An updated measurement of alpha_s(m_tau) from ALEPH tau hadronic spectral functions is presented. We report a study of the perturbative prediction(s) showing that the fixed-order perturbation theory manifests convergence or principle problems not presented in the contour-improved calculation. Potential systematic effects from quark-hadron duality violations are estimated to be within the quoted systematic errors. The fit result is alpha_s(m_tau) = 0.344 +- 0.005 +- 0.007, where the first error is experimental and the second theoretical. After evolution, the alpha_s(M_Z) determined from tau data is one of the most precise to date, in agreement with the corresponding NNNLO value derived from Z decays.
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 present an update of the measurement of alpha_s(m_tau) from ALEPH tau hadronic spectral functions. We report a study of the perturbative prediction(s) showing that the fixed-order perturbation theory manifests convergence problems not presented in the contour-improved calculation. Potential systematic effects from quark-hadron duality violations are estimated to be within the quoted systematic errors. The fit result is alpha_s(m_tau) = 0.344 +- 0.005 +- 0.007, where the first error is experimental and the second theoretical. After evolution, the alpha_s(M_Z) determined from tau data is the …
The results of calculation of light gluino contributions to Gamma(Z--->hadrons) and Gamma(tau--->hadrons) to O(alpha_s^3) are presented. The net effect in the case of Z decay is noticeable. For the tau width the effect is very large and, if a light gluino exists, suggests that alpha_s increases by more than 15% relative to the Standard Model analysis.
Until recently, determinations of alpha_s(M_Z) from hadronic tau decays and the analysis of short-distance-sensitive lattice observables yielded results which, though precise, were not in good agreement. I review new analyses that bring these into good agreement and provide some details on the source of the main changes in the tau decay analysis.
We report on some technical aspects of our calculation of alpha_s^4 corrections to R(s) and the semi-leptonic tau decay width [1-3]. We discuss the inner structure of the result as well as the issue of its correctness. We demonstrate recently appeared independent evidence positively testing one of two components of the full result.
We present the electroweak one-loop corrections to the processes e+e- -> f bar-f, f = tau, c, b, t, at energies relevant for a future linear collider. The results of two independent calculations are compared and agreement is found at a technical-precision level of ten to twelve digits.
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.
Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha_s^4 for the cross section of electron-positron annihilation into hadrons and for the decay rates of the Z-boson and the tau-lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alpha_s, as extracted from these measurements, and to a small shift of the central value, moving two central values closer together. The agreement between two values …
We review the present status in the determination of the $accurate$ value of $α_s$ from $τ$-decays, where we discuss in detail the different sources of theoretical errors.
We discuss the extraction of alpha_s using isovector hadronic tau decay data and sum rules constructed specifically to suppress contributions associated with poorly known higher dimension condensates. We show, first, that problems with the treatment of such contributions affect earlier related analyses and, second, that these problems can be brought under good theoretical control through the use of an alternate analysis strategy. Our results, run up to the n_f=5 regime, correspond to alpha_s(M_Z^2)=0.1187(16), in excellent agreement with the recently updated global fit to electroweak data at t…
Various moments of the hadronic spectral functions have been employed in the determination of the strong coupling alpha_s from tau decays. In this work we study the behaviour of their perturbative series under different assumptions for the large-order behaviour of the Adler function, extending previous work on the tau hadronic width. We find that the moments can be divided into a small number of classes, whose characteristics depend only on generic features of the moment weight function and Adler function series. Some moments that are commonly employed in alpha_s analyses from tau decays shoul…
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. \\
We perform an extraction of alpha_s based on sum rules involving isovector hadronic tau decay data. The particular sum rules employed are constructed specifically to suppress contributions associated with poorly known higher dimension condensates, and hence reduce theoretical systematic uncertainties associated with the treatment of such contributions which are shown to be present in earlier related analyses. Running our results from the n_f=3 to n_f=5 regime we find alpha_s(M_Z^2)=0.1187(16), in excellent agreement with the recently updated global fit to electroweak data at the Z scale, 0.119…
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.
The first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate is presented including its real part at the four-loop level. This allows to perform the extraction of the strange quark mass m_s from the decay width of the tau-lepton with full O(alpha_s^3) accuracy. In agreement with previous estimates the newly computed alpha_s^3 term proves to be rather large. This justifies inclusion of the similarly estimated alpha_s^4 term in phenomenological analysis. Combined with an updated value…
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 …
Recently computed terms of orders O(α_s^4 n_f^2) in the perturbative series for the tau decay rate, and similar (new) strange quark mass corrections, are used to discuss the validity of various optimization schemes. The results are then employed to arrive at improved predictions for the complete terms order O(α_s^4) and O(α_s^5) in the massless limit as well as for terms due to the strange quark mass. Phenomenological implications are presented.
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…
We present the analytical $α_{s}^3$ correction to the $Z^{0}$ decay rate into hadrons. We calculate this correction up to (and including) terms of the order $(m_Z^2/m_{top}^2)^3$ in the large top quark mass expansion. We rely on the technique of the large mass expansion of individual Feynman diagrams and treat its application in detail. We convert the obtained results of six flavour QCD to the results in the effective theory with five active flavours, checking the decoupling relation of the QCD coupling constant. We also derive the large charm quark mass expansion of the semihadronic $τ$ lepto…
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…
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 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…
Assuming a minimal seesaw model with two heavy neutrinos (N), we examine effects of leptonic CP violation induced by approximate mu-tau symmetric interactions. As long as N is subject to the mu-tau symmetry, we can choose CP phases of Dirac mass terms without loss of generality in such a way that these phases arise from mu-tau symmetry breaking interactions. In the case that no phase is present in heavy neutrino mass terms, leptonic CP phases are controlled by two phases alpha and beta. The similar consideration is extended to N blind to the mu-tau symmetry. It is argued that N subject (blind)…
The hadronic decays of the tau lepton can be used to determine the effective charge alpha_tau(m^2_tau') for a hypothetical tau-lepton with mass in the range 0 < m_tau' < m_tau. This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of alpha_tau at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales s = m^2_tau' of order 1 GeV^2 with a magnitude a…
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…
Different choices exist for the renormalisation group resummation in the determination of $α_s$ from hadronic $τ$ decays: namely fixed-order (FOPT) and contour-improved perturbation theory (CIPT). The two approaches lead to systematic differences in the resulting $α_s$. On the basis of a model for higher-order terms in the perturbative series, which incorporates well-known structure from renormalons, it is found that while CIPT is unable to account for the fully resummed series, FOPT smoothly approaches the Borel sum. Employing the model to determine $α_s$ yields $α_s(M_τ)=0.316 \pm 0.006$, wh…
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…
Minimal R-parity violating supergravity predicts a value for $alpha_s(M_Z)$ smaller than in the case with conserved R-parity, and therefore closer to the experimental world average. We show that the R-parity violating effect on the $alpha_s$ prediction comes from the larger two-loop b-quark Yukawa contribution to the renormalization group evolution of the gauge couplings which characterizes R-parity violating supergravity. The effect is correlated to the tau neutrino mass and is sensitive to the initial conditions on the soft supersymmetry breaking parameters at the unification scale. We show …
We consider extensions of the Standard Model with an extra U(1) gauge boson which couples to B-(alpha L_e + beta L_mu + gamma L_tau) with alpha + beta + gamma = 3. We show that the extra gauge boson necessarily mixes with the Z leading to potentially significant corrections to the Z-f-fbar vertex. The constraints on the size of this correction imposed by the Z-pole data from LEP and SLD are derived.
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 .
We discuss the quantitative impact of duality violations on the determination of the strong coupling constant from hadronic tau decays, based on a preliminary analysis of OPAL data.
We derive precise standard model predictions for the dilepton invariant mass and the tau energy distributions in inclusive B -> Xc tau nu decay. We include Lambda_QCD^2/m_b^2 and alpha_s corrections using the 1S short-distance mass scheme, and estimate shape function effects near maximal tau energy. These results can improve the sensitivity of b -> c tau nu related observables to beyond standard model physics.
We have derived constraints on the tau neutrino mass and fourth generation mixing from an analysis of the partial widths of tau lepton decays, in particular: tau -> e nu nu_tau, tau -> mu nu nu_tau, tau -> pi nu_tau, tau -> K nu_tau. We present predictions for the tau decay widths, allowing for a non-zero tau neutrino mass, m(nu_tau), and for mixing with a neutrino of mass m(nu_L) > M_Z/2, which is parametrised using a Cabibbo-like mixing angle, theta_L. By comparison of these theoretical predictions with the experimental measurements, we obtain the following bounds at the 90% confidence level…
We discuss some key issues associated with duality-violating and non-perturbative OPE contributions to the theoretical representations of light quark current-current two-point functions and relevant to precision determinations of alpha_s from hadronic tau decay and electroproduction cross-section data. We demonstrate that analyses with an explicit representation of duality-violating effects are required to bring theoretical errors in such extractions under control, motivating the accompanying paper in these proceedings, which presents the results of such an analysis.
Hadronic tau decays represent a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables (sum rules) based on the spectral functions of hadronic tau decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong coupling constant, parameters of the chiral Lagrangian, |V_us|, the mass of the strange quark, and to simultaneously test the concept of quark-hadron duality. Using the best available measurements and a revisited analysis of the theoretical framework, the value alpha_s(m_tau) = 0.345 +- 0.004[exp] +- 0.009[theo] is o…
We re-examine recent determinations of power corrections from tau-decay and confront the results with the existing ones from QCD spectral sum rules (QSSR). We conclude that contrary to the QSSR analysis, which lead to <alpha_s G^2>=(6.8+-1.3)10^{-2} GeV^4, tau-decay is not a good place for extracting the gluon condensate due to its extra alpha_s^2 coefficient which suppresses its contribution in this process. Results from e^+e^- sum rules and tau-decay: rho alpha_s<uu>^2= (4.5+-0.3)10^{-4}GeV^6, where rho=3.0+-0.2 confirm the deviation from the vacuum saturation estimate of the four-quark cond…
I calculate the QED coupling, alpha, directly in the MS-bar scheme using an unsubtracted dispersion relation for the three light quarks, and perturbative QCD for charm and bottom quarks. Compact analytical expressions are presented, making this approach particularly suitable for electroweak fits. After alpha^(-1) (m_tau) = 133.513 +- 0.025 is obtained in a first step, I perform a 4-loop renormalization group evolution with 3-loop matching conditions to arrive at alpha^(-1) (M_Z) = 127.934 +- 0.026 for alpha_s (M_Z) = 0.120. The corresponding hadronic contribution to the on-shell coupling is De…
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.
Modifications of the mu+ lifetime in matter due to muonium (M = mu+ e-) formation and other medium effects are examined. Muonium and free mu+ decay spectra are found to differ at O(alpha m_e/m_mu) from Doppler broadening and O(alpha^2 m_e/m_mu) from the Coulomb bound state potential. However, both types of corrections are shown to cancel in the total decay rate due to Lorentz and gauge invariance respectively, leaving a very small time dilation lifetime difference, (tau_M - tau_mu+)/tau_mu+ = alpha^2 m_e^2/ 2m_mu^2 \simeq 6\times 10^-10, as the dominant bound state effect. It is argued that ot…
The present status of some selected topics on tau physics is presented: charged-current universality tests, bounds on lepton-flavour violation, 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.
We have calculated the O(alpha) radiative corrections to the tau decay tau -> pi (K) nu, taking into account both the point meson contribution and the structure dependent radiation. We find for the ratio Gamma(tau -> pi nu (gamma)) / Gamma(pi -> mu nu (gamma)) a radiative correction of + 1.2% and for Gamma(tau -> K nu (gamma)) / Gamma(K -> mu nu (gamma)) one of + 2.0%. We compare our results with an earlier estimation and with experimental data.
The thorough analysis of the ALEPH data on hadronic tau-decay is performed in the framework of QCD. The perturbative calculations are performed in 3 and 4-loop approximations. The terms of the operator product expansion (OPE) are accounted up to dimension D=8. The value of the QCD coupling constant alpha_s(m_tau^2)=0.355 pm 0.025 was found from hadronic branching ratio R_tau. The V+A and V spectral function are analyzed using analytical properties of polarization operators in the whole complex q^2-plane. Borel sum rules in the complex q^2 plane along the rays, starting from the origin, are use…
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.
Being a determination at low energies, the analysis of hadronic tau decay data provides a rather precise determination of the strong coupling alpha_s after evolving the result to M_Z. At such a level of precision, even small non-perturbative effects become relevant for the central value and error. While those effects had been taken into account in the framework of the operator product expansion, contributions going beyond it, so-called duality violations, have previously been neglected. The following investigation fills this gap through a finite-energy sum rule analysis of tau decay spectra fr…
I review recent estimates of the non-perturbative hadronic vacuum polarization contributions. Since these at present can only be evaluated in terms of experimental data of limited precision, the related uncertainties pose a serious limitation in our ability to make precise predictions. Besides e+e- - annihilation data also tau decay spectra can help to get better predictions. Here, it is important to account for all possible iso-spin violations in tau - decay spectra, from which e+e- cross sections may be obtained by an iso-spin rotation. The observed 10% discrepancy in the region above the rh…
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 present a complete precision analysis of the sfermion pair production process e+e- -> sf_i sf_j (f = t, b, tau, nu_tau) in the Minimal Supersymmetric Standard Model. Our results extend the previously calculated weak corrections by including all one-loop corrections together with higher order QED corrections. We present the details of the analytical calculation and discuss the renormalization scheme. The numerical analysis shows the results for total cross-sections, forward-backward and left-right asymmetries. It is based on the SPS1a' point from the SPA project. The complete corrections are…
Hadronic corrections to the muon lifetime are calculated in the Fermi theory in the presence of QED using dispersion relations. The result, after convolution of hadron data with the calculated perturbative kernel is Delta Gamma_had = -Gamma_0(alpha/pi)^2(0.042) where Gamma_0 is the tree-level width. The results are also used to obtain the corrections to the muon lifetime coming from virtual muon and tau loops Delta Gamma_muon = Gamma_0(alpha/pi)^2[(16987/576)-(85/36)zeta(2)-(64/3)zeta(3)] = -Gamma_0(alpha/pi)^2(0.0364333) Delta Gamma_tau = -Gamma_0(alpha/pi)^2)(0.00058)
Using the type-II seesaw mechanism with three Higgs doublets phi_alpha (alpha = e, mu, tau) and four Higgs triplets, we build a model for lepton mixing based on a 384-element horizontal symmetry group, generated by the permutation group S_3 and by six Z_2 transformations. The charged-lepton mass matrix is diagonal; the symmetries of the model would require all the three masses m_alpha to be equal, but different vacuum expectation values of the phi_alpha allow the m_alpha to split. The number of parameters in the Majorana neutrino mass matrix m_nu depends on two options: full breaking of the pe…
With the help of a physically motivated ansatz, which is fitted to the data, we estimate the size of possible duality violations in hadronic tau decay. The result is that the uncertainty associated with these violations could impact the alpha_s determination from the total decay width at a level which we estimate to be δalpha_s(m_tau) \sim 0.003-0.010. Consequently, it cannot be neglected.
We formulate a general scheme to improve the truncated perturbative expansion in alpha_s by means of the renormalization group in QCD for the single-scale quantities. The procedure is used for the evaluation of hadronic decay rates of tau-lepton and eta_c-charmonium. The scale dependence of result for eta_c is studied in the scheme of fixed value for the MS-bar mass of charmed quark.
In the determination of alpha_s from tau decays several different moments of the hadronic spectral functions have been used. In a recent work, we performed an analysis of their perturbative behaviour under two different assumptions for the higher-order coefficients of the Adler function. We showed that the various moments can be divided in a small number of classes. We concluded that some of the moments commonly employed in alpha_s extractions should be avoided due to their bad perturbative behaviour. Furthermore, for the moments that have a good perturbative behaviour, and under reasonable as…
The recent results in QCD at low energies are reported. The theoretical analysis of hadronic tau-decay is performed in complex q^2-plane. The terms of perturbation theory (PT) up to alpha^3_s are accounted, the terms of operator product expansion (OPE) -- up do dimension 8. The momenta of charmed quark vector current polarization operator are analyzed in 3 loops with account of dimension 4 and 6 OPE terms. The main conclusion is that in the range of low-energy phenomena under consideration PT and OPE are in good agreement with experiment starting from Q^2=-q^2 ~ 1 GeV^2. The values of alpha_s(…
Analytic formulae are given for order alpha_s perturbative QCD corrections to the double differential distribution of the tau lepton energy and the invariant mass of the tau + antineutrino system in semileptonic decays of the bottom quark. The corresponding distribution for B meson decays are obtained by combining these results and the nonperturbative QCD corrections calculated by Falk et al. The moments of the energy distribution of the tau lepton are calculated.
Improved values for the two- and three-loop mass-dependent QED contributions to the anomalous magnetic moments of the electron, muon, and tau lepton are presented. The Standard Model prediction for the electron (g-2) is compared with its most precise recent measurement, providing a value of the fine-structure constant in agreement with a recently published determination. For the tau lepton, differences with previously published results are found and discussed. An updated value of the fine-structure constant is presented in "Note added after publication."
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 hadronic vacuum-polarization contribution to the muon anomalous magnetic moment a_{mu}(hadr) and to the value of the eleectromagnetic coupling constant at q^2 = M^2_z are determined more precisely in connection with a new more exact value of the electronic width of rho-meson. The QCD model with infinite number of vector mesons is used. The more precisely determined results are: a_{mu}(hadr) = 678(7)*10^{-10}, δα_{hadr}(M^2_z) = 0.02786(6).
The next-to-next-to-leading order perturbative QCD corrections to R_tau and the higher moments of the invariant mass distribution in the hadronic tau decays are considered. The renormalization scheme dependence of these corrections is discussed. The optimized predictions are obtained, using the principle of minimal sensitivity as a guide to select the preferred renormalization scheme. A simplified fit is performed, using R_tau and R^12_tau, to see how the use of the optimized expansion may affect the determination of the alpha_s and the dimension six condensates from the experimental data.
The complete electroweak O(alpha) corrections are calculated for the charged-current four-fermion production processes e+e- --> nu_tau tau+ mu- anti-nu_mu, u anti-d mu- anti-nu_mu, and u anti-d s anti-c. The calculation is performed using complex gauge-boson masses, supplemented by complex couplings to restore gauge invariance. The evaluation of the occurring one-loop tensor integrals, which include 5- and 6-point functions, requires new techniques. Explicit numerical results are presented for total cross sections in the energy range from the W-pair-production threshold region up to a scatteri…
