Precise extractions of $α_s$ from $τ\to {\rm (hadrons)}+ν_τ$ and from $e^+e^-\to {\rm (hadrons)}$ below the charm threshold rely on finite energy sum rules (FESRs) where the experimental side is given by integrated spectral function moments. Here we study the renormalons that appear in the Borel transform of polynomial moments in the large-$β_0$ limit and in full QCD. In large-$β_0$, we establish a direct connection between the renormalons and the perturbative behaviour of moments often employed in the literature. The leading IR singularity is particularly prominent and is behind the fate of moments whose perturbative series are unstable, while those with good perturbative behaviour benefit from partial cancellations of renormalon singularities. The conclusions can be extended to QCD through a convenient scheme transformation to the $C$-scheme together with the use of a modified Borel transform which make the results particularly simple; the leading IR singularity becomes a simple pole, as in large-$β_0$. Finally, for the moments that display good perturbative behaviour, we discuss an optimized truncation based on renormalisation scheme (or scale) variation. Our results allow for a deeper understanding of the perturbative behaviour of integrated spectral function moments and provide theoretical support for low-$Q^2$ $α_s$ determinations.
We suggest a method of summing the perturbation theory (PT) asymptotic series related to infrared (IR) renormalons in QCD by using special renormalization schemes in which the running coupling can be integrated over the region of small momenta. For the method to work, one should consider higher order PT corrections to the standard bubble-chain diagrams. High-order corrections allow one to choose a scheme in which the coupling evolution can smoothly be extrapolated to small momenta. In such schemes the sum of an (extended) IR-renormalon asymptotic series is defined as an integral of the running…
Precise theoretical predictions are a key ingredient for an accurate determination of the structure of the Langrangian of particle physics, including its free parameters, which summarizes our understanding of the fundamental interactions among particles. Furthermore, due to the absence of clear new-physics signals, precise theoretical calculations are required in order to pin down possible subtle deviations from the Standard Model predictions. The error associated with such calculations must be scrutinized, as non-perturbative power corrections, dubbed infrared renormalons, can limit the ultim…
Double-pinched Borel-Laplace sum rules are applied to ALEPH $τ$-decay data. For the leading-twist ($D=0$) Adler function a renormalon-motivated extension is used, and the 5-loop coefficient is taken to be $d_4=275 \pm 63$. Two $D=6$ terms appear in the truncated OPE ($D \leq 6$) to enable cancellation of the corresponding renormalon ambiguities. Two variants of the fixed order perturbation theory, and the inverse Borel transform, are applied to the evaluation of the $D=0$ contribution. Truncation index $N_t$ is fixed by the requirement of local insensitivity of the momenta $a^{(2,0)}$ and $a^{…
The single renormalon-chain contribution to the correlator of scalar currents in QCD is calculated in the $\bar{MS}$-scheme in the limit of a large $N_f$. We find that in the factorial growth of the coefficients due to renormalons takes over almost immediatelly in the euclidean region. The essential differences between the large-order growth of coefficients in the scalar case, and in the vector case are analysed. In the timelike region a stabilization of the perturbative series for the imaginary part, with $n$-loop behaviour $S_n/[\log(s/Λ^2)]^{n-1}$, where $S_n$ is essential constant for $n\l…
We perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients involving the leading power of b, the first beta-function coefficient, is resummed. To avoid a renormalization scale dependence when we match the resummation to the exactly known NLO and NNLO results, we employ the Complete Renormalization Group Improvement (CORGI) approach. These fixed-order and resummed CORGI results are analytically continued by numerically performing a contour integral to obtain corresponding fixed and all-orders ``contour-improved''…
We investigate the behaviour of the perturbative relation between the photon energy spectrum in B -> Xs gamma and the hadronic P+ spectrum in semileptonic B -> Xu l nu decay at high orders in perturbation theory in the "large-beta_0" limit, in which only terms of order alpha_s^n beta_0^(n-1) are retained. The leading renormalon in the weight function W(Delta,P_gamma) relating the two spectra is confirmed to be at u=1/2, corresponding to nonperturbative corrections at O(Lambda_QCD/m_b). We show that the P_gamma dependent pieces of the weight function have no infrared renormalons in this limit, …
We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-$β_0$ limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our results are used to study the higher-order behaviour of dimensionless ratios of vector and pseudo-scalar moments used for the precise extraction of the strong coupling, $α_s$, from relativistic quarkonium sum rules and lattice data, respectively. We show that these ratios benefit from a partial cancellation of the leading renormalon singularities. Our results can gu…
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…
We use improved truncated Operator Product Expansion (OPE) for the Adler function, involving two types of terms with dimension $D=6$, in the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules for the V+A channel strangeless semihadronic $τ$ decays. The generation of the higher order perturbative QCD terms of the $D=0$ part of the Adler function is carried out using a renormalon-motivated ansatz incorporating the leading UV renormalon and the first two leading IR renormalons. The trunacted $D=0$ part of the Sum Rules is evaluated by two variants of the fixed-order perturbation t…
We performed the detailed NLO analysis of the combined CCFR $xF_3$ and $F_2$ structure functions data and extracted the value of $α_s$, parameters of distributions and higher-twist (HT) terms using the direct solution of the DGLAP equation. The value of $α_s(M_Z)=0.1222\pm 0.0048 (exp)\pm 0.0040(theor)$ was obtained. The result has larger central value and errors, than the original result of the CCFR collaboration, in view of the incorporation into the fits of the HT terms as the free model independent parameters. The $x$-shapes of the HT contributions to $xF_3$ and $F_2$ are in agreement with…
A detailed next-to-next-to-leading order (NNLO) QCD analysis is performed for the experimental data of the CCFR collaboration for the $xF_3$ structure function. Theoretical ambiguities of the results of our NNLO fits are estimated by application of the Padé resummation technique and variation of the factorization and renormalization scales. The NNLO and N$^3$LO $α_s(Q^2)$ $\bar{MS}$-matching conditions are used. In the process of the fits we are taking into account of twist-4 $1/Q^2$-terms. We found that the amplitude of the $x$-shape of the twist-4 factor is decreasing in NLO and NNLO, though…
In the extraction of $α_s$ from hadronic tau decay data several moments of the spectral functions have been employed. Furthermore, different renormalization group improvement (RGI) frameworks have been advocated, leading to conflicting values of $α_s$. Recently, we performed a systematic study of the perturbative behavior of these moments in the context of the two main-stream RGI frameworks: Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT). The yet unknown higher order coefficients of the perturbative series were modelled using the available knowledge of t…
An extraction of the top mass from cross section measurements in the dilepton and lepton+jets channels with an integrated luminosity of about 1fb-1 is given. Two ways are presented : one based on the simple lecture of the graph of the cross section as a function of the top mass and the other based on the use of probability density functions. The final result is consistent with direct measurements but with a greater uncertainty.
Using the results for the NNLO QCD corrections to anomalous dimensions of odd $xF_3$ Mellin moments and N$^3$LO corrections to their coefficient functions we improve our previous analysis of the CCFR'97 data for $xF_3$. The possibility of extracting from the fits of $1/Q^2$-corrections is analysed using three independent models,including infrared renormalon one. Theoretical quetion of applicability of the renormalon-type inspired large-$β_0$ approximation for estimating corrections to the coefficient functions of odd $xF_3$ and even non-singlet $F_2$ moments are considered. The comparison with…
A simple method for the extraction of the times of maximal emission for kaons and pions using the combined fitting of their transverse momentum spectra and the longitudinal interferometry radii dependencies on the pair transverse mass $m_T$ is applied to Pb+Pb collisions at the LHC energy $\sqrt{s_{NN}}=5.02$ TeV. The method is based on the analytical formulas, that were earlier successfully utilized in the studies of Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. To test the method, the spectra, radii and particle radiation picture are calculated within the integrated hydrokinetic model (iHKM)…
The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling $α_s$ and other QCD parameters from the hadronic decays of the $τ$ lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two …
We discuss the simultaneous determination of m_s and V_us from flavor-breaking hadronic tau decay sum rules, focussing on weight choices designed to better control problems associated with the slow convergence of the relevant integrated D=2 OPE series. The results are found to display improved stability and consistency relative to those of conventional analyses based on the ``(k,0) spectral weights''. The results for m_s agree well with those of recent strange scalar sum rule and strange pseudoscalar sum rule and lattice analyses. Results for V_us agree within errors with those of lattice-inpu…
