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Resolving the Tevatron Top Quark Forward-Backward Asymmetry Puzzle: Fully Differential Next-to-Next-to-Leading-Order Calculation

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Michal Czakon, Paul Fiedler, Alexander Mitov

High Energy Physics - Phenomenology · Submitted 11 Nov 2014 · 64 references

Pith's verdict: The NNLO correction to Tevatron AFB is real and large, and the cross-checks are convincing — but the ±0.007 on 0.095 is tighter than the paper's own two definitions justify.

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arXiv ID1411.3007 (version 2)
Pith IDD6SL5KJO, Pith's permanent record of this paper and its review
CitationAlexander Mitov, Michal Czakon, Paul Fiedler. "Resolving the Tevatron Top Quark Forward-Backward Asymmetry Puzzle: Fully Differential Next-to-Next-to-Leading-Order Calculation." arXiv:1411.3007 (2014). https://pith.science/paper/D6SL5KJO
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The paper

The paper claims

The missing QCD correction to the Tevatron top-quark forward-backward asymmetry turns out to be large, not small, and it brings the Standard Model prediction into agreement with the D0 measurement.

The reading

At the Tevatron, top quarks emerge preferentially along the proton beam direction, and for years the measured size of that forward-backward asymmetry sat a couple of standard deviations above the next-to-leading-order QCD prediction, which left room for new-physics explanations. This paper computes the next order in QCD, NNLO, in full: every partonic channel contributing to $pbar p to t bar t + X$ is included exactly, with no approximation, and the calculation reproduces the known NNLO total cross section to better than one permil. Contrary to what soft-gluon resummation had suggested, the correction is large: roughly a 27% shift relative to NLO under the unexpanded definition, and about 13% under the expanded one. Combining this with known electroweak corrections gives $A_{FB}^{SM} = 0.095 pm 0.007$, which sits on top of the D0 value $0.106 pm 0.03$ and about $1.5sigma$ below CDF's $0.164 pm 0.047$. The consequence is that the Standard Model is no longer the underdog in this particular anomaly; what tension remains is with CDF rather than with the theory.

What carries the argument

The carrying object is the ratio of two NNLO-accurate cross sections: the antisymmetric numerator $N$ (the $Delta y$-odd part of the $t bar t$ rate) divided by the total rate $D$, both computed from the same fully differential NNLO code so that the scale variation is taken consistently in numerator and denominator. The authors use two definitions: an unexpanded one, eq. (2), in which the exact results sit in both numerator and denominator, and an expanded one, eq. (3), in which the ratio is expanded in powers of $alpha_S$. The two agree within uncertainties at NNLO, and the quoted central value uses the expanded definition with the electroweak numerator added. The paper's diagnostic move is to decompose the NNLO numerator $N_4$ into real-real, real-virtual, virtual-virtual and collinear-factorisation pieces: the real-virtual term ($+5.34$, in units of $alpha_S^4 N_4$) and the real-real term ($-0.47$) nearly cancel against the virtual-virtual term ($-3.90$), so the net asymmetry is a small residue of individually large corrections, arising almost entirely from the $q bar q$ channel. That structure, together with the shape of the $P_{T,t bar t}$ distribution, is what distinguishes the exact result from the soft-gluon approximation, which had predicted a negligible correction because it only controls the small-$P_T$ region.

Extended reading notes

Core claim

The paper's claim is that the dominant missing Standard Model piece of the inclusive top-quark forward-backward asymmetry has now been computed exactly, and that it is large. Defined as $(sigma_{+} - sigma_{-})/(sigma_{+} + sigma_{-})$ with $Delta y = y_t - y_{bar t}$, the asymmetry is obtained at NNLO in QCD from a fully differential calculation of $pbar p to t bar t + X$ that includes all partonic reactions without approximation. The authors report that the ratio $A_{FB}^{NNLO}/A_{FB}^{NLO}$ is 1.27 under the unexpanded definition and 1.13 under the expanded one, and that the corresponding ratio for the numerator of the asymmetry is 1.33. Adding the electroweak numerator of the asymmetry to the QCD result yields $A_{FB}^{SM} = 0.095 pm 0.007$, in agreement with D0 and about $1.5sigma$ below CDF. The paper also reports differential asymmetries in $|Delta y|$, in the $t bar t$ invariant mass, and in the transverse momentum of the $t bar t$ pair, all of which are in agreement with the corresponding D0 data even before electroweak corrections are added. The authors emphasise that this is the first complete fully differential NNLO calculation in QCD of a two-to-two process with all coloured partons.

Load-bearing premise

The quoted $pm 0.007$ uncertainty is a scale-variation-only estimate with $mu_R = mu_F$, and the central value is taken from the expanded definition, whose pure-QCD scale error the authors themselves describe as appearing too small to be realistic; a genuinely larger theory error would soften the stated agreement with D0.

Editorial extensions

If this is right

  • The Standard Model prediction for the inclusive Tevatron asymmetry moves to $0.095 pm 0.007$, which is consistent with the D0 full-data-set measurement and about $1.5sigma$ below the CDF value, so the anomaly no longer requires a new-physics explanation for the inclusive number.
  • Because the shift comes from radiation at moderate and large $P_{T,t bar t}$ rather than from soft gluons, soft-gluon resummation alone is not a reliable proxy for the size of higher-order corrections to this observable.
  • The differential asymmetries in $|Delta y|$, in $M_{t bar t}$ and in $P_{T,t bar t}$ predicted here, computed without electroweak corrections, can be compared bin by bin with Tevatron data and with any future analysis.
  • The same machinery supplies a template for fully differential NNLO predictions of other two-to-two processes with coloured partons, where the same pattern of large cancellations between real and virtual corrections may recur.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the large correction is really driven by hard, wide-angle radiation rather than by the soft region, then jet-vetoed or boosted top-pair measurements at the LHC should show related, currently unaccounted-for NNLO shifts in the same kinematic corners; that is a check the paper does not perform.
  • The authors note that the asymmetry-generating diagrams are the same as those behind the perturbatively generated strange and charm asymmetries of the proton, up to crossing and taking the top mass to zero. If that analogy holds quantitatively, the missing four-loop spacelike splitting functions could carry corrections of a size comparable to what is seen here, which would matter for precision PDF
  • The fact that the exact NNLO correction differs sharply from the resummed approximation in the second $P_{T,t bar t}$ bin suggests that threshold and small-$P_T$ resummations should be matched to fixed order before being used to quote theory errors on asymmetry-like ratios.
  • Since the quoted error bar is a scale-variation estimate rather than a full theory covariance, an independent replication of the numerator $N_4$ and of the $P_{T,t bar t}$ distribution by a second implementation is the cheapest way to test whether the agreement with D0 survives a more honest uncertainty.
Original abstract

We determine the dominant missing Standard Model (SM) contribution to the top quark pair forward-backward asymmetry at the Tevatron. Contrary to past expectations, we find a large, around 27%, shift relative to the well-known value of the inclusive asymmetry in next-to-leading order (NLO) QCD. Combining all known Standard Model corrections, we find that AFB^{SM} = 0.095 +- 0.007. This value is in agreement with the latest D0 measurement [V. M. Abazov et al. (D0 Collaboration), Phys. Rev. D 90, 072011 (2014)] AFB^{D0} = 0.106+- 0.03 and about 1.5 sigma below that of CDF [T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D 87, 092002 (2013)] AFB^{CDF} =0.164 +- 0.047. Our result is derived from a fully differential calculation of the next-to-next-to leading order (NNLO) QCD corrections to inclusive top pair production at hadron colliders and includes - without any approximation - all partonic channels contributing to this process. This is the first complete fully differential calculation in NNLO QCD of a two-to-two scattering process with all coloured partons.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. 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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,485 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.95 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.17 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We determine the dominant missing Standard Model (SM) contribution to the top quark pair forward-backward asymmetry at the Tevatron. Contrary to past expectations, we find a large, around 27%, shift relative to the well-known value of the inclusive asymmetry in next-to-leading order (NLO) QCD. Combining all known Standard Model corrections, we find that AFB^{SM} = 0.095 +- 0.007. This value is in agreement with the latest D0 measurement [V. M. Abazov et al. (D0 Collaboration), Phys. Rev. D 90, 072011 (2014)] AFB^{D0} = 0.106+- 0.03 and about 1.5 sigma below that of CDF [T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D 87, 092002 (2013)] AFB^{CDF} =0.164 +- 0.047. Our result is derived from a fully differential calculation of the next-to-next-to leading order (NNLO) QCD corrections to inclusive top pair production at hadron colliders and includes - without any approximation - all partonic channels contributing to this process. This is the first complete fully differential calculation in NNLO QCD of a two-to-two scattering process with all coloured partons.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We determine the dominant missing Standard Model (SM) contribution to the top quark pair forward-backward asymmetry at the Tevatron. contribution 0.93 0.95 0.44 asserted 1.00
s1 Contrary to past expectations, we find a large, around 27%, shift relative to the well-known value of the inclusive asymmetry in next-to-leading order (NLO) QCD. result 0.99 0.96 0.29 asserted 1.00
s2 Combining all known Standard Model corrections, we find that AFB^{SM} = 0.095 +- 0.007. result 1.00 0.96 0.63 asserted 1.00
s3 This value is in agreement with the latest D0 measurement [V. M. interpretation 0.51 0.50 0.11 asserted 0.90
s4 Abazov et al. (D0 Collaboration), Phys. Rev. D 90, 072011 (2014)] AFB^{D0} = 0.106+- 0.03 and about 1.5 sigma below that of CDF [T. result 0.71 0.19 0.06 asserted 0.95
s5 Aaltonen et al. (CDF Collaboration), Phys. Rev. D 87, 092002 (2013)] AFB^{CDF} =0.164 +- 0.047. result 0.55 0.05 0.04 asserted 0.97
s6 Our result is derived from a fully differential calculation of the next-to-next-to leading order (NNLO) QCD corrections to inclusive top pair production at hadron colliders and includes - without any approximation - all partonic channels contributing to this process. method 0.90 0.96 0.10 asserted 1.00
s7 This is the first complete fully differential calculation in NNLO QCD of a two-to-two scattering process with all coloured partons. contribution 0.92 0.92 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from simulation or computation 0.87.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1: The inclusive asymmetry in pure QCD (black) and
Figure 3. FIG. 3: As in fig. 2 but for the
Figure 4. FIG. 4: As in fig. 2 but for the

Showing 3 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:1411.3007 by the authors.

References
How later papers used it

90 later papers cite it

Evidence: substantial. 74 of the citing papers share no author with it, and 13 of those carry a confident label from Pith's citation classifier.

Pith read 27 of the 167 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Builds on it 1 of 3 papers with this label · 1 by the same authors

By the same authors

Uses its data or values 1 of 7 papers with this label
Compares with it 1 of 8 papers with this label
How the literature uses it

87 arXiv papers cite this in 162 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 · 93 sentences without a confident label

Contests it 1 paper
Builds on it 3 papers
Uses its method or tool 4 papers
Uses its data or values 6 papers
Compares with it 8 papers
Cites it as background 26 papers

What it cites · 40 sentences without a confident label

Uses the method or tool of 12 papers
Uses data or values from 1 paper
Compares with 14 papers
Cites as support 1 paper
Cites as background 28 papers

Discussion

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