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

At the Fermilab Tevatron proton-antiproton (<math display="inline"><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math>) collider, high-mass electron-neutrino (<math display="inline"><mi>e</mi><mi>ν</mi></math>) pairs are produced predominantly in the process <math display="inline"><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><mi>W</mi><mo stretchy="false">(</mo><mo stretchy="false">→</mo><mi>e</mi><mi>ν</mi><mo stretchy="false">)</mo><mo>+</mo><mi>X</mi></math>. The asymmetry of the electron and positron yield as a function of their pseudorapidity constrain the slope of the ratio of the <math display="inline"><mi>u</mi></math>- to <math display="inline"><mi>d</mi></math>-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 <math display="inline"><mrow><mn>9.1</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fb</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math> 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.