Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential

Andre H. Hoang; Maximilian Stahlhofen

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Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential

Andre H. Hoang, Maximilian Stahlhofen

High Energy Physics - Phenomenology · Submitted 1 Feb 2011

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

The authors' main claim The results are numerically important and complete the description of ultrasoft next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair production and annihilation close to threshold.

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Using the nonrelativistic effective field theory vNRQCD, we determine the contribution to the next-to-leading logarithmic (NLL) running of the effective quark-antiquark potential at order v (1/mk) from diagrams with one potential and two ultrasoft loops, v being the velocity of the quarks in the c.m. frame. The results are numerically important and complete the description of ultrasoft next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair production and annihilation close to threshold.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Using the nonrelativistic effective field theory vNRQCD, we determine the contribution to the next-to-leading logarithmic (NLL) running of the effective quark-antiquark potential at order v (1/mk) from diagrams with one potential and two ultrasoft loops, v being the velocity of the quarks in the c.m. frame.	contribution 0.97	0.96	0.45	asserted 1.00
s1	The results are numerically important and complete the description of ultrasoft next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair production and annihilation close to threshold.	interpretation 0.97	0.69	0.48	asserted 1.00

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The paper

Original abstract

Using the nonrelativistic effective field theory vNRQCD, we determine the contribution to the next-to-leading logarithmic (NLL) running of the effective quark-antiquark potential at order v (1/mk) from diagrams with one potential and two ultrasoft loops, v being the velocity of the quarks in the c.m. frame. The results are numerically important and complete the description of ultrasoft next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair production and annihilation close to threshold.

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References

Forward citations

Cited by 3 Pith papers

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

Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter
hep-ph 2018-05 conditional novelty 6.0 of 10

The gluon-mediated and photon-like contributions to radiative bound-state formation add coherently rather than canceling, raising the capture rate into the tightest bound state and shifting dark matter coannihilation bounds.
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...

How the literature uses it

12 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 · 22 sentences without a confident label

Uses its method or tool 2 papers

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
Here, we will follow the conventions of [ref] .

Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter · The non-relativistic Hamiltonian from effective field theory · 0.93

Uses its data or values 1 paper

The ultrasoft contribution to $ξ^NNLL_m$ determined in Ref. [ref] reads[The form of Eq. [ref] implies the convention that the $z$ and $ω=1/(2-z)$ parameters in $ξ^NLL$, as given in Ref. [ref] , are according to Eq. [ref].] [equation] with [equation] Together with $ξ^NNLL_nm$ from Ref. [ref] it gives the dominant contribution to the NNLL running of $c_1(ν)$ (in the $$ scheme).

NNLL top-antitop production at threshold · Current renormalization · 0.85

Compares with it 1 paper

We will demonstrate that (a) we recover the same sign as in [ref] using our conventions <ref>, and that (b) this sign disagrees with the result of [ref] .

Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter · The non-relativistic Hamiltonian from effective field theory · 0.92

What it cites · 67 sentences without a confident label

Contests 1 paper

At LL order it has the form [equation] The first term arises from soft renormalization and the second represents the evolution from ultrasoft UV divergences.[ There is a misprint in Eq.(4) of Ref. [ref] where a factor $1/2$ is missing for the soft contributions.

Three-Loop Anomalous Dimension of the Heavy Quark Pair Production Current in Non-Relativistic QCD · Introduction · contest 0.90

Uses the method or tool of 4 papers

we instead introduce the sum operators $O_ki$ as they are suitable to carry out the ultrasoft renormalization procedure [ref] .

Three-Loop Anomalous Dimension of the Heavy Quark Pair Production Current in Non-Relativistic QCD · Theoretical Setup · 0.88
we instead introduce the sum operators $O_ki$ as they are suitable to carry out the ultrasoft renormalization procedure [ref] .

Ultrasoft Renormalization in Non-Relativistic QCD · Theoretical Setup · 0.88
For the $=4-D/2$ expansion of the hypergeometric functions resulting from the two-loop integrations we used the Mathematica package HypExp 1.1 [ref] and checked the results numerically.

HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters · NLL Calculation · 1.00

Uses data or values from 2 papers

The ultrasoft one-loop coefficients $A_i$ were given in Ref. [ref] and can be read off Eq. [ref].

Ultrasoft Renormalization in Non-Relativistic QCD · NLL Calculation · 0.92
The next-to-next-to-leading order (NNLO) predictions in this “fixed-order” approach were estimated to have a normalization uncertainty of order $20%$ [ref] .

Top-Antitop Pair Production close to Threshold: Synopsis of recent NNLO Results · Introduction · 0.85

Compares with 4 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.

Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case · Conclusion · 0.98
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.

Two-Loop Ultrasoft Running of the O(v^2) QCD Quark Potentials · Conclusion · 0.98
Adding them to the $$ diagrams [ref] a-c gives [equation] The result is exactly the same as obtained in Refs. [ref] where Coulomb gauge has been used.

Ultrasoft Renormalization in Non-Relativistic QCD · LL Calculation · 1.00

Cites as support 1 paper

As demonstrated in Ref. [ref] the additional potential loop entails the renormalization of the $O_ki^(1,T)$ sum operators instead of the potentials in Eq. ([ref]).

Ultrasoft Renormalization in Non-Relativistic QCD · Renormalization Procedure · 0.96

Cites as background 7 papers

Except for the coefficient of the Coulomb potential $V_c^(s)$ [ref] and for the spin-dependent potential $V_s^(s)$ [ref] no complete determination for the subleading evolution exists at present.

$M(B^*_c)-M(B_c)$ Splitting from Nonrelativistic Renormalization Group · Introduction · 0.85
Except for the coefficient of the Coulomb potential $V_c^(s)$ [ref] and for the spin-dependent potential $V_s^(s)$ [ref] no complete determination for the subleading evolution exists at present.

Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum · Introduction · 0.85
Except for the coefficient of the Coulomb potential $V_c^(s)$ [ref] and for the spin-dependent potential $V_s^(s)$ [ref] no complete determination for the subleading evolution exists at present.

Ultrasoft Renormalization in Non-Relativistic QCD · Introduction · 0.85

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