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Calculating Soft Radiation at One Loop
High Energy Physics - Phenomenology · Submitted 2 Dec 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We present an efficient way to calculate the effect of soft QCD radiation at one loop, which is needed for predictions at next-to-next-to-leading logarithmic accuracy.
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The abstract, sentence by sentence
We present an efficient way to calculate the effect of soft QCD radiation at one loop, which is needed for predictions at next-to-next-to-leading logarithmic accuracy. We use rapidity coordinates and isolate the divergences in the integrand. By performing manipulations with cumulative variables, we avoid complications from plus distributions. We address rapidity divergences, divergences with an azimuthal dependence, complicated jet boundaries and multi-differential measurements. The process and measurements can be easily adjusted, as we demonstrate by reproducing many existing soft functions. The results for a general LHC process with multiple Wilson lines are obtained by treating Wilson lines that are not back-to-back using a boost. We also obtain, for the first time, the N-jettiness soft function for generic jet angularities, and the collinear-soft function for the measurement of two angularities.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present an efficient way to calculate the effect of soft QCD radiation at one loop, which is needed for predictions at next-to-next-to-leading logarithmic accuracy. | contribution 0.99 | 0.92 | 0.49 | asserted 1.00 |
| s1 | We use rapidity coordinates and isolate the divergences in the integrand. | method 1.00 | 0.94 | 0.04 | asserted 1.00 |
| s2 | By performing manipulations with cumulative variables, we avoid complications from plus distributions. | method 1.00 | 0.94 | 0.06 | asserted 1.00 |
| s3 | We address rapidity divergences, divergences with an azimuthal dependence, complicated jet boundaries and multi-differential measurements. | contribution 0.90 | 0.87 | 0.08 | asserted 0.99 |
| s4 | The process and measurements can be easily adjusted, as we demonstrate by reproducing many existing soft functions. | contribution 0.41 | 0.89 | 0.10 | asserted 0.99 |
| s5 | The results for a general LHC process with multiple Wilson lines are obtained by treating Wilson lines that are not back-to-back using a boost. | method 0.88 | 0.93 | 0.12 | asserted 1.00 |
| s6 | We also obtain, for the first time, the N-jettiness soft function for generic jet angularities, and the collinear-soft function for the measurement of two angularities. | result 0.68 | 0.96 | 0.28 | asserted 1.00 |
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The paper
Original abstract
We present an efficient way to calculate the effect of soft QCD radiation at one loop, which is needed for predictions at next-to-next-to-leading logarithmic accuracy. We use rapidity coordinates and isolate the divergences in the integrand. By performing manipulations with cumulative variables, we avoid complications from plus distributions. We address rapidity divergences, divergences with an azimuthal dependence, complicated jet boundaries and multi-differential measurements. The process and measurements can be easily adjusted, as we demonstrate by reproducing many existing soft functions. The results for a general LHC process with multiple Wilson lines are obtained by treating Wilson lines that are not back-to-back using a boost. We also obtain, for the first time, the N-jettiness soft function for generic jet angularities, and the collinear-soft function for the measurement of two angularities.
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References
How the literature uses it
10 arXiv papers cite this in 12 sentences
Papers citing it · 8 sentences without a confident label
Uses its method or tool 4 papers
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[ref] , and noting that the jet region corresponds to rapidity $y>-ln(R/2)$ with respect to the jet axis, we obtain
The Energy Distribution of Subjets and the Jet Shape · Factorization for $r ≪R$ · 0.99
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Using the approach in Ref. [ref] , we obtain the double differential soft function at one-loop order[Azimuthal symmetry implies $^(2)(p⃗_⊥- …) = (p_T^2 - …) / π$, allowing us to eliminate vector quantities.]
Joint transverse momentum and threshold resummation beyond NLL · Soft function · 0.98
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Let us boost the reference frame in order that two lightcone vectors $n_i$ and $n_j$ become back-to-back [ref] .
Consistent treatment of rapidity divergence in soft-collinear effective theory · The $N$-jet operator · 0.87
What it cites · 28 sentences without a confident label
Builds on 2 papers
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We extend the hemisphere decomposition [ref] to handle the azimuthally dependent phase-space boundaries between regions arising from the more general $N$-jettiness measurement.
The Soft Function for Exclusive N-Jet Production at Hadron Colliders · $N$-jettiness with generic jet angularities · 1.00
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We extend the thrust-like $N$-jettiness definition [ref] , by considering the measurement of a different angularity for each jet[Here we use the term `jets' to refer to both final-state and beam jets.]
N-Jettiness: An Inclusive Event Shape to Veto Jets · $N$-jettiness with generic jet angularities · 1.00
Uses the method or tool of 7 papers
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This is corrected for through zero-bin subtractions [ref] that remove the overlap with soft radiation, but vanish in pure dimensional regularization.] For collinear-soft radiation going into the $y<0$ hemisphere,
The Zero-Bin and Mode Factorization in Quantum Field Theory · Thrust and transverse momentum · 0.96
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Other regulators are possible [ref] , and the expression corresponding to start for ref.
Soft-Collinear Factorization and Zero-Bin Subtractions · Dijets · 0.80
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Other regulators are possible [ref] , and the expression corresponding to start for ref.
Analytic Regularization in Soft-Collinear Effective Theory · Dijets · 0.80
Compares with 9 papers
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[ref] , and agree once the different scheme for dimensional regularization is taken into account, as discussed in detail below.
Factorization and resummation for transverse thrust · Transverse thrust in $e^+e^-$ · 1.00
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[ref] in Njettiness.
The Soft Function for Exclusive N-Jet Production at Hadron Colliders · $N$-jettiness with generic jet angularities · 0.95
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[ref] , when converting their $p⃗_T$ measurement.
A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory · Transverse momentum · 1.00
Cites as background 6 papers
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The transverse thrust event shape $T_⊥$ [ref] , is designed for hadron collisions, but has also been calculated for $e^+e^- →2$ jets [ref] ,
Factorization and resummation for transverse thrust · Transverse thrust in $e^+e^-$ · 0.89
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The transverse thrust event shape $T_⊥$ [ref] , is designed for hadron collisions, but has also been calculated for $e^+e^- →2$ jets [ref] ,
Resummed event shapes at hadron-hadron colliders · Transverse thrust in $e^+e^-$ · 0.89
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The origin of these large logarithms is the enhancement of collinear and soft radiation, which are treated as dynamic degrees of freedom in Soft-Collinear Effective Theory (SCET) [ref] .
An effective field theory for collinear and soft gluons: heavy to light decays · Introduction · 0.92
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