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The constants that appear in ([ref]) are given by [ref] $b=-β_1/(2β_0^2)$ and [equation] Note that we have corrected some misprints in the expression for $b$ and $s_2$ given in [ref] (eqs.","intent_p":0.71,"contests_p":0.86},{"arxiv_id":"1606.06166","title":"Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling","url":"/paper/1606.06166","section":"Introduction","sentence":"[ref] , where the scalar correlation function has been calculated in the large-$N_f$ approximation [ref] , or relatedly the large-$β_0$ approximation [ref] (for a review see [ref] ), to all orders in the strong coupling.[For historical reasons, we shall speak about the “large-$β_0$” approximation, although in the notation employed in this work, the leading coefficient of the $β$-function is termed $β_1$.] However, as will be discussed in more detail below, the large-$β_0$ approximation does not provide a satisfactory representation of the scalar correlator in full QCD.","intent_p":0.48,"contests_p":0.75}]},{"kind":"extends","label":"Builds on it","papers":1,"sentences":2,"quotes":[{"arxiv_id":"2106.01614","title":"Higher-order behaviour of two-point current correlators","url":"/paper/2106.01614","section":"General renormalon-pole structure","sentence":"[ref] , but closely follows the material already presented there and in part in the review [ref] .","intent_p":0.9,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":8,"sentences":8,"quotes":[{"arxiv_id":"2111.06792","title":"The QCD Adler function and the muon $g-2$ anomaly from renormalons","url":"/paper/2111.06792","section":"Introduction","sentence":"We estimate the large order behavior in Eq. [ref] using the “Naive non-abelianization”, namely the $δ_n∼0$ for $n≥4$, such that we are able to estimate $d_n$ to all orders from the fermion bubble graphs [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1909.12134","title":"Renormalons in integrable field theories","url":"/paper/1909.12134","section":"Large order behavior from renormalons","sentence":"Using standard RG arguments (see e.g. [ref] ), and evaluating the non-perturbative correction at $μ=Q$, we find","intent_p":0.81,"contests_p":null},{"arxiv_id":"2108.08897","title":"On linear power corrections in certain collider observables","url":"/paper/2108.08897","section":"Introduction","sentence":"Indeed, in such cases the appearance of linear power corrections can be investigated by computing $𝒪(α_s)$ corrections to the process (and observable) under consideration that originate from virtual exchanges and real emissions of massive gluons, in the limit of a small gluon mass $λ$, see Ref. [ref] .[Since by assumption the underlying process does not contain gluons, this does not lead to any issue with gauge invariance.] The presence of terms that are linear in $λ$ implies that a particular observable receives leading power corrections that are of the type $𝒪(Λ_QCD/Q)$, while their absence can be interpreted as an indication that non-perturbative corrections are further suppressed.","intent_p":0.84,"contests_p":null},{"arxiv_id":"1706.08526","title":"On the Light Massive Flavor Dependence of the Large Order Asymptotic Behavior and the Ambiguity of the Pole Mass","url":"/paper/1706.08526","section":"General Comments and Estimation Method","sentence":"They adopted a prescription given in Ref. [ref] , which defined the top quark pole mass uncertainty as the imaginary part of the inverse Borel integral of Eq. [ref], $Δm_Borel^(=5)$, divided by $π$, which gives about $65$ MeV.","intent_p":0.95,"contests_p":null},{"arxiv_id":"2011.14114","title":"Infrared Renormalons in Kinematic Distributions for Hadron Collider Processes","url":"/paper/2011.14114","section":"Introduction","sentence":"A very valuable method for the study of IR renormalons is the so-called large-$$ approximation (see [ref] and references therein).","intent_p":0.81,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":2,"sentences":3,"quotes":[{"arxiv_id":"2111.06792","title":"The QCD Adler function and the muon $g-2$ anomaly from renormalons","url":"/paper/2111.06792","section":"Introduction","sentence":"The Adler function is known up to $n=3$ [ref] or up to $𝒪(α_s^4)$, from which the coefficients $d_n$ and $δ_n$ can be taken from Ref. [ref] .","intent_p":0.83,"contests_p":null},{"arxiv_id":"1502.02698","title":"Flavor dependence of normalization constant for an infrared renormalon","url":"/paper/1502.02698","section":"Introduction","sentence":"where $ν=2β_1/β_0^2$, and the following large-$β_0$ result is used [ref] : C_0=3/4C_F e^10/3 .","intent_p":0.99,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":6,"sentences":7,"quotes":[{"arxiv_id":"1701.00347","title":"A discussion on leading renormalon in the pole mass","url":"/paper/1701.00347","section":"Leading renormalon from recurrence relation","sentence":"This result is identical to the leading renormalon in the pole mass (see for instance Refs. [ref] ).","intent_p":0.83,"contests_p":null},{"arxiv_id":"1802.04334","title":"On the Light Massive Flavor Dependence of the Top Quark Mass","url":"/paper/1802.04334","section":"Pole Mass Ambiguity","sentence":"The recent estimate of the ambiguity in Ref. [ref] following the prescription of [ref] is about $60%$ smaller and coincides with the size of the minimal correction term $Δ(n_min)$ and also the scale variation at $(α_s^min)$ for $R=163$ GeV.","intent_p":0.95,"contests_p":null},{"arxiv_id":"1704.01580","title":"The MSR Mass and the ${\\cal O}(\\Lambda_{\\rm QCD})$ Renormalon Sum Rule","url":"/paper/1704.01580","section":"QCD beta-Function and Coefficients","sentence":"The coefficients $g_ℓ$ agree with the coefficients $s_ℓ$ given in Refs. [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"1510.03812","title":"Anomalous dimensions of four-quark operators and renormalon structure of mesonic two-point correlators","url":"/paper/1510.03812","section":"Flavour non-diagonal vector and axial-vector correlators","sentence":"[ref] , we find complete agreement.[The same subset of anomalous dimensions was already considered in a previous attempt to investigate the $u=3$ renormalon structure [ref] .] Regarding the RGE, again, it is straightforward to verify that by using $γ̂_Q_+^(1)$ and the coefficient function of eq.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1401.7999","title":"Perturbative expansion of the plaquette to ${\\cal O}(\\alpha^{35})$ in four-dimensional SU(3) gauge theory","url":"/paper/1401.7999","section":"Summary and Conclusions","sentence":"The above value is by a factor of 3.5 bigger than the large-$β_0$ result and by about one order of magnitude larger than many previous estimates of the ambiguity of the gluon condensate, see, for instance, Eq. 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[ref] .","intent_p":0.97,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2310.08178","title":"Elimination of QCD Renormalization Scale and Scheme Ambiguities","url":"/paper/2310.08178","section":"Introduction","sentence":"This procedure is scheme-independent and leads to results free from divergent renormalon terms [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"2105.04819","title":"Conformal mappings in perturbative QCD","url":"/paper/2105.04819","section":"Introduction","sentence":"The divergent pattern can be inferred alternatively from particular classes of Feynman diagrams, which indicate a factorial growth of the expansion coefficients in both QED [ref] , [ref] and QCD [ref] , [ref] , [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":105,"sentences":146,"quotes":[{"arxiv_id":"2002.12419","title":"Renormalons in integrated spectral function moments and $\\alpha_s$ extractions","url":"/paper/2002.12419","section":"Introduction","sentence":"These singularities are the renormalons of perturbation theory [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1002.2968","title":"A note on renormalon models for the determination of alpha_s(M_tau)","url":"/paper/1002.2968","section":"Introduction","sentence":"[ref] , based on renormalon calculus [ref] .","intent_p":0.86,"contests_p":null},{"arxiv_id":"0906.5463","title":"Hadronisation corrections for jets in the k_t algorithm","url":"/paper/0906.5463","section":"Introduction","sentence":"Analytical models based on renormalons [ref] have in the past been met with great success in the description of LEP and HERA event-shape variables [ref] , but have not really been utilised outside that context.","intent_p":0.97,"contests_p":null},{"arxiv_id":"1401.7999","title":"Perturbative expansion of the plaquette to ${\\cal O}(\\alpha^{35})$ in four-dimensional SU(3) gauge theory","url":"/paper/1401.7999","section":"Renormalon analysis of the plaquette","sentence":"We skip the detailed derivation, which is quite standard (see, e.g., Ref. [ref] ), and directly state the result of the Borel integral for large orders $n$: [equation] Note that the parameters $b_1$ and $b_2$ that describe the leading pre-asymptotic corrections depend on the expansion coefficients $c_0$ and $c_1$, defined in CP, of the Wilson coefficient of the gluon condensate.","intent_p":0.87,"contests_p":null},{"arxiv_id":"2105.11222","title":"On the Difference between FOPT and CIPT for Hadronic Tau Decays","url":"/paper/2105.11222","section":"Introduction","sentence":"In this context a number of theoretical studies [ref] were carried out using the renormalon calculus [ref] based on concrete models for the Borel (transformation) function of the Adler function.","intent_p":0.84,"contests_p":null}]}],"unlabelled_sentences":243},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. 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