Scattering of massless particles in arbitrary dimensions.

By F. Cachazo, Song He, E. Y. Yuan. Physical Review Letters, 2013

675 citations recorded by the source corpus.

We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions. The new formula for the scattering of n particles is given by an integral over the positions of n points on a sphere restricted to satisfy a dimension-independent set of equations. The integrand is constructed using the reduced Pfaffian of a 2n×2n matrix, Ψ, that depends on momenta and polarization vectors. In its simplest form, the gravity integrand is a reduced determinant which is the square of the Pfaffian in the Yang-Mills integrand. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/04b311a7eca8244c3d72e45e0a249da2d110be46

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Citations in the corpus

Celestial operator products of gluons and gravitons (2019, neutral): “This resonates with similar findings in the amplitudes program [26–30].”
Λ scattering equations (2016, background): “J H E P 0 6 ( 2 0 1 6 ) 1 0 1 the contour integral [1] ∫ n ∏”
Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM (2014, methodology): “The reason this matrix is singled out is that its Pfaffian is multi-linear in polarization vectors, it is manifestly gauge invariant and it factorizes very cleanly in a soft limit [5].”
Gluon Amplitudes as 2d Conformal Correlators (2017, background): “Indeed several constructions including the scattering equations [17] and twistor space [18–20] seem close to achieving this goal.”
TASI Lectures on Scattering Amplitudes (2017, background): “A partial explanation can be found in the scattering equations of Cachazo, He, and Yuan [98, 99, 75], who proposed an extraordinarily compact construction for the S-matrices of all the theories in Fig.”
Scattering forms and the positive geometry of kinematics, color and the worldsheet (2017, background): “[28, 30]), an object whose importance has been highlighted in Nair’s observation [31] and Witten’s twistor string [4], and especially in the story of scattering equations and the CHY formulas for scattering amplitudes [5, 6, 15, 32].”
Color-kinematics duality for QCD amplitudes (2015, background): “The BCJ amplitude relations motivated the discovery of the scattering equations and associated elegant string-like formulas for gauge and gravity tree amplitudes [86–89].”