RECORD
Covariant calculation of a two-loop test of nonrelativistic QCD factorization
High Energy Physics - Phenomenology · Submitted 12 Oct 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The results of both calculations are consistent with the NRQCD factorization conjecture.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We test the nonrelativistic QCD factorization conjecture for inclusive quarkonium production at two loops by carrying out a covariant calculation of the nonrelativistic quantum chromodynamics (NRQCD) long-distance matrix element (LDME) for a heavy-quark pair in an $S$-wave, color-octet state to fragment into a heavy-quark pair in a color-singlet state of arbitrary orbital angular momentum. The NRQCD factorization conjecture for the universality of the LDME requires that infrared divergences that it contains be independent of the direction of the Wilson line that appears in its definition. We find this to be the case in our calculation. The results of our calculation differ in some respects from those of a previous calculation that was carried out by Nayak, Qiu, and Sterman using light-cone methods. We have identified the sources of some of these differences. The results of both calculations are consistent with the NRQCD factorization conjecture. However, the general principle that underlies this confirmation of NRQCD factorization at two-loop order has yet to be revealed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We test the nonrelativistic QCD factorization conjecture for inclusive quarkonium production at two loops by carrying out a covariant calculation of the nonrelativistic quantum chromodynamics (NRQCD) long-distance matrix element (LDME) for a heavy-quark pair in an $S$-wave, color-octet state to fragment into a heavy-quark pair in a color-singlet state of arbitrary orbital angular momentum. | contribution 0.99 | 0.96 | 0.09 | asserted 0.93 |
| s1 | The NRQCD factorization conjecture for the universality of the LDME requires that infrared divergences that it contains be independent of the direction of the Wilson line that appears in its definition. | background 1.00 | 0.06 | 0.06 | asserted 0.98 |
| s2 | We find this to be the case in our calculation. | result 1.00 | 0.97 | 0.37 | asserted 1.00 |
| s3 | The results of our calculation differ in some respects from those of a previous calculation that was carried out by Nayak, Qiu, and Sterman using light-cone methods. | result 0.91 | 0.50 | 0.05 | asserted 0.99 |
| s4 | We have identified the sources of some of these differences. | contribution 0.51 | 0.92 | 0.04 | asserted 0.98 |
| s5 | The results of both calculations are consistent with the NRQCD factorization conjecture. | result 0.70 | 0.38 | 0.38 | hedged possibility 0.73 |
| s6 | However, the general principle that underlies this confirmation of NRQCD factorization at two-loop order has yet to be revealed. | limitation 0.43 | 0.26 | 0.14 | asserted 0.94 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We test the nonrelativistic QCD factorization conjecture for inclusive quarkonium production at two loops by carrying out a covariant calculation of the nonrelativistic quantum chromodynamics (NRQCD) long-distance matrix element (LDME) for a heavy-quark pair in an $S$-wave, color-octet state to fragment into a heavy-quark pair in a color-singlet state of arbitrary orbital angular momentum. The NRQCD factorization conjecture for the universality of the LDME requires that infrared divergences that it contains be independent of the direction of the Wilson line that appears in its definition. We find this to be the case in our calculation. The results of our calculation differ in some respects from those of a previous calculation that was carried out by Nayak, Qiu, and Sterman using light-cone methods. We have identified the sources of some of these differences. The results of both calculations are consistent with the NRQCD factorization conjecture. However, the general principle that underlies this confirmation of NRQCD factorization at two-loop order has yet to be revealed.
Human review
How the literature uses it
11 arXiv papers cite this in 26 sentences
Papers citing it · 17 sentences without a confident label
Compares with it 1 paper
-
The sum of diagrams $C$ and $D$ in Ref. [ref] corresponds to the contribution from the planar diagrams in this work.
Resummation of threshold double logarithms in quarkonium fragmentation functions · Results and discussion · 0.97
Cites it as support 2 papers
-
Nonetheless, such effects do not appear at least until three-loop accuracy, as can be seen in explicit calculations of the color-octet LDME in perturbative QCD [ref] .
Inclusive Production of Heavy Quarkonia in pNRQCD · Consistency with NRQCD factorization · 0.99
-
Although there is no all-order proof of NRQCD factorization for quarkonium production yet, it is found that the factorization holds at least to next-to-next-to-leading order (NNLO) in $α_s$ if the LDMEs are modified to be gauge complete [ref] .
A short theoretical review of charmonium production · Quarkonium production mechanism · 0.96
Cites it as background 1 paper
-
Moreover, from the theoretical point of view, quarkonium production processes have exquisite theoretical issues pinning down factorization in strongly coupled theories, definition and calculation of nonperturbative matrix elements, and resummation of logarithms of large ratios of scales [ref] .
Inclusive Hadroproduction of $P$-Wave Heavy Quarkonia in Potential Nonrelativistic QCD · Introduction · 0.87
What it cites · 40 sentences without a confident label
Contests 1 paper
-
Consequently, the entire contribution in Eq. ([ref]) was taken to be a one-loop contribution to an SDC times the one-loop contribution to the LDME, and it was dropped in Ref. [ref] .
Fragmentation, NRQCD and NNLO Factorization Analysis in Heavy Quarkonium Production · Diagram V · contest 0.73
Uses the method or tool of 3 papers
-
The Feynman rules for the eikonal lines and Wilson lines are given in Refs. [ref] .
Fragmentation, NRQCD and NNLO Factorization Analysis in Heavy Quarkonium Production · Preliminaries · 0.90
-
The Feynman rules for the eikonal lines and Wilson lines are given in Refs. [ref] .
NRQCD Factorization and Velocity-dependence of NNLO Poles in Heavy Quarkonium Production · Preliminaries · 0.90
-
We then evaluate the Mellin-Barnes integrations by isolating poles in $ϵ$, using the methods of Tausk [ref] or Smirnov [ref] , and computing the remaining finite integrals as a sum over residues in the complex plane of Mellin-Barnes integration variable.
Non-planar massless two-loop Feynman diagrams with four on-shell legs · Method of calculation · 1.00
Compares with 3 papers
-
Our result for the sum of the ladder and crossed ladder diagrams $𝒜+ℬ$ contains no IR poles, which is in agreement with the order-$v^2$ results for $I+II$ in Ref. [ref] .
Fragmentation, NRQCD and NNLO Factorization Analysis in Heavy Quarkonium Production · Comparison · 1.00
-
Our results for the non-Abelian diagrams $ℱ$ agree with those in Refs. [ref] , up to an overall sign, and are independent of the Wilson line direction.
NRQCD Factorization and Velocity-dependence of NNLO Poles in Heavy Quarkonium Production · Conclusions · 1.00
-
Our results for the non-Abelian diagrams $ℱ$ agree with those in Refs. [ref] , up to an overall sign, and are independent of the Wilson line direction.
Fragmentation, Factorization and Infrared Poles in Heavy Quarkonium Production · Conclusions · 1.00
Cites as background 3 papers
-
The nonrelativistic quantum chromodynamics (NRQCD) factorization conjecture for inclusive quarkonium production in hard-scattering QCD processes [ref] postulates that the production rates for those processes at large momentum transfer can be written as a sum of products of short-distance coefficients (SDCs) and NRQCD long-distance matrix elements (LDMEs).
Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium · Introduction · 0.99
-
A proof of NRQCD factorization for exclusive quarkonium production at leading power in the inverse of the hard-scattering momentum transfer is given in Refs. [ref] .
Factorization theorems for exclusive heavy-quarkonium production · Introduction · 0.80
-
A proof of NRQCD factorization for exclusive quarkonium production at leading power in the inverse of the hard-scattering momentum transfer is given in Refs. [ref] .
Factorization of low-energy gluons in exclusive processes · Introduction · 0.80
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.