Jet mass with a jet veto at two loops and the universality of non-global structure

Hua Xing Zhu; Matthew D. Schwartz; Randall Kelley; Robert M. Schabinger

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Jet mass with a jet veto at two loops and the universality of non-global structure

Randall Kelley, Matthew D. Schwartz, Robert M. Schabinger, Hua Xing Zhu

High Energy Physics - Phenomenology · Submitted 14 Dec 2011

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

The authors' main claim Somewhat surprisingly, we find that, in the small R limit, there is a precise and simple correspondence between the non-global contribution to the integrated jet thrust distribution and the previously calculated non-global contribution to the integrated hemisphere soft function, including subleading terms.

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arXiv ID1112.3343 (version 1)

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CitationHua Xing Zhu, Matthew D. Schwartz, Randall Kelley, Robert M. Schabinger. "Jet mass with a jet veto at two loops and the universality of non-global structure." arXiv:1112.3343 (2011). https://pith.science/paper/CQO2EQCN

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What the abstract itself states, as probabilities: claims first 0.39 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.95 · mentions code or data availability 0.02.

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We investigate the exclusive jet mass distribution in e+e- events, defined with a veto on the out-of-jet radiation, at two-loop order. In particular, we calculate the two-loop soft function, which is required to describe this distribution in the threshold region. When combined with other ingredients using soft-collinear effective theory, this generates the complete singular distribution for jet thrust, the sum of the jet masses, at two-loop order. The result is in excellent agreement with full QCD. The integrated jet thrust distribution is found to depend in an intricate way on both the finite jet cone size, R, and the jet veto scale. The result clarifies the structure of the potentially large logarithms (both global and non- global) which arise in jet observables for the first time at this order. Somewhat surprisingly, we find that, in the small R limit, there is a precise and simple correspondence between the non-global contribution to the integrated jet thrust distribution and the previously calculated non-global contribution to the integrated hemisphere soft function, including subleading terms. This suggests that the small R limit may provide a useful expansion for studying other exclusive jet substructure observables.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the exclusive jet mass distribution in e+e- events, defined with a veto on the out-of-jet radiation, at two-loop order.	contribution 1.00	0.92	0.05	asserted 0.93
s1	In particular, we calculate the two-loop soft function, which is required to describe this distribution in the threshold region.	contribution 0.89	0.95	0.06	asserted 1.00
s2	When combined with other ingredients using soft-collinear effective theory, this generates the complete singular distribution for jet thrust, the sum of the jet masses, at two-loop order.	method 0.39	0.84	0.13	asserted 1.00
s3	The result is in excellent agreement with full QCD.	result 0.98	0.83	0.11	asserted 1.00
s4	The integrated jet thrust distribution is found to depend in an intricate way on both the finite jet cone size, R, and the jet veto scale.	result 1.00	0.95	0.12	asserted 1.00
s5	The result clarifies the structure of the potentially large logarithms (both global and non- global) which arise in jet observables for the first time at this order.	interpretation 0.92	0.88	0.18	asserted 1.00
s6	Somewhat surprisingly, we find that, in the small R limit, there is a precise and simple correspondence between the non-global contribution to the integrated jet thrust distribution and the previously calculated non-global contribution to the integrated hemisphere soft function, including subleading terms.	result 0.98	0.96	0.48	asserted 1.00
s7	This suggests that the small R limit may provide a useful expansion for studying other exclusive jet substructure observables.	future work 0.64	0.49	0.17	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.90.

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The paper

Original abstract

We investigate the exclusive jet mass distribution in e+e- events, defined with a veto on the out-of-jet radiation, at two-loop order. In particular, we calculate the two-loop soft function, which is required to describe this distribution in the threshold region. When combined with other ingredients using soft-collinear effective theory, this generates the complete singular distribution for jet thrust, the sum of the jet masses, at two-loop order. The result is in excellent agreement with full QCD. The integrated jet thrust distribution is found to depend in an intricate way on both the finite jet cone size, R, and the jet veto scale. The result clarifies the structure of the potentially large logarithms (both global and non- global) which arise in jet observables for the first time at this order. Somewhat surprisingly, we find that, in the small R limit, there is a precise and simple correspondence between the non-global contribution to the integrated jet thrust distribution and the previously calculated non-global contribution to the integrated hemisphere soft function, including subleading terms. This suggests that the small R limit may provide a useful expansion for studying other exclusive jet substructure observables.

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References

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Cited by 10 Pith papers

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

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Two-Loop Anomalous Dimension for Non-Global and Clustering Logarithms
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Non-Global Logarithms, Factorization, and the Soft Substructure of Jets
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Factorization and Resummation for Jet Processes
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Cone-jet cross sections factorize into hard functions times multi-Wilson-line soft operators, whose renormalization-group evolution resums non-global logarithms and reproduces the Banfi-Marchesini-Smye equation at lea...

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Jet Mass Spectra in Higgs + One Jet at NNLL
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On jet mass distributions in Z+jet and dijet processes at the LHC
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Introduction to Soft-Collinear Effective Theory
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A self-contained pedagogical construction of Soft-Collinear Effective Theory, from the strategy of regions through the effective Lagrangian to renormalization-group resummation for Drell-Yan and the infrared structure...

How the literature uses it

31 arXiv papers cite this in 84 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 · 43 sentences without a confident label

Builds on it 1 paper

Unfortunately, while completing the calculation of [ref] is in principle straightforward given a thorough understanding of the original work, it requires modern techniques to write the final result in a compact way in terms of known, linearly independent, transcendental functions.

The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory · Introduction · 0.89

Uses its method or tool 3 papers

Finally, following the analysis performed in Section 5.2 of reference [ref] , we can approximate $ℓ_j^- - r^2 k_j^+$ and $ℓ_j^- + k_j^+ r$ by $ℓ_j^-$ in the small $r$ limit and then immediately write

The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory · The Structure of the $ln(r)$ Terms · 0.93
The other two terms involve two real gluons, and following [ref] we split them into “In-Out" and “Out-Out" configurations with one and two gluons outside the jet cone.

Factorization and Resummation for Jet Processes · Two-loop soft function $𝒮_2$ · 0.83
For all of the integrals except $I_5()$ and $I_9()$, we found that the phase space integrals over $k_1$ and $k_2$ that remain once $q$ has been integrated out could be numerically checked in Mathematica for appropriate real, negative values of $$ using a parametrization employed in earlier work (see Refs. [ref] ).

N$^3$LO Higgs and Drell-Yan production at threshold: the one-loop two-emission contribution · Introduction · 0.95

Uses its data or values 3 papers

K^all-in (2)_TC(,ω,r,μ) = (K^⇒^ (2)_hemi(,μ) + K^⇐^ (2)_hemi(,μ)) r^2 = 2 r^2 ∫_0^ ^'∫k_L k_R k_R^-1-4 (k_L)μ^4 g_hemi^(2)()(^'- k_L + k_RQ) = 2 r^2 (-1)4(μQ)^4 [C_A C_F( 4/^3+22/3^2 +(134/9-4π^2/3 )1/ + 772/27+11π^2/9-116 ζ_33 + ( 4784/81 + 67π^2/27 - 137π^4/90 + 484ζ_3/9 ) + (^2)) + C_F n_f T_F ( -8/3^2 - 40/9 - 152/27 - 4π^2/9 - (952/81 + 20π^2/27 + 176ζ_3/9) + (^2))], where we have used Eq. (3.16) of reference [ref] in deriving the third line of Eq. ([ref]).

The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory · All-In Contributions · 0.83
Explicitly, we find [equation] where $S_R^r_3 (r_4)$ is given in [ref] .

Factorization and Resummation for Jet Processes · Two-loop soft function $𝒮_2$ · 0.92
Taking the thrust vector as the jet axis leads to a simpler form of the phase-space constraints and enables us to use existing two-loop results for the cone-jet soft function obtained in [ref] .

An Effective Field Theory for Jet Processes · Momentum regions in cone-jet processes · 0.83

Compares with it 1 paper

Notice that identical formulae to Eqs.[ref], [ref], [ref] and [ref] have been found in [ref] [Note that in [ref] one has $= /4π$.] using SCET.

QCD resummation for high-p$_T$ jet shapes at hadron colliders · N$^3$LL non-global structure · 0.93

Cites it as support 3 papers

This supports the conjecture made in reference [ref] that the resummation of the logarithms of $r$ is tied up with the resummation of the logarithms of $Q2ω$; the form of Eq. ([ref]) suggests that these two classes of potentially large logarithms not controlled by the factorization theorem for jet thrust are naturally intertwined.

The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory · The Structure of the $ln(r)$ Terms · 1.00
However, this (collinear-)soft radiation will displace the jet axis and contaminate the transverse momentum distribution, again introducing a sensitivity to NGLs.[From the direct two-loop calculations for related jet shapes in the soft approximation [ref] , one sees that NGLs are present for all jet radii.

Jet axes and universal transverse-momentum-dependent fragmentation · Introduction · 0.97
The contributions to subleading NGLs from such splittings is apparent from a detailed study of the fixed order calculation at two loops [ref] .

Non-Global Logarithms, Factorization, and the Soft Substructure of Jets · Going Beyond the Soft Approximation · 0.96

Cites it as background 20 papers

For further details, we refer the interested reader to reference [ref] .

The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory · The General Structure of the Calculation · 0.86
A two-loop calculation of the soft function for hemispherical jets was performed in [ref] and for cone or anti-$k_T$ jets, with an out-of-jet veto, in [ref] .

Resummation of Jet Mass at Hadron Colliders · The Role of Non-Global Logarithms · 0.86
Here we address how these can be removed by a refactorization of the soft function, with corrections from the true higher order non-global logarithms (see Refs. [ref] for earlier refactorization discussions).

Jet Mass Spectra in Higgs + One Jet at NNLL · Refactorization of the Soft Function · 0.84

What it cites · 86 sentences without a confident label

Uses the method or tool of 1 paper

We therefore followed the approach of Ref. [ref] in Section [ref] and calculated only those contributions to the soft function which depend on ratios of dimensionful scales.

Double Non-Global Logarithms In-N-Out of Jets · The Jet Thrust Distribution at Two-Loops · 0.97

Compares with 5 papers

To see this, after performing the trivial integrations over $k_L$ and $k_R$ in Eq. ([ref]) above, replace the phase-spaces cuts that depend on $k^-$ and $q^-$ using ([ref]) and then compare the resulting product of thetas and deltas in the integrand to the second line of Eq. (13) in Ref. [ref] (with $k_L = 2 r λ$ and $k_R = Q ^'$).

The two-loop hemisphere soft function · In-out rescaling at small $R$ · 0.93
For example, in Eq. ([ref]) above, the leading NGL is simply C_F C_A(16 Li_2(r^2)-8/3π^2)ln^2 (τ_ωQ/2 ω) . which agrees with results from Refs. [ref] .

Resummation of jet mass with and without a jet veto · Analytic checks and definition of the non-global contribution · 0.94
For example, in Eq. ([ref]) above, the leading NGL is simply C_F C_A(16 Li_2(r^2)-8/3π^2)ln^2 (τ_ωQ/2 ω) . which agrees with results from Refs. [ref] .

Double Non-Global Logarithms In-N-Out of Jets · Analytic checks and definition of the non-global contribution · 0.94

Cites as background 14 papers

In this section, we briefly review the definition of $τ_ω$ and recapitulate the main results of Ref. [ref] which sets the stage for the exact results calculated in the present paper.

Resummation of jet mass with and without a jet veto · Jet Thrust in SCET · 0.87
Resummation of these NGLs seems difficult [ref] .

Soft gluons away from jets: distribution and correlation · Conclusions · 0.81
Resummation of these NGLs seems difficult [ref] .

The two-loop hemisphere soft function · Conclusions · 0.81

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