Nucleon matrix elements of the antisymmetric quark tensor

If physics beyond the Standard Model enters well above the electroweak scale, its low-energy effects are described by Standard Model Effective Field Theory. Already at dimension six many operators involve the antisymmetric quark tensor $\bar q σ^{μν} q$, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.

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