Chiral-odd structure of the $N\to \Delta$ transition: tensor form factors from QCD light-cone sum rules

Abstract

We present the first direct calculation of the tensor transition form factors (TFFs) of the $N\to \Delta$ transition using the QCD light-cone sum rules. The matrix element of the tensor current sandwiched between the nucleon and $\Delta$ states is parametrized in terms of four independent form factors, derived from Lorentz covariance, Hermiticity, parity, time-reversal, and the Rarita--Schwinger constraints. The natural-parity character of the $1/2^{+}\to 3/2^{+}$ channel combined with the spin-$1$ polarization content of the Rarita--Schwinger spinor imposes a trailing ${\gamma }_5$ in the parametrization, in analogy with the gravitational $N\to \Delta$ case. Using the nucleon distribution amplitudes expanded in wavefunctions of different twists, we compute the four TFFs in the spacelike range $1\le Q^2\le 10$~GeV${}^2$ for two sets of light-cone input parameters, and extrapolate to the static limit through multipole fit functions. A flavor decomposition into $u$- and $d$-quark contributions reveals three qualitatively distinct patterns among the four TFFs: $d$-quark dominance with $|F^d|\gg |F^u|$ for $F_1$ and $F_2$ -- in marked contrast to the diagonal nucleon tensor charges where the $u$-quark dominates; an antisymmetric flavor structure $F^u\approx -F^d$ for $F_3$, which naturally explains the absence of a stable isoscalar sum rule for this form factor; and comparable but opposite-sign flavor contributions to $F_4$, with a suppressed isoscalar combination. The TFFs provide chiral-odd information complementary to the electromagnetic and gravitational $N\to \Delta$ transitions and offer model-independent input for future analyses of transversity-related transition observables, to be checked against lattice QCD and other phenomenological approaches.

Comments: 22 pages, 4 Tables, 3 figures,