{"work":{"id":"360be703-48d8-4bf8-a4ff-957eedb78108","openalex_id":null,"doi":null,"arxiv_id":"1309.0885","raw_key":null,"title":"Scattering of Massless Particles: Scalars, Gluons and Gravitons","authors":null,"authors_text":"F","year":2013,"venue":"hep-th","abstract":"In a recent note we presented a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper we show that a natural formulation also exists for a massless colored cubic scalar theory. In Yang-Mills, the formula is an integral over the space of n marked points on a sphere and has as integrand two factors. The first factor is a combination of Parke-Taylor-like terms dressed with U(N) color structures while the second is a Pfaffian. The S-matrix of a U(N)xU(N') cubic scalar theory is obtained by simply replacing the Pfaffian with a U(N') version of the previous U(N) factor. Given that gravity amplitudes are obtained by replacing the U(N) factor in Yang-Mills by a second Pfaffian, we are led to a natural color-kinematics correspondence. An expansion of the integrand of the scalar theory leads to sums over trivalent graphs and are directly related to the KLT matrix. We find a connection to the BCJ color-kinematics duality as well as a new proof of the BCJ doubling property that gives rise to gravity amplitudes. We end by considering a special kinematic point where the partial amplitude simply counts the number of color-ordered planar trivalent trees, which equals a Catalan number. The scattering equations simplify dramatically and are equivalent to a special Y-system with solutions related to roots of Chebyshev polynomials.","external_url":"https://arxiv.org/abs/1309.0885","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-24T14:36:13.032505+00:00","pith_arxiv_id":"1309.0885","created_at":"2026-05-11T22:46:15.444065+00:00","updated_at":"2026-06-05T21:23:00.469572+00:00","title_quality_ok":true,"display_title":"Scattering of Massless Particles: Scalars, Gluons and Gravitons","render_title":"Scattering of Massless Particles: Scalars, Gluons and Gravitons"},"hub":{"state":{"work_id":"360be703-48d8-4bf8-a4ff-957eedb78108","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":25,"external_cited_by_count":null,"distinct_field_count":2,"first_pith_cited_at":"2020-06-22T12:32:12+00:00","last_pith_cited_at":"2026-05-20T18:00:01+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-06-06T20:41:04.894196+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":3}],"polarity_counts":[{"context_polarity":"background","n":2},{"context_polarity":"unclear","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}