{"paper":{"title":"Bounds on scattering amplitudes of non-identical scalar particles in 4d","arxiv_id":"2609.09282","primary_cat":"hep-th","submitted_at":"2026-09-08T18:00:02+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":true,"role":"contribution","text":"We initiate the study of two-to-two scattering amplitudes involving two distinct scalar particles in $d = 4$ spacetime dimensions using the primal S-matrix bootstrap.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.93,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.67,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":1,"p":0.88,"id":"s1","own":true,"role":"method","text":"We impose a $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$ global symmetry under which the two particles are the lightest ones carrying charges $(-,+)$ and $(+,-)$, guaranteeing their absolute stability and absence of triangular anomalous thresholds.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.39,"role_probabilities":{"gap":0.0,"method":0.88,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.12,"interpretation":0.0}},{"i":2,"p":0.38,"id":"s2","own":false,"role":"result","text":"For unequal masses, the presence of a pseudo-physical cut whose discontinuity is not directly constrained by physical unitarity qualitatively changes the bootstrap problem.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.4,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.02,"method":0.01,"result":0.38,"background":0.2,"limitation":0.02,"future_work":0.0,"contribution":0.05,"interpretation":0.32}},{"i":3,"p":1.0,"id":"s3","own":true,"role":"result","text":"We find several observables to be unbounded, while others obey non-trivial one-sided bounds or become bounded once another observable is fixed.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.67,"quantitative":true,"quantitative_p":0.71,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":0.99,"id":"s4","own":true,"role":"result","text":"In the equal-mass limit, where the pseudo-physical region disappears, two-sided bounds are recovered.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.87,"main_claim_p":0.18,"quantitative":true,"quantitative_p":0.75,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.01}},{"i":5,"p":0.56,"id":"s5","own":true,"role":"result","text":"As a proof of concept, we show that supplying information about the pseudo-physical discontinuity through an Omn\\`es parametrisation also restores 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