Flavour decomposition of the nucleon tensor multipole moments
Abstract
We compute the chiral-odd form factors HT, ET and hT of the nucleon in light-cone QCD sum rules, separately for the u and d quarks, and organise them into the tensor monopole, dipole and quadrupole moments gT, κT and QT. The quadrupole moment, with no chiral-even counterpart at leading twist, and the isoscalar channel, whose sum rules were derived but never evaluated, are new in this framework. The form factors are read from a Lorentz basis independent only after canonical ordering of the Dirac strings; three of the eight surviving structures give the three form factors separately, and the one usually used for the tensor charge is not among the eight. Two exact results follow analytically. The d-quark contributions to ET and hT are equal and opposite in the chiral limit, broken in proportion to the quark mass and the twist-six amplitude 𝒱6, so the d-quark sector carries a single independent function; and the isoscalar tensor charge receives no leading-twist contribution, its twist-three terms cancelling between the flavours. Neither is visible without resolving the flavours. At μ2=1~GeV2 the two distribution-amplitude sets give gTu−d=1.27(7), 1.08(6), κTu−d=1.35(62), 1.58(59), QTu−d=−4.40(83), $-4.20(73)$ and gTu+d=0.39(7), 0.38(6), κTu+d=4.47(62), 4.32(59), QTu+d=2.41(53), 1.56(30). The mean-field relation 2hTu−d=−ETu−d, tested without any large-Nc assumption, holds in sign and order of magnitude, with ratio 0.64(16) and 0.67(15) against the predicted unity. In the impact-parameter plane the moments displace the two flavour distributions in opposite transverse directions by nearly equal amounts, ⟨ by⟩=0.37 and −0.37~fm, and elongate both across the polarisation axis, the d quark some five to six times more strongly
Related
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- Chiral anomaly and nucleon spin decomposition in the chiral quark soliton model
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BibTeX
@misc{ozdem2026flavour,
title = {{Flavour decomposition of the nucleon tensor multipole moments}},
author = {U. Özdem},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11745},
eprint = {2610.11745},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11745},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Flavour decomposition of the nucleon tensor multipole moments
AU - U. Özdem
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11745
UR - https://arxiv.org/abs/2610.11745
AB - We compute the chiral-odd form factors H_T, E_T and hT of the nucleon in light-cone QCD sum rules, separately for the u and d quarks, and organise them into the tensor monopole, dipole and quadrupole moments g_T, κ_T and Q_T. The quadrupole moment, with no chiral-even counterpart at leading twist, and the isoscalar channel, whose sum rules were derived but never evaluated, are new in this framework. The form factors are read from a Lorentz basis independent only after canonical ordering of the Dirac strings; three of the eight surviving structures give the three form factors separately, and the one usually used for the tensor charge is not among the eight. Two exact results follow analytically. The d-quark contributions to E_T and hT are equal and opposite in the chiral limit, broken in proportion to the quark mass and the twist-six amplitude 𝒱_6, so the d-quark sector carries a single independent function; and the isoscalar tensor charge receives no leading-twist contribution, its twist-three terms cancelling between the flavours. Neither is visible without resolving the flavours. At μ^2=1~GeV^2 the two distribution-amplitude sets give g_T^u−d=1.27(7), 1.08(6), κ_T^u−d=1.35(62), 1.58(59), Q_T^u−d=−4.40(83), $-4.20(73)$ and g_T^u+d=0.39(7), 0.38(6), κ_T^u+d=4.47(62), 4.32(59), Q_T^u+d=2.41(53), 1.56(30). The mean-field relation 2hT^u−d=−E_T^u−d, tested without any large-N_c assumption, holds in sign and order of magnitude, with ratio 0.64(16) and 0.67(15) against the predicted unity. In the impact-parameter plane the moments displace the two flavour distributions in opposite transverse directions by nearly equal amounts, ⟨ b_y⟩=0.37 and −0.37~fm, and elongate both across the polarisation axis, the d quark some five to six times more strongly
ER -