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Nuclear TheoryEnglishPublished

Only two independent amplitudes exist for elastic spin‑zero–spin‑1/2 scattering in the five‑dimensional DKP algebra

October 29, 2026arXiv: 2610.37263v1

A recent analysis shows that the rich set of Lorentz covariants of the five‑dimensional Duffin‑Kemmer‑Petiau (DKP) algebra collapses to just two on‑shell physical amplitudes when applied to elastic spin‑zero–spin‑1/2 scattering. The six Lorentz classes—two scalars, two vectors, one antisymmetric tensor and one symmetric tensor—are all reduced by contracting DKP matrix elements with free spinors and Dirac bilinears. Explicit relations (equations 17–20 in the study) demonstrate that the scalar structures become proportional, the genuine non‑minimal vector transverse and vanishes when contracted with the conserved fermion current, and the tensor covariants contribute no new directions. Consequently, both scalar–vector choices used historically in meson–nucleus optical‑potential calculations correspond to the same two on‑shell directions. The different invariant functions among the four past DKP‑RIA cases are merely rescalings (see equations 53–55). When these covariants are folded into nuclear optical potentials, the projected‑vector and minimal‑vector couplings diverge only at quadratic order in the vector potential, while the projected‑scalar and identity‑scalar couplings differ only beyond first order through additional quadratic and derivative terms. Thus the apparent case dependence observed in earlier phenomenology is a feature of the optical embedding rather than of the underlying elementary amplitudes. The longitudinal non‑minimal vector cannot be extracted from free on‑shell amplitudes, and its effect first arises only after iteration in the optical equation.

Source paper

On-shell reduction of spin-zero Duffin-Kemmer-Petiau covariants and implications for the relativistic impulse approximation

Nuclear TheoryHigh Energy Physics - TheoryMathematics
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Only two independent amplitudes exist for elastic spin‑zero–spin‑1/2 scattering in the five‑dimensional DKP algebra | arXiv News