Flavour decomposition of the nucleon tensor multipole moments

Abstract

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 $\mathcal{V}_6$, 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 $2\hT^{u-d}=-E_T^{u-d}$, 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, $\langle b_y\rangle=0.37$ and $-0.37$~fm, and elongate both across the polarisation axis, the $d$ quark some five to six times more strongly