A spectral metric for collider geometry
Abstract By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celes...
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| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2023
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| Online Access: | https://hdl.handle.net/1721.1/152191 |
| _version_ | 1826194259765624832 |
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| author | Larkoski, Andrew J. Thaler, Jesse |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Larkoski, Andrew J. Thaler, Jesse |
| author_sort | Larkoski, Andrew J. |
| collection | MIT |
| description | Abstract
By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celestial sphere and then define the metric in terms of optimal transport in two dimensions. In this paper, we advocate for representing events in terms of a spectral function that encodes pairwise particle angles and products of particle energies, which enables a metric distance defined in terms of one-dimensional optimal transport. This approach has the advantage of automatically incorporating obvious isometries of the data, like rotations about the colliding beam axis. It also facilitates first-principles calculations, since there are simple closed-form expressions for optimal transport in one dimension. Up to isometries and event sets of measure zero, the spectral representation is unique, so the metric on the space of spectral functions is a metric on the space of events. At lowest order in perturbation theory in electron-positron collisions, our metric is simply the summed squared invariant masses of the two event hemispheres. Going to higher orders, we present predictions for the distribution of metric distances between jets in fixed-order and resummed perturbation theory as well as in parton-shower generators. Finally, we speculate on whether the spectral approach could furnish a useful metric on the space of quantum field theories. |
| first_indexed | 2024-09-23T09:53:20Z |
| format | Article |
| id | mit-1721.1/152191 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:53:20Z |
| publishDate | 2023 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1521912024-02-02T21:38:41Z A spectral metric for collider geometry Larkoski, Andrew J. Thaler, Jesse Massachusetts Institute of Technology. Center for Theoretical Physics Abstract By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celestial sphere and then define the metric in terms of optimal transport in two dimensions. In this paper, we advocate for representing events in terms of a spectral function that encodes pairwise particle angles and products of particle energies, which enables a metric distance defined in terms of one-dimensional optimal transport. This approach has the advantage of automatically incorporating obvious isometries of the data, like rotations about the colliding beam axis. It also facilitates first-principles calculations, since there are simple closed-form expressions for optimal transport in one dimension. Up to isometries and event sets of measure zero, the spectral representation is unique, so the metric on the space of spectral functions is a metric on the space of events. At lowest order in perturbation theory in electron-positron collisions, our metric is simply the summed squared invariant masses of the two event hemispheres. Going to higher orders, we present predictions for the distribution of metric distances between jets in fixed-order and resummed perturbation theory as well as in parton-shower generators. Finally, we speculate on whether the spectral approach could furnish a useful metric on the space of quantum field theories. 2023-09-21T19:42:45Z 2023-09-21T19:42:45Z 2023-08-18 2023-08-20T03:10:21Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/152191 Journal of High Energy Physics. 2023 Aug 18;2023(8):107 PUBLISHER_CC en https://doi.org/10.1007/JHEP08(2023)107 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Larkoski, Andrew J. Thaler, Jesse A spectral metric for collider geometry |
| title | A spectral metric for collider geometry |
| title_full | A spectral metric for collider geometry |
| title_fullStr | A spectral metric for collider geometry |
| title_full_unstemmed | A spectral metric for collider geometry |
| title_short | A spectral metric for collider geometry |
| title_sort | spectral metric for collider geometry |
| url | https://hdl.handle.net/1721.1/152191 |
| work_keys_str_mv | AT larkoskiandrewj aspectralmetricforcollidergeometry AT thalerjesse aspectralmetricforcollidergeometry AT larkoskiandrewj spectralmetricforcollidergeometry AT thalerjesse spectralmetricforcollidergeometry |