Higher-order behaviour of two-point current correlators

Matthias Jamin

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Higher-order behaviour of two-point current correlators

Matthias Jamin

High Energy Physics - Phenomenology · Submitted 3 Jun 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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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What the abstract itself states, as probabilities: claims first 0.15 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.95 · mentions code or data availability 0.02.

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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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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	background 1.00	0.05	0.03	asserted 0.99
s1	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.	contribution 0.88	0.94	0.07	asserted 1.00
s2	As a novel ingredient, the QCD coupling is employed in the so-called $C$-scheme, which has certain advantages.	method 0.60	0.77	0.05	asserted 0.89
s3	For the Adler function, previous results obtained directly in the $\overline{\rm MS}$ scheme are supported.	result 0.93	0.31	0.07	asserted 0.95
s4	Corresponding results for the scalar correlation function are new.	contribution 0.64	0.86	0.07	asserted 1.00
s5	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.	interpretation 0.53	0.91	0.71	asserted 1.00

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Original abstract

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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5 arXiv papers cite this in 13 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 10 sentences without a confident label

Uses its data or values 2 papers

We also include an $𝒪(α_s^5)$ contribution, using as input for the fifth-order coefficient the value $c_51=283±142$, which covers the range of estimates found in dedicated studies [ref] .

Quark-hadron duality and the determination of $\alpha_s$ from hadronic $\tau$ decay: facts vs. myths · Theoretical framework · 0.95
There are several independent estimates of this 6-loop coefficient, all of them in good agreement, and we adopt [equation] which covers all the estimates available in the recent literature [ref] .

Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments I: Renormalon-Free Gluon Condensate Scheme · Theoretical Setup · 0.96

Compares with it 1 paper

The coefficients $d_n,1$ were calculated from the estimated values of $c_n$ and $r_n$, the coefficients of the imaginary part and the second derivative of the scalar correlator respectively, given in Tab. [ref]; the final results for $d_n,1$ are in Tab. [ref].[Performing our analysis with $N_f=3$ we find $d_5,1 =77808 ±1400$ in excellent agreement with the recent estimate of Ref. [ref] , based on a model for the Borel transform.] The central values are calculated as the average between the largest and the smallest estimated coefficients.

Higher-order QCD corrections to $H\to b\bar b$ from rational approximants · Final results and uncertainties in H to bb · 0.89

What it cites · 24 sentences without a confident label

Builds on 2 papers

[ref] , but closely follows the material already presented there and in part in the review [ref] .

alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory · General renormalon-pole structure · 0.90
[ref] , but closely follows the material already presented there and in part in the review [ref] .

Renormalons · General renormalon-pole structure · 0.90

Uses the method or tool of 1 paper

[ref] , we have included the lowest lying IR renormalon pole at $u=2$, for which most information is available, as well as the next-to-leading IR pole at $u=3$, together with a UV pole at $u=-1$ which dominates the perturbative series at large orders.

alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory · Borel model for the Adler function · 0.84

Uses data or values from 8 papers

Again, setting $N_c=3$ and $N_f=3$, as well as employing the $$-scheme, the coefficients $d_n,1$ up to $(^4)$ were found to be [ref] : [equation]

Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses · The scalar two-point correlator · 1.00
Again, setting $N_c=3$ and $N_f=3$, as well as employing the $$-scheme, the coefficients $d_n,1$ up to $(^4)$ were found to be [ref] : [equation]

Correlator of the quark scalar currents and \Gamma_{tot}(H --> hadrons) at O(\alpha_s^3) in pQCD · The scalar two-point correlator · 1.00
The independent coefficients $c_n,1$ are known analytically up to order $^4$ [ref] .

Hadronic Z- and tau-Decays in Order alpha_s^4 · The vector two-point correlator · 0.84

Compares with 3 papers

[ref] , which might give an idea of the uncertainties induced by reasonable assumptions about the Borel model.

alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory · Borel model for the Adler function · 0.97
Our result can be compared to other recent predictions for $c_5,1$ from Padé approximants [ref] , $c_5,1=277±51$, or conformal mappings [ref] , $c_5,1=287±40$, finding good agreement.

Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings · Borel model for the Adler function · 0.99
Our result can be compared to other recent predictions for $c_5,1$ from Padé approximants [ref] , $c_5,1=277±51$, or conformal mappings [ref] , $c_5,1=287±40$, finding good agreement.

Higher-order QCD corrections to hadronic $\tau$ decays from Pad\'e approximants · Borel model for the Adler function · 0.99

Cites as background 1 paper

In this work, a Borel model for the vector correlation function, or Adler function, that has already been presented in the literature [ref] , was reviewed.

alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory · Summary · 0.87

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