values of gluon, four-quark and quark-gluon condensates are derived from the requirement of consistency of the sum rules for various correlators of the hybrid current $a_μ=g\bar dγ_ρ\tilde G_{ρμ}u$. The upper bound for the gluon condensate is found to be less then twice its standard value while for the four-quark condensates the violation of factorization by a factor 3-4 is allowed. The value of the quark-gluon condensate is given as a function of $\left<\frac{α_s}π G^2\right>$ and $\left<(\bar qΓq)^2\right >$ which for the standard values yields $m_0^2=0.63~\mbox{GeV}^2$ . O…
The weak interaction between the first and second generation of quarks, the Cabibbo-Kobayashi-Maskawa matrix (CKM) element |Vus|, can be probed using hadronic tau decays. In this paper, we present the recent measurements of hadronic tau decays from BELLE and BABAR and the improvements in the determination of |Vus| from tau decays.
Precise measurements of the tau lepton properties provide stringent tests of the Standard Model structure and accurate determinations of its parameters. We overview the present status of a few selected topics: lepton universality, QCD tests and the determination of alpha_s, m_s and V_us from hadronic tau decays, and lepton flavor violation phenomena.
We discuss the ratio of hadronic to leptonic tau-decays, that can be expanded in an operator product expansion. The sensitivity to the strange mass is increased, if only the flavor-breaking difference of strange to non-strange currents is considered, which leaves us with terms that are at leading order proportional to m_s^2. In this sum rule the scalar channel exhibits a very bad convergence behavior in the perturbation series, that we control by replacing the scalar OPE with a phenomenological ansatz for the scalar and pseudoscalar spectral functions. The spectral ansatz is compared to the th…
Hadronic tau decays offer the possibility of determining the strong coupling alpha_s at relatively low energy. Precisely for this reason, however, good control over the perturbative QCD corrections, the non-perturbative condensate contributions in the framework of the operator product expansion (OPE), as well as the corrections going beyond the OPE, the duality violations (DVs), is required. On the perturbative QCD side, the contour-improved versus fixed-order resummation of the series is still an issue, and will be discussed. Regarding the analysis, self-consistent fits to the data including …
We determine the Cabibbo-Kobayashi-Maskawa matrix (CKM) element |Vus| in several different ways using updated preliminary HFAG averages for the tau lepton branching fractions and we compare the results with the determinations obtained from the kaon decays and from the unitarity of the CKM matrix.
We update the extraction of |V_{us}| from hadronic tau decay data in light of recent BaBar and Belle results on the branching fractions of a number of important strange decay modes. A range of sum rule analyses is performed, particular attention being paid to those based on "non-spectral weights", developed previously to bring the slow convergence of the relevant integrated D=2 OPE series under improved control. Results from the various sum rules are shown to be in good agreement with one another, but ~3 sigma below expectations based on 3-family unitarity. Important avenues for future study a…
QCD finite energy sum rules, together with the latest updated ALEPH data on hadronic decays of the tau-lepton are used in order to determine the vacuum condensates of dimension $d=2$ and $d=4$. These data are also used to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension $d=6$ and $d=8$, as well as the chiral correlator at zero momentum, proportional to the counter term of the ${\cal{O}}(p^4)$ Lagrangian of chiral perturbation theory, $\bar{L}_{10}$. Suitable (pinched) integration kernels are introduced in the sum rules in order to suppress pote…
We use a light-cone sum rule (LCSR) analysis of the branching ratios of radiative meson decays to contrain the value of the magnetic susceptibility of the quark condensate $χ(μ)$. For the first time, we use a complete set of three-particle distribution amplitudes that enables us to give a consistent prediction for the branching ratios. Furthermore we will make use of a very recent update of several non-perturbative parameters. Our final result for $χ(μ= 1 {\rm GeV})= 2.85 \pm 0.5 {\rm GeV}^{-2}$ (assuming asymptotic wave functions) agrees with the currently used value of $3.15 \pm 0.3 {\rm GeV…
A sum rule for determining |V_us| from a combination of hadronic tau decay and electroproduction data is discussed. Indications of problems with analogous, purely tau-decay-based analyses, most likely associated with slow convergence of the relevant D=2 OPE series, are outlined, and advantages of the mixed sum rule approach identified. With current data, one obtains |V_us|= 0.2208 (39)_exp (3)_th, a determination amenable to significant near-term reduction in experimental error, and with the smallest theoretical error of all current |V_us| determinations.
A critical review of hadronic tau decay data based determinations of |V_{us}| is given, focussing on the impact of the slow convergence of the integrated D=2 OPE series for the conventional flavor-breaking sum rule determination and the potential role of as-yet-unmeasured multiparticle contributions to the strange spectral distribution. Additional information obtainable from analyses of inclusive strange decay data alone, and from mixed electroproduction-tau sum rules with much reduced OPE uncertainties, is also discussed. Self-consistency tests are shown to favor determinations which reduce s…
ALEPH/OPAL data on the V-A spectral functions from hadronic tau decays are used in connection with a set of Laplace transform sum rules (LSR) for fixing the size of the QCD vacuum condensates up to dimension 18. Our results favour the ones from large-N_c QCD within the Minimal Hadronic Approximation (MHA) and show a violation of about a factor 2-5 of the vacuum saturation estimate of the dimension-six to -ten condensates. We scrutinize the different determinations of the QCD vacuum condensates using tau-decays data. After revisiting some of the existing results, we present coherent values of t…
We have reevaluated the hadronic contribution to the anomalous magnetic moment of the muon (g-2) and to the running of the QED fine structure constant alpha(s) at s=M_Z**2. We incorporated new data from hadronic tau decays, recently published by the ALEPH Collaboration. In addition, compared to previous analyses, we use more extensive e+e- annihilation data sets. The integration over the total hadronic cross section is performed using experimental data up to 40 GeV and results from perturbative QCD above 40 GeV. The improvement from tau data concerns mainly the pion form factor, where the unce…
We investigate a method for determining the CP nature of a neutral Higgs boson or spin-zero resonance at a future linear e+e- collider (ILC) in its tau decay channel. Our procedure is applicable if the production vertex of the Higgs boson can be measured. This will be the case, for example, for the Higgs-strahlung process. We show that the method is feasible for both the leptonic and the hadronic 1-prong tau decay modes.
A very precise determination of V_us can be obtained from the semi-inclusive hadronic decay width of the tau lepton into final states with strangeness. The ratio of the Cabibbo-suppressed and Cabibbo-allowed tau decay widths directly measures (V_us/V_ud)^2, up to very small SU(3)-breaking corrections which can be theoretically estimated with the needed accuracy. Together with previous LEP and CLEO data, the recent measurements by Babar and Belle of some Cabibbo-suppressed tau decays imply V_us= 0.2165 +- 0.0026_exp +- 0.0005_th, which is already competitive with the standard extraction from K_…
Updated determinations of |V$_{us}$| with tau decays using new recent estimates of radiative corrections for light-meson leptonic decay rates
本文结合HFLAV 2018报告的tau分支比结果以及$π\ell2$和$K\ell2$辐射修正的最新估计，更新了|V$_{us}$|的测定，结果显示中心值和不确定性仅有微小变化。
It is known that the discrepancy in pion spectral functions extracted from positron-electron annihilation and tau decay leads to different predictions for the muon anomalous magnetic moment. We will show that this discrepancy effects also the extraction of the Cabibbo angle from the hadronic tau decays. The corrections to the tau branching fractions, corresponding to the presence of new centi-weak tensor interactions, allow us to extract the Cabibbo angle from tau decays in agreement with its other precision determinations. Thus a more precise value of |V_us|=0.2246 +/- 0.0012 is obtained and …
The relation of the strong coupling constant as measured in tau decay to other low energy determinations is considered with special attention to its impact on the question of the possible existence of light gluinos.
We review the current status of the determination of the strong coupling from tau decay. Using the most recent release of the ALEPH data, a very comprehensive phenomenological analysis has been performed, exploring all strategies previously considered in the literature and several complementary approaches. Once their actual uncertainties are properly assessed, the results from all adopted methodologies are in excellent agreement, leading to a very robust and reliable value of the strong coupling, $α_s^{(n_f=3)}(m_τ^2) = 0.328\pm 0.013$, which implies $α_s^{(n_f=5)}(M_Z^2) = 0.1197\pm 0.0015$.
One of the largest theoretical uncertainties assigned to the strong coupling constant alpha_s as determined from hadronic tau decays stems from the differences in the results for Fixed Order Perturbation Theory (FOPT), Contour Improved Perturbation Theory (CIPT) and Renormalon Chain Perturbation Theory (RCPT). It is often argued that the three methods differ in the treatment of higher orders only and therefore the full difference should be treated as theoretical error. Recently other arguments either in favor of FOPT, CIPT or RCPT have been given, but none of those is able to combine all three…
Gradient-flow renormalon subtraction and the hadronic tau decay series
本文提出用梯度流定义规范不变算符，通过微扰级数重排自动实现重整子减除，使强子τ衰变中 CI 级数与 FO 级数达成一致，从而证明固定阶方法更优。
We discuss the issue of duality violations in hadronic tau decay. After introducing a physically motivated ansatz for duality violations, we estimate their possible size by fitting this ansatz to the tau experimental data provided by the ALEPH collaboration. Our conclusion is that these data do not exclude significant duality violations in tau decay. This may imply an additional systematic error in the value of alpha_s(m_tau), extracted from tau decay, as large as δalpha_s(m_tau) \sim 0.003-0.010 .
The measurement of possible Higgs sector CP-violation in the tau decay channels at the LHC is investigated. A CP-violating effect would manifest itself in these decay modes in characteristic spin-spin correlations of the tau lepton pairs which can be accessed using the momenta and impact parameters of the charged tau decay particles. We examine a CP-sensitive observable for a 125 GeV Higgs boson resonance in the gluon fusion channel at the LHC. Furthermore, we consider the distribution of this observable for the irreducible Drell-Yan background. By splitting these events into two categories we…
With cooling of the cosmological plasma during phase transitions in the early Universe vacuum condensates of quantum fields were produced with negative energy density. Probably these condensates have compensated the initial vacuum energy. The present vacuum is the vacuum condensate of the last relativistic phase transition ($T_{cr}\sim 100$ MeV) (its information is carried by pseudo-Goldstone bosons ($π$-mesons)). This allows us to use Zeldovich's formula that can calculate exactly the value of the cosmological constant in the present epoch. If the most likely values $Ω_Λ$ are 0.7-0.8 then $H_…
Hadronic tau decay data provides access to the light quark vector (V) and axial vector (A) spectral functions. This makes possible investigations of the dynamics of QCD at intermediate scales and improved determinations of certain QCD/Standard Model parameters. We discuss three such applications: (1) the investigation of the nature of duality violation in QCD at intermediate scales (and its relation to the determination of alpha_s); (2) the extraction of m_s from flavor-breaking differences of flavor 'ud' and 'us' data; and (3) the determination of the dimension D=6 term in the OPE for the fla…
In the chiral limit, the $D=6$ contribution to the Operator Product Expansion (OPE) of the $\mathrm{VV-AA}$ correlator of quark currents only depends on two vacuum condensates, which can be related to hadronic matrix elements associated to CP violation in non-leptonic kaon decays. We use those relations to determine $\langle(ππ)_{I=2}|\mathcal{Q}_{8}|K\rangle$, using the updated ALEPH spectral functions. Alternatively, we use those relations in the opposite direction. Taking the values of the matrix elements from the lattice to obtain the $D=6$ vacuum elements provides a new short-distance con…
We determine the strong coupling constant α_s from the τhadroni width using a renormalization group summed (RGS) expansion of the QCD Adler function. The main theoretical uncertainty in the extraction of α_s is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behaviour of the series is similar to that of the standard CIPT expansion. The value of the strong coupling in {\bar{\rm MS}} scheme obtained with the …
Some important aspects of hadronic tau decays are reviewed: the determination of alpha_s from the inclusive tau hadronic width, the measurement of |V_{us}| through the Cabibbo-suppressed decays of the tau, and the theoretical description of the tau -> nu_tau K pi spectrum. The present status of other relevant electroweak topics, such as charged-current universality tests or bounds on lepton-flavour violation, has been already summarized in a previous review.
The interpretation of results of recent tau decay determinations of |V_us|, which yield values ~3 sigma low compared to 3-family unitarity expectations, is complicated by the slow convergence of the relevant integrated D=2 OPE series. We introduce a class of sum rules involving both electroproduction and tau decay data designed to deal with this problem by strongly suppressing D=2 OPE contributions at the correlator level. Experimental complications are briefly discussed and an example of the improved control over theoretical errors presented. The uncertainty on the resulting determination, |V…
Using the most recent release of the ALEPH $τ$ decay data, we present a very detailed phenomenological update of the $α_s(m_τ^2)$ determination. We have exploited the sensitivity to the strong coupling in many different ways, exploring several complementary methodologies. All determinations turn out to be in excellent agreement, allowing us to extract a very reliable value of the strong coupling. We find $α_{s}^{(n_f=3)}(m_τ^2) = 0.328 \pm 0.012$ which implies $α_{s}^{(n_f=5)}(M_Z^{2}) = 0.1197\pm 0.0014$. We critically revise previous work, and point out the problems flawing some recent analy…
The QCD analysis of hadronic tau decays is reviewed and a summary of the present phenomenological status is presented. The following topics are discussed: the determination of alpha_s(m_tau) = 0.338 +- 0.012 from the inclusive tau hadronic width, the measurement of |V_us| through the Cabibbo-suppressed decays of the tau, and the extraction of chiral-perturbation-theory couplings from the spectral tau data.
We determine the non-perturbative gluon condensate of four-dimensional SU(3) gauge theory in a model independent way. This is achieved by carefully subtracting high order perturbation theory results from non-perturbative lattice QCD determinations of the average plaquette. No indications of dimension two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition.
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