arXiv subjects

Matthias Jamin

Publications and source records attributed to Matthias Jamin.

At least 19 recordsLinked to original sources

arXiv2022

Reconciling the Contour-Improved and Fixed-Order Approaches for $τ$ Hadronic Spectral Moments II: Renormalon Norm and Application in $α_s$ Determinations

In a previous article, we have shown that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $τ$ hadronic spectral function moments, which had affected the precision of $α_s$ determinations for many years, may be reconciled by employing a renormalon-free (RF) scheme for the gluon condensate (GC) matrix element. In addition, the perturbative convergence of spectral function moments with a sizeable GC correction can be improved. The RF GC scheme depends on an IR factorization scale $R$ and the normalization $N_g$ of the GC renormalon. In the present work, we use three different methods to determine $N_g$, yielding a result with an uncertainty of $40\%$. Following two recent state-of-the-art strong coupling determination analyses at ${\cal O}(α_s^5)$, we show that using the renormalon-free GC scheme successfully reconciles the results for $α_s({m_τ^2})$ based on CIPT and FOPT. The uncertainties due to variations of $R$ and the uncertainty of $N_g$ only lead to a small or moderate increase of the final uncertainty of $α_s(m_τ^2)$, and affect mainly the CIPT expansion method. The FOPT and CIPT results obtained in the RF GC scheme may be consistently averaged. The RF GC scheme thus constitutes a powerful new ingredient for future analyses of $τ$ hadronic spectral function moments.

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arXiv2022

Inclusive $τ$ Hadronic Decay Rate in a Renormalon-Free Gluon Condensate Scheme

In a recent work by some of us it was shown that the long-standing discrepancy between the QCD perturbation series for the inclusive hadronic tau decay rate computed in the CIPT and FOPT expansion approaches can be understood from the fact that CIPT has an infrared (IR) sensitivity that it not compatible with the standard form of the operator production expansion (OPE). For concrete IR renormalon models for the QCD Adler function the resulting CIPT-FOPT discrepancy, the asymptotic separation, can be calculated analytically from the Borel representation of the CIPT series expansion. If the known perturbative corrections for the QCD Adler function at the 5-loop level already have a sizeable contribution from the asymptotic behavior related to the gluon condensate (GC) renormalon, the asymptotic separation is dominated by that renormalon. This implies that the CIPT expansion can be reconciled with FOPT, when a renormalon-free scheme for the GC is adopted. In this talk we discuss such a renormalon-free scheme for the GC, which involves perturbative subtractions in analogy to using short-distance quark mass schemes instead of the pole mass. Using a concrete realistic high-order Borel model for the Adler function consistent with the known corrections up to 5 loops and containing a sizeable GC renormalon contribution, we show that the CIPT-FOPT discrepancy can be avoided when switching to the renormalon-free GC scheme. At the same time, the perturbative convergence of $τ$ hadronic spectral funtion moments strongly sensitive to the GC OPE corrections is considerably improved. We show that these improvements may lead to higher precision for strong coupling determinations.

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arXiv2022

Reconciling the Contour-Improved and Fixed-Order Approaches for $τ$ Hadronic Spectral Moments I: Renormalon-Free Gluon Condensate Scheme

We propose a simple and easy-to-implement scheme for a renormalon-free gluon condensate (GC) matrix element, which is analogous to implementations of short-distance heavy-quark mass renormalization schemes existing in the literature already for a long time. Because the scheme is based on a perturbative subtraction at the level of the matrix element, with a freely adaptable infrared factorization scale, it can be implemented with little effort for any observable where the GC is relevant. The scheme depends on the renormalon norm of the GC which has to be supplemented independently. We apply the scheme to the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions of $τ$ hadronic spectral function moments. These expansions exhibit a long-standing discrepancy for moments used in high-precision determinations of the strong coupling in the commonly used GC scheme that is not renormalon-free. We show that the scheme is capable of resolving the FOPT-CIPT discrepancy problem. At the same time, the perturbative behaviour of the moments that previously showed bad convergence properties and for which the non-perturbative corrections from the GC are sizeable, is substantially improved. The new GC scheme may provide a powerful theoretical tool for future phenomenological applications.

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arXiv2021

Reconciling the FOPT and CIPT Predictions for the Hadronic Tau Decay Rate

In a recent work it was suggested that the discrepancy observed in the perturbation series behavior of the $τ$ hadronic decay rate determined in the FOPT and CIPT approaches can be explained from a different infrared sensitivity inherent to both methods, assuming that the major source of the discrepancy is the asymptotic behavior of the series related to the gluon condensate renormalon. This implies that the predictions of both methods may be reconciled in infrared subtracted perturbation theory. In this talk we explore this implication concretely in the large-$β_0$ approximation, where the perturbation series is known to all orders, using a renormalon-free scheme for the gluon condensate.

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arXiv2021

Higher-order behaviour of two-point current correlators

Estimates of higher-order contributions for perturbative series in QCD, in view of their asymptotic nature, are delicate, though indispensable for a reliable error assessment in phenomenological applications. In this work, the Adler function and the scalar correlator are investigated, and models for Borel transforms of their perturbative series are constructed, which respect general constraints from the operator product expansion and the renormalisation group. As a novel ingredient, the QCD coupling is employed in the so-called $C$-scheme, which has certain advantages. For the Adler function, previous results obtained directly in the $\overline{\rm MS}$ scheme are supported. Corresponding results for the scalar correlation function are new. It turns out that the substantially larger perturbative corrections for the scalar correlator in $\overline{\rm MS}$ are dominantly due to this scheme choice, and can be largely reduced through more appropriate renormalisation schemes, which are easy to realise in the $C$-scheme.

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arXiv2018

Absence of even-integer $ζ$-function values in Euclidean physical quantities in QCD

At order $α_s^4$ in perturbative quantum chromodynamics, even-integer $ζ$-function values are present in Euclidean physical correlation functions like the scalar quark correlation function or the scalar gluonium correlator. We demonstrate that these contributions cancel when the perturbative expansion is expressed in terms of the so-called $C$-scheme coupling $\hatα_s$ which has recently been introduced in Ref. [1]. It is furthermore conjectured that a $ζ_4$ term should arise in the Adler function at order $α_s^5$ in the $\overline{\rm MS}$-scheme, and that this term is expected to disappear in the $C$-scheme as well.

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arXiv2016

Scheme variations of the QCD coupling and tau decays

The QCD coupling, $α_s$, is not a physical observable since it depends on conventions related to the renormalization procedure. Here we discuss a redefinition of the coupling where changes of scheme are parametrised by a single parameter $C$. The new coupling is denoted $\hat α_s$ and its running is scheme independent. Moreover, scheme variations become completely analogous to renormalization scale variations. We discuss how the coupling $\hat α_s$ can be used in order to optimize predictions for the inclusive hadronic decays of the tau lepton. Preliminary investigations of the $C$-scheme in the presence of higher-order terms of the perturbative series are discussed here for the first time.

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arXiv2016

Scheme variations of the QCD coupling

The Quantum Chromodynamics (QCD) coupling $α_s$ is a central parameter in the Standard Model of particle physics. However, it depends on theoretical conventions related to renormalisation and hence is not an observable quantity. In order to capture this dependence in a transparent way, a novel definition of the QCD coupling, denoted by $\hat a$, is introduced, whose running is explicitly renormalisation scheme invariant. The remaining renormalisation scheme dependence is related to transformations of the QCD scale $Λ$, and can be parametrised by a single parameter $C$. Hence, we call $\hat a$ the $C$-scheme coupling. The dependence on $C$ can be exploited to study and improve perturbative predictions of physical observables. This is demonstrated for the QCD Adler function and hadronic decays of the $τ$ lepton.

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arXiv2016

Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling

In this work, the perturbative QCD series of the scalar correlation function $Ψ(s)$ is investigated. Besides ${\rm Im}Ψ(s)$, which is relevant for Higgs decay into quarks, two other physical correlators, $Ψ^{"}(s)$ and $D^L(s)$, have been employed in QCD applications like quark mass determinations or hadronic $τ$ decays. $D^L(s)$ suffers from large higher-order corrections and, by resorting to the large-$β_0$ approximation, it is shown that this is related to a spurious renormalon ambiguity at $u=1$. Hence, this correlator should be avoided in phenomenological analyses. Moreover, it turns out advantageous to express the quark mass factor, introduced to make the scalar current renormalisation group invariant, in terms of the renormalisation invariant quark mass $\hat m_q$. To further study the behaviour of the perturbative expansion, we introduce a QCD coupling $\hatα_s$, whose running is explicitly renormalisation scheme independent. The scheme dependence of $\hatα_s$ is parametrised by a single parameter $C$, being related to transformations of the QCD scale parameter $Λ$. It is demonstrated that appropriate choices of $C$ lead to a substantial improvement in the behaviour of the perturbative series for $Ψ^{"}(s)$ and ${\rm Im}Ψ(s)$.

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arXiv2016

Scheme variations of the QCD coupling and hadronic $τ$ decays

The Quantum Chromodynamics (QCD) coupling, $α_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by $\hatα_s$, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling $\hatα_s$ is parameterized by a single parameter $C$, related to transformations of the QCD scale $Λ$. It is demonstrated that appropriate choices of $C$ can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study $e^+e^-$ scattering and decays of the $τ$ lepton into hadrons, both being governed by the QCD Adler function.

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arXiv2015

Anomalous dimensions of four-quark operators and renormalon structure of mesonic two-point correlators

In this work, we calculate leading-order anomalous dimension matrices for dimension-6 four-quark operators which appear in the operator product expansion of flavour non-diagonal and diagonal vector and axial-vector two-point correlation functions. The infrared renormalon structure corresponding to four-quark operators is reviewed and it is investigated how the eigenvalues of the anomalous dimension matrices influence the singular behaviour of the $u=3$ infrared renormalon pole. It is found that compared to the large-$β_0$ approximation where at most quadratic poles are present, in full QCD at $N_f=3$ the most singular pole is more than cubic with an exponent $κ\approx 3.2$.

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arXiv2015

Improved anatomy of epsilon'/epsilon in the Standard Model

We present a new analysis of the ratio epsilon'/epsilon within the Standard Model (SM) using a formalism that is manifestly independent of the values of leading (V-A)x(V-A) QCD penguin, and EW penguin hadronic matrix elements of the operators Q_4, Q_9, and Q_10, and applies to the SM as well as extensions with the same operator structure. It is valid under the assumption that the SM exactly describes the data on CP-conserving K -> pi pi amplitudes. As a result of this and the high precision now available for CKM and quark mass parameters, to high accuracy epsilon'/epsilon depends only on two non-perturbative parameters, B_6^(1/2) and B_8^(3/2), and perturbatively calculable Wilson coefficients. Within the SM, we are separately able to determine the hadronic matrix element _0 from CP-conserving data, significantly more precisely than presently possible with lattice QCD. Employing B_6^(1/2) = 0.57+-0.19 and B_8^(3/2) = 0.76+-0.05, extracted from recent results by the RBC-UKQCD collaboration, we obtain epsilon'/epsilon = (1.9+-4.5) 10^-4, substantially more precise than the recent RBC-UKQCD prediction and 2.9 sigma below the experimental value (16.6+-2.3) 10^-4, with the error being fully dominated by that on B_6^(1/2). Even discarding lattice input completely, but employing the recently obtained bound B_6^(1/2) <= B_8^(3/2) <= 1 from the large-N approach, the SM value is found more than 2 sigma below the experimental value. At B_6^(1/2) = B_8^(3/2) = 1, varying all other parameters within one sigma, we find epsilon'/epsilon = (8.6+-3.2) 10^-4. We present a detailed anatomy of the various SM uncertainties, including all sub-leading hadronic matrix elements, briefly commenting on the possibility of underestimated SM contributions as well as on the impact of our results on new physics models.

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arXiv2013

Low-energy constants and condensates from the tau hadronic spectral functions

We use results of fits to the OPAL spectral data, obtained from non-strange hadronic τdecays, to evaluate the difference between the vector and axial current correlators, Π_{V-A}(Q^2). The behavior of Π_{V-A}(Q^2) near euclidean momentum Q^2=0 is used to determine the effective low-energy constants L_10^eff and C_87^eff related to the renormalized low-energy constants L_10^r and C_87^r in the chiral lagrangian. We also investigate how well two-loop chiral perturbation theory describes Π_{V-A}(Q^2) as a function of Q^2. This is the first determination of L_10^eff and C_87^eff to employ a fully self-consistent model for the violations of quark-hadron duality in both the vector and axial channels. We also discuss the values of the coefficients C_{6,V-A} and C_{8,V-A} governing the dimension six and eight contributions to the operator product expansion representation of Π_{V-A}(Q^2).

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arXiv2013

Determination of alpha_s from tau decays

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.

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arXiv2012

The strong coupling from tau decays without prejudice

We review our recent determination of the strong coupling α_s from the OPAL data for non-strange hadronic tau decays. We find that α_s(m^2_τ) =0.325+-0.018 using fixed-order perturbation theory, and α_s(m^2_τ)=0.347+-0.025 using contour-improved perturbation theory. At present, these values supersede any earlier determinations of the strong coupling from hadronic tau decays, including those from ALEPH data.

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arXiv2012

Perturbative expansion of tau hadronic spectral function moments and alpha_s extractions

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 should be avoided because of their perturbative instability. This conclusion is corroborated by a simplified alpha_s extraction from individual moments. Furthermore, under reasonable assumptions for the higher-order behaviour of the perturbative series, fixed-order perturbation theory (FOPT) provides the preferred framework for the renormalization group improvement of all moments that show good perturbative behaviour. Finally, we provide further evidence for the plausibility of the description of the Adler function in terms of a small number of leading renormalon singularities.

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arXiv2012

The scalar gluonium correlator: large-beta_0 and beyond

The investigation of the scalar gluonium correlator is interesting because it carries the quantum numbers of the vacuum and the relevant hadronic current is related to the anomalous trace of the QCD energy-momentum tensor in the chiral limit. After reviewing the purely perturbative corrections known up to next-next-to-leading order, the behaviour of the correlator is studied to all orders by means of the large-beta_0 approximation. Similar to the QCD Adler function, the large-order behaviour is governed by the leading ultraviolet renormalon pole. The structure of infrared renormalon poles, being related to the operator product expansion are also discussed, as well as a low-energy theorem for the correlator that provides a relation to the renormalisation group invariant gluon condensate, and the vacuum matrix element of the trace of the QCD energy-momentum tensor.

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arXiv2012

An updated determination of α_s from tau decays

Employing our previous framework to treat non-perturbative effects self-consistently, including duality violations, we update the determination of the strong coupling, α_s, using a modified version of the 1998 OPAL data, updated to reflect current values of exclusive mode hadronic τdecay branching fractions. Our best n_f=3 values from the updated OPAL data are α_s(m^2_τ)=0.325+-0.018 and α_s(m^2_τ)=0.347+-0.025 in fixed-order and contour-improved perturbation theory, respectively. To account for non-perturbative effects, non-linear, multi-parameter fits are necessary. We have, therefore, investigated the posterior probability distribution of the model parameters underlying our fits in more detail. We find that OPAL data alone provide only weak constraints on some of the parameters needed to model duality violations, especially in the case of fits involving axial vector channel data, making additional prior assumptions on the expected size of these parameters necessary at present. We provide evidence that this situation could be greatly improved if hadronic spectral functions based on the high-statistics BaBar and Belle data were to be made available.

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