Speaker
Description
The Ji sum rules [1] permit to calculate contributions of quarks and gluons to the nucleon spin using the generalized parton distributions (GPDs).
This solves the spin-crisis problem. In order to obtain GPDs from experimental data on vector-meson production (VMP), helicity amplitudes of the process are needed. In the present work, the amplitude method (AM) is discussed [2], which is direct extraction of the helicity-amplitude ratios from angular distributions of final particles normalized to unity. The AM is compared with the standard method of spin-density matrix-element (SDME) extraction (SDME method). It is shown that the angular distribution of the final particles from the vector-meson decay is non-negative for any non-zero amplitudes [3].
The non-negativity is absent for the SDME method but this property is important for application of the maximum likelihood method of data treating. The exact formulas for the helicity-amplitude ratios in terms of the SDMEs for spinless targets are presented [4]. It is argued that these formulas are applicable to VMP on the unpolarized nucleons if unnatural-parity-exchange amplitudes and nucleon-spin-flip amplitudes are much smaller than natural-parity-exchange amplitudes without the nucleon spin flip [3]. It is argued and illustrated with examples that the SDMEs (especially ``polarized'' ones) calculated with the amplitude ratios obtained in the AM have experimental errors smaller than those extracted by the SDME method [2, 5]. The new approximate formula for the longitudinal-to-transverse cross-section ratio for the VMP is discussed [3, 4].
References
1. X. D. Ji, Phys. Rev. Lett. ${\bf 78}$ 610 (1997).
2. A. Airapetian et al. (HERMES Collaboration), Eur. Phys. J. C ${\bf 71}$ 1609 (2011).
3. S.I. Manaenkov, Phys. of Atomic Nuclei ${\bf 87}$ 505 (2024).
4. S.I. Manaenkov, Phys. of Part. and Nucl. Lett. ${\bf 21}$ 34 (2024).
5. A. Airapetian et al. (HERMES Collaboration), Eur. Phys. J. C ${\bf 77}$ 378 (2017).
