Connected-Sea Partons

TL;DR

It is shown that the CS and DS components of ū( x) + d(x) can be extracted by using recent data on the strangeness parton distribution, the CT10 global fit, and the lattice result of the ratio of the strange to u(d) moments in the disconnected insertion.

Abstract

According to the path-integral formalism of the hadronic tensor, the nucleon sea contains two distinct components called connected sea (CS) and disconnected sea (DS). We discuss how the CS and DS are accessed in the lattice QCD calculation of the moments of the parton distributions. We show that the CS and DS components for $\bar u(x) + \bar d(x)$ can be extracted by using recent data on the strangeness parton distribution, the CT10 global fit, and the lattice result of the ratio of the strange to $u(d)$ moments in the disconnected insertion. The extracted CS and DS for $\bar u(x) + \bar d(x)$ have distinct Bjorken $x$ dependence in qualitative agreement with expectation. The analysis also shows that the momentum fraction of the $\bar u(x) + \bar d(x)$ is about equally divided between CS and DS at $Q^2 = 2.5 {\rm GeV}^2$. Implications on future global analysis for parton distributions are presented.

Figures (5)

• Figure 1: Three gauge invariant and topologically distinct diagrams in the Euclidean path-integral formalism of the nucleon hadronic tensor in the large momentum frame. In between the currents at $t_1$ and $t_2$, the parton degrees of freedom are (a) the valence and CS partons $q^{v+cs}$, (b) the CS anti-partons $\bar{q}^{cs}$, and (c) the DS partons $q^{ds}$ and anti-partons $\bar{q}^{ds}$ with $q = u, d, s,$ and $c$. Only $u$ and $d$ are present in (a) and (b).
• Figure 2: The three-point functions after the short-distance expansion of the hadronic tensor from Fig. 1. (a) The connected insertion (CI) is derived from Fig. \ref{['val+CS']} and Fig. \ref{['CS']}. (b) The disconnected insertion (DI) originates from Fig. \ref{['DS']}. $\mathcal{O}_q^n$ are local operators which are the same as derived from OPE.
• Figure 3: The strange quark PDF from HERMES semi-inclusive DIS experiment of kaon production on deuteron. It is compared to CT10 results.
• Figure 4: $x(\bar{d}^{cs}(x) + \bar{u}^{cs}(x))$ obtained from Eq. (\ref{['udCS']}) is plotted together with $x(\bar{d}(x) - \bar{u}(x))$ from E866 Drell-Yan experiment tma01 and from SIDIS HERMES experiment ack98.
• Figure 5: $x(\bar{u}^{cs}(x) + \bar{d}^{cs}(x))$ obtained from Eq. (\ref{['udCS']}) is plotted together with $x(\bar{u}(x) + \bar{d}(x))$ from CT10 and $\frac{1}{R}x(s(x)+\bar{s}(x))$ which is taken to be $x(\bar{u}^{ds}(x)+\bar{d}^{ds}(x))$.