{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T04:22:11Z","timestamp":1773116531428,"version":"3.50.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T00:00:00Z","timestamp":1746230400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T00:00:00Z","timestamp":1746230400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Karlsruher Institut f\u00fcr Technologie (KIT)"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Softw Big Sci"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We present the study of an end-to-end multi-track reconstruction algorithm for the central drift chamber of the Belle\u00a0II experiment at the SuperKEKB collider using Graph Neural Networks for an unknown number of particles. The algorithm uses detector hits as inputs without pre-filtering to simultaneously predict the number of track candidates in an event and their kinematic properties. In a second step, we cluster detector hits for each track candidate to pass to a track fitting algorithm. Using a realistic full detector simulation including beam-induced backgrounds and detector noise taken from actual collision data, we find significant improvements in track finding efficiencies for tracks in a variety of different event topologies compared to the existing baseline algorithm used in Belle\u00a0II. For events involving a hypothetical long-lived massive particle with a mass in the GeV-range, decaying uniformly along its flight direction into two charged particles, the GNN achieves a combined track finding and fitting charge efficiency of 85.4% per track, with a fake rate of 2.5%, averaged over the full detector acceptance. In comparison, the baseline algorithm achieves 52.2% efficiency and a fake rate of 4.1%. This is the first end-to-end multi-track machine learning algorithm for a drift chamber detector that has been utilized in a realistic particle physics environment.<\/jats:p>","DOI":"10.1007\/s41781-025-00135-6","type":"journal-article","created":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T08:05:28Z","timestamp":1746259528000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["End-to-End Multi-track Reconstruction Using Graph Neural Networks at Belle\u00a0II"],"prefix":"10.1007","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5930-6237","authenticated-orcid":false,"given":"L.","family":"Reuter","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8442-107X","authenticated-orcid":false,"given":"G.","family":"De Pietro","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2628-530X","authenticated-orcid":false,"given":"S.","family":"Stefkova","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6849-0427","authenticated-orcid":false,"given":"T.","family":"Ferber","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9971-1176","authenticated-orcid":false,"given":"V.","family":"Bertacchi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4137-938X","authenticated-orcid":false,"given":"G.","family":"Casarosa","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2577-9909","authenticated-orcid":false,"given":"L.","family":"Corona","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6817-6868","authenticated-orcid":false,"given":"P.","family":"Ecker","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8553-7338","authenticated-orcid":false,"given":"A.","family":"Glazov","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6775-5932","authenticated-orcid":false,"given":"Y.","family":"Han","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7400-6013","authenticated-orcid":false,"given":"M.","family":"Laurenza","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3915-2506","authenticated-orcid":false,"given":"T.","family":"Lueck","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1762-4699","authenticated-orcid":false,"given":"L.","family":"Massaccesi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3054-8400","authenticated-orcid":false,"given":"S.","family":"Mondal","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1771-9161","authenticated-orcid":false,"given":"B.","family":"Scavino","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9601-405X","authenticated-orcid":false,"given":"S.","family":"Spataro","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0959-4784","authenticated-orcid":false,"given":"C.","family":"Wessel","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4957-805X","authenticated-orcid":false,"given":"L.","family":"Zani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,3]]},"reference":[{"key":"135_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2022.137373","volume":"833","author":"T Ferber","year":"2022","unstructured":"Ferber T, Garcia-Cely C, Schmidt-Hoberg K (2022) Belle II sensitivity to long-lived dark photons. Phys Lett B 833:137373","journal-title":"Phys Lett B"},{"key":"135_CR2","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/JHEP02(2020)039","volume":"2","author":"M Duerr","year":"2020","unstructured":"Duerr M et al (2020) Invisible and displaced dark matter signatures at Belle II. J High Energy Phys 2:39","journal-title":"J High Energy Phys"},{"key":"135_CR3","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/JHEP04(2021)146","volume":"4","author":"M Duerr","year":"2021","unstructured":"Duerr M et al (2021) Long-lived dark Higgs and inelastic dark matter at Belle II. J High Energy Phys 4:146","journal-title":"J High Energy Phys"},{"key":"135_CR4","unstructured":"Natochii A et\u00a0al (2022) Beam background expectations for Belle II at SuperKEKB. https:\/\/arxiv.org\/abs\/2203.05731"},{"issue":"2","key":"135_CR5","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/abbf9a","volume":"2","author":"J Shlomi","year":"2020","unstructured":"Shlomi J, Battaglia P, Vlimant J-R (2020) Graph neural networks in particle physics. Mach Learn Sci Technol 2(2):021001","journal-title":"Mach Learn Sci Technol"},{"key":"135_CR6","unstructured":"Wang Y et\u00a0al (2018) Dynamic graph CNN for learning on point clouds. https:\/\/arxiv.org\/abs\/1801.07829"},{"issue":"7","key":"135_CR7","doi-asserted-by":"publisher","first-page":"608","DOI":"10.1140\/epjc\/s10052-019-7113-9","volume":"79","author":"SR Qasim","year":"2019","unstructured":"Qasim SR et al (2019) Learning representations of irregular particle-detector geometry with distance-weighted graph networks. Eur Phys J C 79(7):608","journal-title":"Eur Phys J C"},{"key":"135_CR8","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/s41781-023-00105-w","volume":"7","author":"F Wemmer","year":"2023","unstructured":"Wemmer F et al (2023) Photon reconstruction in the Belle II calorimeter using graph neural networks. Comput Softw Big Sci 7:13","journal-title":"Comput Softw Big Sci"},{"issue":"9","key":"135_CR9","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1140\/epjc\/s10052-020-08461-2","volume":"80","author":"J Kieseler","year":"2020","unstructured":"Kieseler J (2020) Object condensation: one-stage grid-free multi-object reconstruction in physics detectors, graph and image data. Eur Phys J C 80(9):886","journal-title":"Eur Phys J C"},{"issue":"8","key":"135_CR10","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1140\/epjc\/s10052-022-10665-7","volume":"82","author":"SR Qasim","year":"2022","unstructured":"Qasim SR et al (2022) End-to-end multi-particle reconstruction in high occupancy imaging calorimeters with graph neural networks. Eur Phys J C 82(8):753","journal-title":"Eur Phys J C"},{"key":"135_CR11","doi-asserted-by":"crossref","unstructured":"Amrouche S et\u00a0al (2019) The tracking machine learning challenge: accuracy phase. In: The NeurIPS \u201918 competition. pp 231\u2013264","DOI":"10.1007\/978-3-030-29135-8_9"},{"issue":"1","key":"135_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s41781-023-00094-w","volume":"7","author":"S Amrouche","year":"2023","unstructured":"Amrouche S et al (2023) The tracking machine learning challenge: throughput phase. Comput Softw Big Sci 7(1):1","journal-title":"Comput Softw Big Sci"},{"key":"135_CR13","unstructured":"Choma N et\u00a0al (2020) Track seeding and labelling with embedded-space graph neural networks. https:\/\/arxiv.org\/abs\/2007.00149"},{"key":"135_CR14","doi-asserted-by":"publisher","first-page":"09028","DOI":"10.1051\/epjconf\/202429509028","volume":"295","author":"S Caillou","year":"2024","unstructured":"Caillou S et al (2024) Novel fully-heterogeneous GNN designs for track reconstruction at the HL-LHC. EPJ Web Conf 295:09028","journal-title":"EPJ Web Conf"},{"issue":"10","key":"135_CR15","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1140\/epjc\/s10052-021-09675-8","volume":"81","author":"X Ju","year":"2021","unstructured":"Ju X et al (2021) Performance of a geometric deep learning pipeline for HL-LHC particle tracking. Eur Phys J C 81(10):876","journal-title":"Eur Phys J C"},{"key":"135_CR16","unstructured":"Lieret K et\u00a0al (2023) High pileup particle tracking with object condensation. https:\/\/arxiv.org\/abs\/2312.03823"},{"key":"135_CR17","doi-asserted-by":"crossref","unstructured":"Correia A et\u00a0al (2024) Graph neural network-based track finding in the LHCb vertex detector. https:\/\/arxiv.org\/abs\/2407.12119","DOI":"10.1088\/1748-0221\/19\/12\/P12022"},{"key":"135_CR18","doi-asserted-by":"publisher","first-page":"03030","DOI":"10.1051\/epjconf\/202429503030","volume":"295","author":"S Caillou","year":"2024","unstructured":"Caillou S et al (2024) Physics performance of the ATLAS GNN4ITk track reconstruction chain. EPJ Web Conf 295:03030","journal-title":"EPJ Web Conf"},{"key":"135_CR19","unstructured":"Akram A, Ju X (2022) Track reconstruction using geometric deep learning in the straw tube tracker (STT) at the PANDA experiment. https:\/\/arxiv.org\/abs\/2208.12178"},{"key":"135_CR20","doi-asserted-by":"publisher","first-page":"09006","DOI":"10.1051\/epjconf\/202429509006","volume":"295","author":"X Jia","year":"2024","unstructured":"Jia X et al (2024) BESIII track reconstruction algorithm based on machine learning. EPJ Web Conf 295:09006","journal-title":"EPJ Web Conf"},{"key":"135_CR21","doi-asserted-by":"crossref","unstructured":"Kaneko F et\u00a0al (2024) Extracting signal electron trajectories in the COMET Phase-I cylindrical drift chamber using deep learning. https:\/\/arxiv.org\/abs\/2408.04795","DOI":"10.1093\/ptep\/ptaf048"},{"key":"135_CR22","doi-asserted-by":"publisher","first-page":"09004","DOI":"10.1051\/epjconf\/202429509004","volume":"295","author":"K Lieret","year":"2024","unstructured":"Lieret K, DeZoort G (2024) An object condensation pipeline for charged particle tracking at the high luminosity LHC. EPJ Web Conf 295:09004","journal-title":"EPJ Web Conf"},{"key":"135_CR23","unstructured":"Huang A et\u00a0al (2024) A language model for particle tracking. https:\/\/arxiv.org\/abs\/2402.10239"},{"key":"135_CR24","unstructured":"Caron S et\u00a0al (2024) TrackFormers: in search of transformer-based particle tracking for the high-luminosity LHC era. https:\/\/arxiv.org\/abs\/2407.07179"},{"issue":"1","key":"135_CR25","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1007\/s41781-017-0002-8","volume":"1","author":"T Keck","year":"2017","unstructured":"Keck T (2017) FastBDT: a speed-optimized multivariate classification algorithm for the Belle II experiment. Comput Softw Big Sci 1(1):2","journal-title":"Comput Softw Big Sci"},{"key":"135_CR26","unstructured":"B\u00e4hr S et\u00a0al (2024) The neural network first-level hardware track trigger of the Belle II experiment. https:\/\/arxiv.org\/abs\/2402.14962"},{"key":"135_CR27","unstructured":"HEP ML Community (2025) A living review of machine learning for particle physics. https:\/\/iml-wg.github.io\/HEPML-LivingReview\/"},{"key":"135_CR28","unstructured":"Abe T et\u00a0al (2010) Belle II technical design report. https:\/\/arxiv.org\/abs\/1011.0352"},{"key":"135_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2020.107610","volume":"259","author":"V Bertacchi","year":"2021","unstructured":"Bertacchi V et al (2021) Track finding at Belle II. Comput Phys Commun 259:107610","journal-title":"Comput Phys Commun"},{"key":"135_CR30","doi-asserted-by":"publisher","DOI":"10.1093\/ptep\/ptz106","volume":"2019","author":"E Kou","year":"2019","unstructured":"Kou E et al (2019) The Belle II physics book. Prog Theor Exp Phys 2019:123C01 (Erratum: Prog. Theor. Exp. Phys. 2020, 029201 (2020))","journal-title":"Prog Theor Exp Phys"},{"key":"135_CR31","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1016\/S0168-9002(03)01368-8","volume":"506","author":"S Agostinelli","year":"2003","unstructured":"Agostinelli S et al (2003) GEANT4\u2014a simulation toolkit. Nucl Instrum Methods A 506:250\u2013303","journal-title":"Nucl Instrum Methods A"},{"issue":"1","key":"135_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s41781-018-0017-9","volume":"3","author":"T Kuhr","year":"2019","unstructured":"Kuhr T et al (2019) The Belle II core software. Comput Softw Big Sci 3(1):1\u201312","journal-title":"Comput Softw Big Sci"},{"key":"135_CR33","doi-asserted-by":"publisher","unstructured":"Belle II Collaboration (2022) Belle II analysis software framework (basf2) (release-06-00-09). https:\/\/doi.org\/10.5281\/zenodo.6949513","DOI":"10.5281\/zenodo.6949513"},{"key":"135_CR34","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/S0010-4655(00)00048-5","volume":"130","author":"S Jadach","year":"2000","unstructured":"Jadach S, Ward BFL, Wa\u0327s Z (2000) The precision Monte Carlo event generator KK for two-fermion final states in $$e^+e^-$$ collisions. Comput Phys Commun 130:260","journal-title":"Comput Phys Commun"},{"key":"135_CR35","doi-asserted-by":"publisher","first-page":"079","DOI":"10.1007\/JHEP07(2014)079","volume":"07","author":"J Alwall","year":"2014","unstructured":"Alwall J et al (2014) The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations. J High Energy Phys 07:079","journal-title":"J High Energy Phys"},{"key":"135_CR36","doi-asserted-by":"publisher","DOI":"10.1093\/ptep\/ptac097","volume":"2022","author":"RL Workman","year":"2022","unstructured":"Workman RL et al (2022) Review of particle physics. Prog Theor Exp Phys 2022:083C01","journal-title":"Prog Theor Exp Phys"},{"key":"135_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.nima.2022.167168","volume":"1040","author":"ZJ Liptak","year":"2022","unstructured":"Liptak ZJ et al (2022) Measurements of beam backgrounds in SuperKEKB Phase 2. Nucl Instrum Methods Phys Res A 1040:167168","journal-title":"Nucl Instrum Methods Phys Res A"},{"key":"135_CR38","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1016\/j.nima.2010.03.136","volume":"620","author":"C Hoppner","year":"2010","unstructured":"Hoppner C et al (2010) A novel generic framework for track fitting in complex detector systems. Nucl Instrum Methods Phys Res A 620:518\u2013525","journal-title":"Nucl Instrum Methods Phys Res A"},{"issue":"1","key":"135_CR39","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/608\/1\/012042","volume":"608","author":"J Rauch","year":"2015","unstructured":"Rauch J, Schl\u00fcter T (2015) GENFIT\u2014a generic track-fitting toolkit. J Phys Conf Ser 608(1):012042","journal-title":"J Phys Conf Ser"},{"key":"135_CR40","unstructured":"Bilka T et\u00a0al (2019) Implementation of GENFIT2 as an experiment independent track-fitting framework. https:\/\/arxiv.org\/abs\/1902.04405"},{"key":"135_CR41","doi-asserted-by":"publisher","unstructured":"Jojosito et al (2023) GenFit\/GenFit. https:\/\/doi.org\/10.5281\/zenodo.10301439","DOI":"10.5281\/zenodo.10301439"},{"key":"135_CR42","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1016\/j.nima.2008.04.038","volume":"592","author":"T Alexopoulos","year":"2008","unstructured":"Alexopoulos T et al (2008) Implementation of the Legendre transform for track segment reconstruction in drift tube chambers. Nucl Instrum Methods Phys Res A 592:456\u2013462","journal-title":"Nucl Instrum Methods Phys Res A"},{"key":"135_CR43","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1016\/0168-9002(93)90945-E","volume":"329","author":"A Glazov","year":"1993","unstructured":"Glazov A et al (1993) Filtering tracks in discrete detectors using a cellular automaton. Nucl Instrum Methods Phys Res A 329:262\u2013268","journal-title":"Nucl Instrum Methods Phys Res A"},{"key":"135_CR44","unstructured":"Fey M, Lenssen JE (2019) Fast graph representation learning with PyTorch geometric. https:\/\/arxiv.org\/abs\/1903.02428"},{"key":"135_CR45","unstructured":"Lin M, Chen Q, Yan S (2014) Network in network. https:\/\/arxiv.org\/abs\/1312.4400"},{"key":"135_CR46","unstructured":"Ioffe S, Szegedy C (2015) Batch normalization: accelerating deep network training by reducing internal covariate shift. https:\/\/arxiv.org\/abs\/1502.03167"},{"key":"135_CR47","unstructured":"Clevert D-A, Unterthiner T, Hochreiter S (2016) Fast and accurate deep network learning by exponential linear units (ELUs). https:\/\/arxiv.org\/abs\/1511.07289"},{"key":"135_CR48","unstructured":"Biewald L (2020) Experiment tracking with weights and biases, 2020. Software available from https:\/\/wandb.ai\/site\/"},{"issue":"1","key":"135_CR49","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1007\/s41781-024-00117-0","volume":"8","author":"M Neu","year":"2024","unstructured":"Neu M et al (2024) Real-time graph building on FPGAs for machine learning trigger applications in particle physics. Comput Softw Big Sci 8(1):8","journal-title":"Comput Softw Big Sci"},{"key":"135_CR50","doi-asserted-by":"publisher","unstructured":"Reuter L et al (2025) Code for the paper \u201cEnd-to-End Multi-Track Reconstruction using Graph Neural Networks at Belle II\u201d. https:\/\/doi.org\/10.5281\/zenodo.15167005","DOI":"10.5281\/zenodo.15167005"}],"container-title":["Computing and Software for Big Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41781-025-00135-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41781-025-00135-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41781-025-00135-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T08:05:40Z","timestamp":1746259540000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41781-025-00135-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,3]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["135"],"URL":"https:\/\/doi.org\/10.1007\/s41781-025-00135-6","relation":{},"ISSN":["2510-2036","2510-2044"],"issn-type":[{"value":"2510-2036","type":"print"},{"value":"2510-2044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,3]]},"assertion":[{"value":"28 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"6"}}