Constructing the S-matrix With Complex Factorization

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A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates nontrivial (but familiar) constraints on three-particle coupling constants - these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an ... continued below

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35 pages

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Schuster, Philip C.; /SLAC; Toro, Natalia & /Stanford U., ITP June 19, 2009.

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A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates nontrivial (but familiar) constraints on three-particle coupling constants - these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior {approx} 1/z{sup 2}.

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35 pages

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  • Journal Name: JHEP 0906:079,2009

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  • Report No.: SLAC-PUB-13426
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 957443
  • Archival Resource Key: ark:/67531/metadc933969

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  • June 19, 2009

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 15, 2016, 3:22 p.m.

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Schuster, Philip C.; /SLAC; Toro, Natalia & /Stanford U., ITP. Constructing the S-matrix With Complex Factorization, article, June 19, 2009; United States. (digital.library.unt.edu/ark:/67531/metadc933969/: accessed December 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.