Counting parity-violating local S-matrices

Abstract

Four point tree-level local S-matrices form a module over ring of polynomials of Mandelstam invariants s, t and u. The module of local analytic S-matrices can be encoded in terms of a partition function which is enumerated using plethystic techniques. In this paper, we enumerate the plethystic contribution to local four point photon, graviton and gluon multi-particle partition functions that encode parity violating 2 → 2 scattering. We generalise the counting problem solved in [1, 2] to project out parity violating sectors, a subtle task in even dimensions [3]. We explicitly enumerate the parity odd contributions to the multi-letter partition function for gauge fields, gravitons and gluons and evaluate the resulting parity violating partition functions in D = 4, 6. We also perform a large D analysis to show that parity violating local interactions do not contribute to four particle scattering in higher dimensions (D ≥ 8). Our computations and observations for photons, gravitons and gluons agree with the transformation properties of these S-matrices previously conjectured in [1, 2]

Regge constraints on local four-point scattering amplitudes of massive particles with spin

“…Before we explicitly compute the analytic S-matrices, we first record our expectation from a group-theoretic analysis. The enumeration of possible analytic structures contributing to tree-level 2 → 2 scattering of spinning particles can also be formulated as a group theory problem which has been addressed recently in great detail for massless and massive particles in [1,9,[38][39][40][41]. The little group for massive spinning particles is SO(D − 1).…”