Measurement of the charge asymmetry of electrons from the decays of $W$ bosons produced in $pbar{p}$ collisions at $sqrt{s}=1.96$ TeV

At the Fermilab Tevatron proton-antiproton ($pbar{p}$) collider, high-mass electron-neutrino ($e u$) pairs are produced predominantly in the process $p bar{p} rightarrow W(rightarrow e u) + X$. The asymmetry of the electron and positron yield as a function of their pseudorapidity constrain the slope of the ratio of the $u$- to $d$-quark parton distributions versus the fraction of the proton momentum carried by the quarks. This paper reports on the measurement of the electron-charge asymmetry using the full data set recorded by the Collider Detector at Fermilab in 2001--2011 and corresponding to 9.1~fb$^{-1}$ of integrated luminosity. The measurement significantly improves the precision of the Tevatron constraints on the parton-distribution functions of the proton. Numerical tables of the measurement are provided.