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 all theory parameters have to be performed, and this is also explained in some detail. The fit quantities are moment integrals of the tau spectral function data in a certain energy window and care should be taken to have acceptable perturbative behaviour of those moments as well as control over higher-dimensional operator corrections in the OPE.
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.
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 dat…
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 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 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.
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.
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 …
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 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…
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 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 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 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 …
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 .
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…
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…
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…
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…
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 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.
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 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} $.
I review and compare various techniques to obtain the value of the QED coupling, alpha, at the Z pole. GigaZ precisions would require a much more accurate determination than available today. A combination of the virtues of current methods may help to achieve this goal.
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…
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 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.
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…
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…
We describe a determination of the strong coupling alpha_s(M_Z) from scaling violations of the nonsinglet DIS structure function, which is based on two novel techniques aimed at controlling and minimizing the theoretical error: a neural network parametrization of BCDMS and NMC data, and QCD evolution by means of truncated Mellin moments.
Precise determinations of the strong coupling constant in hadronic collisions demand sets of parton densities spanning a sufficiently wide range of values for the QCD scale parameter Lambda. For such applications, we supplement the recent GRV parametrization by five sets of dynamically generated parton distributions for Lambda-values corresponding to alpha_{S}(M_{Z}^{2}) between 0.104 and 0.122. Present DIS data, including recent small-x HERA results, do not appreciably discriminate between these sets.
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…
We describe in detail the method we have used to determine the CKM angles gamma, alpha and beta using flavour symmetries between non-leptonic B decays. This method is valid in the context of the SM but also in presence of New Physics not affecting the amplitudes.
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.
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 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…
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 determine the strong coupling alpha_s(M_Z) from scaling violations of truncated moments of the nonsinglet deep inelastic structure function F_2. Truncated moments are determined from BCDMS and NMC data using a neural network parametrization which retains the full experimental information on errors and correlations. Our method minimizes all sources of theoretical uncertainty and bias which characterize extractions of alpha_s from scaling violations. We obtain alpha_s(M_Z) = 0.124 +0.004-0.007 (exp.) + 0.003- 0.004 (th.).
We compute the proton structure function F_2^p at small x and large Q^2 at next-to-leading order in alpha_s(Q^2), including summations of all leading and subleading logarithms of Q^2 and 1/x in a way consistent with momentum conservation. We perform a detailed comparison to the 1993 HERA data, and show that they may be used to determine alpha_s(M_Z^2)=0.120 pm 0.005(exp) pm 0.009(th). The theoretical error is dominated by the renormalization and factorization scheme ambiguities.
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.
Recently the full O(alpha_S^5 m, alpha_S^5 m log(alpha_S)) correction to the heavy quarkonium 1S energy level has been computed (except the a_3-term in the QCD potential). We point out that the full correction (including the log(alpha_S)-term) is approximated well by the large-beta_0 approximation. Based on the assumption that this feature holds up to higher orders, we discuss why the top quark pole mass cannot be determined to better than O(Lambda_{QCD}) accuracy at a future e^+e^- collider, while the MS-bar mass can be determined to about 40 MeV accuracy (provided the 4-loop MSbar-pole mass …
We determine the strong coupling alpha_s from a next-to-leading order analysis of processes used for the NNPDF2.1 parton determination, which includes data from neutral and charged current deep-inelastic scattering, Drell-Yan and inclusive jet production. We find alpha_s(M_Z)=0.1191+-0.0006 (exp), where the uncertainty includes all statistical and systematic experimental uncertainties, but not purely theoretical uncertainties. We study the dependence of the results on the dataset, by providing further determinations based respectively on deep-inelastic data only, and on HERA data only. The dee…
We investigate two points related to existing treatments of isospin-breaking corrections to the CVC relation between the e^+e^- --> pi^+ pi^- cross-section and dGamma[tau^- --> nu_tau pi^- pi^0]/ds. Implications for the value of the hadronic contribution to a_mu =(g-2)_mu /2 based on those analyses incorporating hadronic tau decay data are also considered. We conclude that the uncertainty on the isospin-breaking correction which must be applied to the tau decay data should be significantly increased, and that the central value of the rho-omega ``mixing'' contribution to this correction may be …
