Mass Corrections to the Tau Decay Rate

In this note radiative corrections to the total hadronic decay rate of the $\tau$-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate ration $R_{\tau}$ to the order ${\cal O}(\alpha_s^2 m^2)$ and find that they contribute appreciably to the Cabbibo supressed decay modes of the $\tau$-lepton. We also discuss corrections of mass dimension D=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.Comment: 13 pages, LaTeX, no figures. This version fixes a typo in eq. (25) of the original paper (Z. Phys. C59 (1993) 525) and an errror in a numerical integration procedure which has resulted to a significant increase of the O(\alpha_s^2) coefficient in eq. (27). As a consequence also some tables in Section 4 have been modifie

Strong coupling constant from τ\tau decay within renormalization scheme invariant treatment

We extract a numerical value for the strong coupling constant \alpha_s from the \tau-lepton decay rate into nonstrange particles. A new feature of our procedure is the explicit use of renormalization scheme invariance in analytical form in order to perform the actual analysis in a particular renormalization scheme. For the reference coupling constant in the \MSsch-scheme we obtain \alpha_s(M_\tau)= 0.3184 \pm 0.0060_{exp} which corresponds to \al_s(M_Z)= 0.1184 \pm 0.0007_{exp} \pm 0.0006_{hq mass}. This new numerical value is smaller than the standard value from $\tau$-data quoted in the literature and is closer to \al_s(M_Z)-values obtained from high energy experiments.Comment: 8 page

Contour-improved versus fixed-order perturbation theory in hadronic tau decays

The hadronic decay rate of the tau lepton serves as one of the most precise determinations of the QCD coupling alpha_s. The dominant theoretical source of uncertainty at present resides in the seeming disparity of two approaches to improving the perturbative expansion with the help of the renormalisation group, namely fixed-order and contour-improved perturbation theory. In this work it is demonstrated that in fact both approaches yield compatible results. However, the fixed-order series is found to oscillate around the contour-improved result with an oscillation frequency of approximately six perturbative orders, approaching it until about the 30th order, after which the expansion reveals its asymptotic nature. Additionally, the renormalisation scale and scheme dependencies of the perturbative series for the tau hadronic width are investigated in detail.Comment: 20 pages, 5 eps-figures; discussion on scale and scheme dependence added as compared to published journal version JHEP 09 (2005) 05

Liquid krypton electromagnetic calorimeter

Abstract A calorimeter using 30 tons of liquid krypton for the KEDR detector is being constructed. The main effects which determine the energy and space resolution have been studied. An energy resolution of 1.7% at 1.2 GeV was obtained with the prototype. A space resolution of 0.4 mm for relativistic particles has been reached with the prototype

Scale setting for alpha_s beyond leading order

We present a general procedure for incorporating higher-order information into the scale-setting prescription of Brodsky, Lepage and Mackenzie. In particular, we show how to apply this prescription when the leading coefficient or coefficients in a series in the strong coupling alpha_s are anomalously small and the original prescription can give an unphysical scale. We give a general method for computing an optimum scale numerically, within dimensional regularization, and in cases when the coefficients of a series are known. We apply it to the heavy quark mass and energy renormalization in lattice NRQCD, and to a variety of known series. Among the latter, we find significant corrections to the scales for the ratio of e+e- to hadrons over muons, the ratio of the quark pole to MSbar mass, the semi-leptonic B-meson decay width, and the top decay width. Scales for the latter two decay widths, expressed in terms of MSbar masses, increase by factors of five and thirteen, respectively, substantially reducing the size of radiative corrections.Comment: 39 pages, 15 figures, 5 tables, LaTeX2

Decay constants, light quark masses and quark mass bounds from light quark pseudoscalar sum rules

The flavor $ud$ and $us$ pseudoscalar correlators are investigated using families of finite energy sum rules (FESR's) known to be very accurately satisfied in the isovector vector channel. It is shown that the combination of constraints provided by the full set of these sum rules is sufficiently strong to allow determination of both the light quark mass combinations $m_u+m_d$, $m_s+m_u$ and the decay constants of the first excited pseudoscalar mesons in these channels. The resulting masses and decay constants are also shown to produce well-satisfied Borel transformed sum rules, thus providing non-trivial constraints on the treatment of direct instanton effects in the FESR analysis. The values of $m_u+m_d$ and $m_s+m_u$ obtained are in good agreement with the values implied by recent hadronic $\tau$ decay analyses and the ratios obtained from ChPT. New light quark mass bounds based on FESR's involving weight functions which strongly suppress spectral contributions from the excited resonance region are also presented.Comment: 28 pages, 10 figure

The Determination of alpha_s from Tau Decays Revisited

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 by the truncation of the series, by 20% with respect to earlier determinations. We discuss to some detail the perturbative prediction and show that the effect of the incomplete knowledge of the series is reduced by using the so-called contour-improved calculation, as opposed to fixed-order perturbation theory which manifests convergence problems. The corresponding theoretical uncertainties are studied at the tau and Z mass scales. Nonperturbative contributions extracted from the most inclusive fit are small, in agreement with earlier determinations. Systematic effects from quark-hadron duality violation are estimated with simple models and found to be within the quoted systematic errors. The fit gives alpha_s(m_tau) = 0.344 +- 0.005 +- 0.007, where the first error is experimental and the second theoretical. After evolution to M_Z we obtain alpha_s(M_Z) = 0.1212 +- 0.0005 +- 0.0008 +- 0.0005, where the errors are respectively experimental, theoretical and due to the evolution. The result is in agreement with the corresponding NNNLO value derived from essentially the Z width in the global electroweak fit. The alpha_s(M_Z) determination from tau decays is the most precise one to date.Comment: 22 pages, 7 figure

The check of QCD based on the tau-decay data analysis in the complex q^2-plane

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 used. It was demonstrated that QCD with OPE terms is in agreement with the data for the coupling constant close to the lower error edge alpha_s(m_tau^2)=0.330. The restriction on the value of the gluonic condensate was found =0.006 pm 0.012 GeV^2. The analytical perturbative QCD was compared with the data. It is demonstrated to be in strong contradiction with experiment. The restrictions on the renormalon contribution were found. The instanton contributions to the polarization operator are analyzed in various sum rules. In Borel transformation they appear to be small, but not in spectral moments sum rules.Comment: 24 pages; 1 latex + 13 figure files. V2: misprints are corrected, uncertainty in alpha_s is explained in more transparent way, acknowledgement is adde

Resummation of the hadronic tau decay width with the modified Borel transform method

A modified Borel transform of the Adler function is used to resum the hadronic tau decay width ratio. In contrast to the ordinary Borel transform, the integrand of the Borel integral is renormalization--scale invariant. We use an ansatz which explicitly accounts for the structure of the leading infrared renormalon. Further, we use judiciously chosen conformal transformations for the Borel variable, in order to map sufficiently away from the origin the other ultraviolet and infrared renormalon singularities. In addition, we apply Pade approximants for the corresponding truncated perturbation series of the modified Borel transform, in order to further accelerate the convergence. Comparing the results with the presently available experimental data on the tau hadronic decay width ratio, we obtain $\alpha_s(M^z) = 0.1192 +- 0.0007_{exp.} +- 0.0010_{EW+CKM} +- 0.0009_{th.} +- 0.0003_{evol.}$. These predictions virtually agree with those of our previous resummations where we used ordinary Borel transforms instead.Comment: 32 pages, 2 eps-figures, revtex; minor changes in the formulations; a typo in Eq.(47) corrected; version as appearing in Phys. Rev.

Measurement of RudsR_{\text{uds}} and RR between 3.12 and 3.72 GeV at the KEDR detector

Using the KEDR detector at the VEPP-4M $e^+e^-$ collider, we have measured the values of $R_{\text{uds}}$ and $R$ at seven points of the center-of-mass energy between 3.12 and 3.72 GeV. The total achieved accuracy is about or better than $3.3\%$ at most of energy points with a systematic uncertainty of about $2.1\%$. At the moment it is the most accurate measurement of $R(s)$ in this energy range