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Top-quark pair production at high invariant mass: an NNLO soft plus virtual approximation
High Energy Physics - Phenomenology · Submitted 6 Jun 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim On the other hand, at high values of invariant mass the new NNLO corrections are dominated by even higher-order effects included in NNLL soft-gluon resummation, reaffirming the need for resummation in describing the highly boosted regime.
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The abstract, sentence by sentence
We obtain a soft plus virtual approximation to the NNLO QCD contributions to the top-pair invariant mass distribution at hadron colliders. It is valid up to corrections of order m_t^2/M^2, with M the pair invariant mass. This is currently the most complete QCD calculation for a differential cross section in top-quark pair production, and is useful for describing the high invariant mass region characteristic of boosted top quarks. We use our results to construct an improved NNLO approximation for the pair invariant mass distribution and compare it with previous, less complete approximations based on logarithmic terms from NNLL soft-gluon resummation alone. We find that the new NNLO approximation produces moderate enhancements of the differential cross section compared to previous ones, the effect being slightly more important at low values of invariant mass than at high ones. On the other hand, at high values of invariant mass the new NNLO corrections are dominated by even higher-order effects included in NNLL soft-gluon resummation, reaffirming the need for resummation in describing the highly boosted regime.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We obtain a soft plus virtual approximation to the NNLO QCD contributions to the top-pair invariant mass distribution at hadron colliders. | contribution 0.99 | 0.96 | 0.32 | asserted 1.00 |
| s1 | It is valid up to corrections of order m_t^2/M^2, with M the pair invariant mass. | limitation 1.00 | 0.81 | 0.07 | asserted 1.00 |
| s2 | This is currently the most complete QCD calculation for a differential cross section in top-quark pair production, and is useful for describing the high invariant mass region characteristic of boosted top quarks. | interpretation 0.71 | 0.51 | 0.30 | asserted 1.00 |
| s3 | We use our results to construct an improved NNLO approximation for the pair invariant mass distribution and compare it with previous, less complete approximations based on logarithmic terms from NNLL soft-gluon resummation alone. | contribution 0.67 | 0.93 | 0.14 | asserted 0.99 |
| s4 | We find that the new NNLO approximation produces moderate enhancements of the differential cross section compared to previous ones, the effect being slightly more important at low values of invariant mass than at high ones. | result 1.00 | 0.96 | 0.29 | asserted 1.00 |
| s5 | On the other hand, at high values of invariant mass the new NNLO corrections are dominated by even higher-order effects included in NNLL soft-gluon resummation, reaffirming the need for resummation in describing the highly boosted regime. | interpretation 0.92 | 0.84 | 0.26 | asserted 1.00 |
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The paper
Original abstract
We obtain a soft plus virtual approximation to the NNLO QCD contributions to the top-pair invariant mass distribution at hadron colliders. It is valid up to corrections of order m_t^2/M^2, with M the pair invariant mass. This is currently the most complete QCD calculation for a differential cross section in top-quark pair production, and is useful for describing the high invariant mass region characteristic of boosted top quarks. We use our results to construct an improved NNLO approximation for the pair invariant mass distribution and compare it with previous, less complete approximations based on logarithmic terms from NNLL soft-gluon resummation alone. We find that the new NNLO approximation produces moderate enhancements of the differential cross section compared to previous ones, the effect being slightly more important at low values of invariant mass than at high ones. On the other hand, at high values of invariant mass the new NNLO corrections are dominated by even higher-order effects included in NNLL soft-gluon resummation, reaffirming the need for resummation in describing the highly boosted regime.
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References
How the literature uses it
15 arXiv papers cite this in 35 sentences
Papers citing it · 17 sentences without a confident label
Uses its method or tool 1 paper
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However, we hope to extract the contribution of the $n_h$-dependent part of NNLO hard function to the coefficient function ([ref]) using the the method followed in [ref] in future work.
Boosted top production: factorization and resummation for single-particle inclusive distributions · Heavy-quark loops · 0.87
Uses its data or values 3 papers
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To get a feeling of the size of the systematics we include the relative systematic uncertainty from [ref] for $√(s)=7$ TeV to Fig. [ref]; the theoretical uncertainty of [ref] is negligible compared to the systematics of [ref] .
Non-standard top substructure · Details, Analysis and Results · 0.92
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We thank Andreas Jung as well as the authors of references [ref] for providing us with their numbers and for cross-checking them.],
NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron · Comparison with approximate NNLO/resummed NLO QCD results · 0.93
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The expected cross section for the simulated reference sample is $252.9^+13.3_-14.5$pb, calculated at NNLO and next-to-next-to-leading-log (NNLL) accuracy [ref] , and describes the data well.
Measurement of the W boson helicity fractions in the decays of top quark pairs to lepton + jets final states produced in pp collisions at sqrt(s) = 8 TeV · Reconstruction of the t-tbar system and reweighting method · 0.95
Compares with it 3 papers
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* $$ (in units of $[10^-2pb/]$): Ref [ref] : $(1.7,2.51,0.773,0.181,0.0126)$; Refs. [ref] : $(1.75,2.712,0.8483,0.2008,0.01414)$.
NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron · Comparison with approximate NNLO/resummed NLO QCD results · 0.98
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In addition, the latest available NLO+NNLL [ref] and approximate NNLO QCD predictions [ref] are also used to compare with the data.
Measurement of the differential cross section for top quark pair production in pp collisions at sqrt(s) = 8 TeV · Event simulation and theoretical calculations · 0.99
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First, for the $qq̅ →Q Q̅$ and $g g →q q̅$ channels, we verified that the trace of functions given in ([ref]) is consistent with the NNLO results derived in [ref] .
NNLO hard functions in massless QCD · Hard functions to NNLO: calculational procedure · 0.99
Cites it as support 1 paper
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On the one hand, the small theoretical uncertainties on the $tt̅$ invariant mass motivates this observable as a suitable choice to examine our BSM hypotheses [ref] .
Non-standard top substructure · Details, Analysis and Results · 1.00
Cites it as background 2 papers
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Scales based on $m_T$ ([ref]) have been used since the early days of NLO calculations [ref] , as well as, more recently, $$-based scales [ref] .
Dynamical scales for multi-TeV top-pair production at the LHC · Overview of past work related to scale setting · 0.93
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Most recent results are to be found in Refs. [ref] .
The soft function for color octet production at threshold · Introduction · 0.97
What it cites · 35 sentences without a confident label
Uses the method or tool of 7 papers
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In particular, we use the factorization formalism of [ref] to obtain an NNLO soft plus virtual approximation to the differential cross section, valid up to easily quantifiable corrections in powers of $m_t^2/M^2$, with $M$ the top-pair invariant mass.
Soft-gluon resummation for boosted top-quark production at hadron colliders · Introduction · 0.99
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We define the Laplace-transformed coefficients as [equation] where[ The Laplace transform in Eq. ([ref]) is identical to the one introduced in [ref] and in [ref] ; the definition of the integration variable is $ξ≡2 E_g/M$, where $E_g = M (1-z)/(2 √(z))$ is the energy available for the emission of final state radiation in addition to the top pair.
Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders · Notation · 0.89
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The row labeled “NNLO approx. PIM” in Table [ref] corresponds to the approximation used for the invariant mass distribution in computing the total cross section in [ref] ; i. e., only part of the scale dependent terms in $c̃_ij^(2,0)$ are included, together with a set of terms which are regular in the $z →1$ limit and are obtained by keeping the exact form of the soft emission energy in the SCET formalism, as explained in detail in [ref] .
RG-improved single-particle inclusive cross sections and forward-backward asymmetry in $t\bar t$ production at hadron colliders · Predictions for the pair invariant mass distribution at the LHC · 0.89
Uses data or values from 2 papers
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In each case, we use the results from [ref] for the logarithmic coefficients $c̃_ij^(2,n)$, with $n=1,2,3,4$.
Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders · Predictions for the pair invariant mass distribution at the LHC · 0.94
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The coefficients proportional to powers of $L ≡ln( M^2 / (𝒩̅^2 μ^2))$ are determined by NNLL soft-gluon resummation and were obtained in [ref] .
Threshold expansion at order alpha_s^4 for the t-tbar invariant mass distribution at hadron colliders · Notation · 0.82
Compares with 5 papers
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Second, we compare the invariant mass distribution calculated using the newly obtained NNLO approximation with that from NNLL soft-gluon resummation [ref] .
Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders · Introduction · 1.00
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In Table [ref] we compare the total cross section obtained by integrating different NNLO approximations to the pair invariant mass distribution to the exact calculation of the total cross section at NNLO [ref] .
The total top quark pair production cross-section at hadron colliders through O(alpha_S^4) · Predictions for the pair invariant mass distribution at the LHC · 0.85
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A study of the NLO corrections within the analogous approximations was carried out for the LHC with $√(s)=7$ TeV in [ref] ; the numbers provided in Table 1 of that work show that the extra terms in approximation C are roughly twice as important at NLO as at NNLO.
Soft-gluon resummation for boosted top-quark production at hadron colliders · Predictions for the pair invariant mass distribution at the LHC · 0.84
Cites as background 1 paper
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The current state-of-the-art calculation for this distribution combines NLO fixed-order results with soft-gluon resummation at next-to-next-to-leading logarithmic (NNLL) accuracy [ref] .
Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders · Introduction · 0.83
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