Higher twists in polarized DIS and the size of the constituent quark

The spontaneous breaking of chiral symmetry implies the presence of a short-distance scale in the QCD vacuum, which phenomenologically may be associated with the size of the constituent quark, $\rho \approx 0.3\mathrm{fm}$. We discuss the role of this scale in the matrix elements of the twist-4 and 3 quark-gluon operators determining the leading power ($1/Q^2$)-corrections to the moments of the nucleon spin structure functions. We argue that the flavor-nonsinglet twist-4 matrix element, $f_2^{u-d}$, has a sizable negative value of the order ${\rho }^{-2}$, due to the presence of sea quarks with virtualities $\sim {\rho }^{-2}$ in the proton wave function. The twist-3 matrix element, $d_2$, is not related to the scale ${\rho }^{-2}$. Our arguments support the results of previous calculations of the matrix elements in the instanton vacuum model. We show that this qualitative picture is in agreement with the phenomenological higher-twist correction extracted from an NLO QCD fit to the world data on $g_1^p$ and $g_1^n$, which include recent data from the Jefferson Lab Hall A and COMPASS experiments. We comment on the implications of the short-distance scale $\rho$ for quark-hadron duality and the $x$-dependence of higher-twist contributions.

Figure 1

Origin of the short-distance scale, $\rho$, associated with chiral-symmetry breaking.

Figure 2

Distribution of quark virtualities, $k^2$, in the proton’s isovector axial charge, as given by the effective chiral theory, Eq. (11). The twist-4 matrix element, $f_2^{u-d}$, is of the order of the integral of $k^{2}f(k)$.

Figure 3

The sea quark contribution to the axial charge, giving rise to the large-virtuality tail ($-k^2\sim {\rho }^{-2}$) in the distribution $f(k)$, Eqs. (12, 13).

Figure 4

The difference of higher-twist corrections to the proton and neutron spin structure functions, $h^p(x)-h^n(x)$, Eq. (19), as extracted from our NLO QCD fit to the world data (see references in Ref. 35), including recent $g_1^n$ data from the Jefferson Lab Hall A experiment [20], as well as deuteron data from COMPASS [21].