Decomposition of Triple Collinear Splitting Functions

Braun-White, Oscar; Glover, Nigel

doi:10.48550/arxiv.2204.10755

Cited by 5 publications

(9 citation statements)

References 41 publications

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“…For a recent discussion in terms of the 1 → 3 splitting function, see ref. [141]. These iterations give rise to the leading singular behavior in the squeezed/OPE limit, where the three-point correlator factorizes into a product of two-point correlators [91,93].…”

Section: Definitionmentioning

confidence: 99%

Non-Gaussianities in collider energy flux

Chen

Moult

Thaler

et al. 2022

J. High Energ. Phys.

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The microscopic dynamics of particle collisions is imprinted into the statistical properties of asymptotic energy flux, much like the dynamics of inflation is imprinted into the cosmic microwave background. This energy flux is characterized by correlation functions $$ \left\langle \mathcal{E}\left({\overrightarrow{n}}_1\right)\cdots \mathcal{E}\left({\overrightarrow{n}}_k\right)\right\rangle $$ E n → 1 ⋯ E n → k of energy flow operators $$ \mathcal{E}\left(\overrightarrow{n}\right) $$ E n → . There has been significant recent progress in studying energy flux, including the calculation of multi-point correlation functions and their direct measurement inside high-energy jets at the Large Hadron Collider (LHC). In this paper, we build on these advances by defining a notion of “celestial non-gaussianity” as a ratio of the three-point function to a product of two-point functions. We show that this celestial non-gaussianity is under perturbative control within jets at the LHC, allowing us to cleanly access the non-gaussian interactions of quarks and gluons. We find good agreement between perturbative calculations of the non-gaussianity and a charged-particle-based analysis using CMS Open Data, and we observe a strong non-gaussianity peaked in the “flattened triangle” regime. The ability to robustly study three-point correlations is a significant step in advancing our understanding of jet substructure at the LHC. We anticipate that the celestial non-gaussianity, and its generalizations, will play an important role in the development of higher-order parton showers simulations and in the hunt for ever more subtle signals of potential new physics within jets.

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Section: Definitionmentioning

confidence: 99%

Non-Gaussianities in collider energy flux

Chen

Moult

Thaler

et al. 2022

J. High Energ. Phys.

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show abstract

“…For a recent discussion in terms of the 1 → 3 splitting function, see Ref. [141]. These iterations give rise to the leading singular behavior in the squeezed/OPE limit, where the three-point correlator factorizes into a product of two-point correlators [91,93].…”

Section: Definitionmentioning

confidence: 99%

Non-Gaussianities in Collider Energy Flux

Chen,

Moult,

Thaler

et al. 2022

Preprint

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The microscopic dynamics of particle collisions is imprinted into the statistical properties of asymptotic energy flux, much like the dynamics of inflation is imprinted into the cosmic microwave background. This energy flux is characterized by correlation functions E( n 1 ) • • • E( n k ) of energy flow operators E( n). There has been significant recent progress in studying energy flux, including the calculation of multi-point correlation functions and their direct measurement inside high-energy jets at the Large Hadron Collider (LHC). In this paper, we build on these advances by defining a notion of "celestial non-gaussianity" as a ratio of the three-point function to a product of two-point functions. We show that this celestial non-gaussianity is under perturbative control within jets at the LHC, allowing us to cleanly access the non-gaussian interactions of quarks and gluons. We find good agreement between perturbative calculations of the non-gaussianity and a charged-particle-based analysis using CMS Open Data, and we observe a strong non-gaussianity peaked in the "flattened triangle" regime. The ability to robustly study three-point correlations is a significant step in advancing our understanding of jet substructure at the LHC. We anticipate that the celestial non-gaussianity, and its generalizations, will play an important role in the development of higher-order parton showers simulations and in the hunt for ever more subtle signals of potential new physics within jets.

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“…In practice, a spectator momentum ℓ is used to define the momentum fractions, 𝑠 𝑖ℓ = 𝑥 𝑖 𝑠 𝑃ℓ . In these proceedings we will focus only on two splittings which illustrate all the features exposed in [2]: 𝑞𝛾𝛾 → 𝑞, 𝑞𝑔𝑔 → 𝑞. We are using a shorthand notation for the splitting functions, 𝑃 𝑎𝑏𝑐→𝑃 (𝑖, 𝑗, 𝑘) ≡ 𝑃 𝑎𝑏𝑐→𝑃 (𝑥 𝑖 , 𝑥 𝑗 , 𝑥 𝑘 ; 𝑠 𝑖 𝑗 , 𝑠 𝑖𝑘 , 𝑠 𝑗 𝑘 , 𝑠 𝑖 𝑗 𝑘 ).…”

Section: Triple Collinear Splitting Functionsmentioning

confidence: 99%

“…However, achieving the necessary analytic control of the corrections to balance against numerical calculations is extremely complex. The work discussed in [2] exposes the single and double unresolved singularities hidden within triple collinear splitting functions [3][4][5], which are fundamental objects relevant to the twoleg corrections at NNLO. These proceedings discuss two of these splitting functions.…”

Section: Introductionmentioning

confidence: 99%

Leading Order Triple Collinear Splitting Functions Revisited

Braun-White¹

2022

Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)

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I review the factorisation properties of tree level amplitudes when three particles 𝑖, 𝑗, 𝑘 are collinear. The triple collinear splitting functions contain both iterated single unresolved contributions, and genuine double unresolved contributions. I make this explicit by rewriting the known triple collinear splitting functions for a quark and two gluons in terms of products of two-particle splitting functions, and a remainder that is explicitly finite when any two of {𝑖, 𝑗, 𝑘 } are collinear.

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Decomposition of Triple Collinear Splitting Functions

Cited by 5 publications

References 41 publications

Non-Gaussianities in collider energy flux

Non-Gaussianities in collider energy flux

Non-Gaussianities in Collider Energy Flux

Leading Order Triple Collinear Splitting Functions Revisited

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