Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case

Antonio Pineda

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Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case

Antonio Pineda

High Energy Physics - Phenomenology · Submitted 17 Jan 2011

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

The authors' main claim We compute the next-to-leading logarithmic (NLL) ultrasoft running of the spin-independent singlet potentials up to ${\cal O}(1/m^2)$, and the corresponding contribution to the spectrum.

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arXiv ID1101.3269 (version 3)

Pith ID47ILSSYX, Pith's permanent record of this paper and its review

CitationAntonio Pineda. "Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case." arXiv:1101.3269 (2011). https://pith.science/paper/47ILSSYX

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.08 · mentions code or data availability 0.02.

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We compute the next-to-leading logarithmic (NLL) ultrasoft running of the spin-independent singlet potentials up to ${\cal O}(1/m^2)$, and the corresponding contribution to the spectrum. This includes the static energy at next-to-next-to-next-to-leading logarithmic (NNNLL) order. As a byproduct of these results one could obtain the heavy quarkonium spectrum with N$^3$LL accuracy for $l\not=0$ (angular momentum) and $s=0$ (spin) states, setting the stage for the full analytic and numerical N$^3$LL analysis of such quantity. We also compute the next-to-next-to-next-to-next-to-leading order (N$^4$LO) ultrasoft spin-independent contribution to the heavy quarkonium mass and static energy.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute the next-to-leading logarithmic (NLL) ultrasoft running of the spin-independent singlet potentials up to ${\cal O}(1/m^2)$, and the corresponding contribution to the spectrum.	contribution 0.97	0.96	0.68	asserted 1.00
s1	This includes the static energy at next-to-next-to-next-to-leading logarithmic (NNNLL) order.	result 0.58	0.81	0.11	asserted 1.00
s2	As a byproduct of these results one could obtain the heavy quarkonium spectrum with N$^3$LL accuracy for $l\not=0$ (angular momentum) and $s=0$ (spin) states, setting the stage for the full analytic and numerical N$^3$LL analysis of such quantity.	interpretation 0.75	0.46	0.19	hedged possibility 1.00
s3	We also compute the next-to-next-to-next-to-next-to-leading order (N$^4$LO) ultrasoft spin-independent contribution to the heavy quarkonium mass and static energy.	result 0.62	0.95	0.18	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.88.

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The paper

Original abstract

We compute the next-to-leading logarithmic (NLL) ultrasoft running of the spin-independent singlet potentials up to ${\cal O}(1/m^2)$, and the corresponding contribution to the spectrum. This includes the static energy at next-to-next-to-next-to-leading logarithmic (NNNLL) order. As a byproduct of these results one could obtain the heavy quarkonium spectrum with N$^3$LL accuracy for $l\not=0$ (angular momentum) and $s=0$ (spin) states, setting the stage for the full analytic and numerical N$^3$LL analysis of such quantity. We also compute the next-to-next-to-next-to-next-to-leading order (N$^4$LO) ultrasoft spin-independent contribution to the heavy quarkonium mass and static energy.

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

High precision fundamental constants at the TeV scale
hep-ph 2014-05 conditional novelty 3.0 of 10

The report compiles 2014 determinations of the strong coupling and the top quark mass, shows that independent extractions scatter beyond their quoted uncertainties, and recommends a standing working group plus scheme-...
Review of Heavy Quarkonium at weak coupling
hep-ph 2011-11 accept novelty 2.0 of 10

pNRQCD is presented as a systematically derived effective field theory that reproduces heavy quarkonium dynamics via Schrödinger equations, with all matching and renormalization steps carried out in dimensional regula...

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15 arXiv papers cite this in 28 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 · 18 sentences without a confident label

Uses its method or tool 1 paper

This can be done starting from the off-shell amplitude as described in [ref] (see also [ref] for a brief summary), or by adopting an effective field theory approach [ref] .[For a comparison of quantum and classical approaches, see [ref] .]

Dark matter bound states via emission of scalar mediators · Radiative transition amplitude · 0.91

Uses its data or values 1 paper

δE_us^|_LO = -C_F r^2(ΔV)^3 V_A^2 (ν_us) /9 π (6lnΔV/ν_us+6ln2-5) , δE_us^|_NLO = C_F r^2(ΔV)^3 V_A^2 ^2(ν_us) /108 π^2 (18 β_0 ln^2(ΔV/ν_us ) . -6 (C_A (13+4 π^2)-2 β_0 (-5+3ln2)) ln(ΔV/ν_us ) -2 C_A (-84+39 ln2+4 π^2 (-2+3ln2)+72 ζ(3))+β_0 (67+3 π^2-60 ln2+18ln^2 2)) , where we take the next-to-leading order (NLO) expression from [ref] .

Determination of $\alpha(M_z)$ from an hyperasymptotic approximation to the energy of a static quark-antiquark pair · Hyperasymptotic expansion of the static energy · 0.88

Compares with it 3 papers

The equivalence of the results obtained in Ref. [ref] and the ones in this work (and in Refs. [ref] ) is technically non-trivial and indicates that the structural differences in the vNRQCD and pNRQCD formulations might not affect the description of purely ultrasoft effects.

Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential · Conclusion · 0.98
Apart from the poles in $1/ϵ$, we have [ref] [equation] while in the large-$$ approximation we have [equation] for $n_f=0$.

Renormalon free part of an ultrasoft correction to the static QCD potential · Discussion · 0.94
This RG equation with respect to $μ$ is different from the RG equations with respect to $μ_f$ considered in Refs. [ref] , which are associated with the IR divergences with respect to the soft scale.

On renormalons of static QCD potential at $u=1/2$ and $3/2$ · $u=3/2$ renormalon · 0.87

Cites it as background 3 papers

In addition, the accuracy of the perturbative prediction of the static potential has also improved significantly over the years [ref] .

Determination of $\alpha(M_z)$ from an hyperasymptotic approximation to the energy of a static quark-antiquark pair · Introduction · 0.83
These include predictions for top quark pair production [ref] ,[ In Ref. [ref] next-to-next-to-leading logarithmic (NNLL) corrections have been obtained, see also [ref] .] the decay of the $Υ(1S)$ meson [ref] , and energy levels of heavy quarkonia ground and excited states [ref] together with phenomenological applications [ref] .

Matching coefficients in NRQCD to two-loop accuracy · Introduction · 0.91
The framework of pNRQCD provides an alternative formulation of the EFT where the soft and ultrasoft scales are treated independently–for more of the setup, see Refs. [ref] .

Manifestly Soft Gauge Invariant Formulation of vNRQCD · Introduction · 0.96

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