We compute the next-to-leading order (NLO) QCD corrections to the class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000630&_mathId=si1.gif&_user=111111111&_pii=S0370269316000630&_rdoc=1&_issn=03702693&md5=1afcafd86c05446e0c2c8b7d71f4ce9d">class="imgLazyJSB inlineImage" height="18" width="163" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316000630-si1.gif">class="mathContainer hidden">class="mathCode"> process, mediated by a massless quark loop, at the LHC. This process first contributes to the hadroproduction of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000630&_mathId=si2.gif&_user=111111111&_pii=S0370269316000630&_rdoc=1&_issn=03702693&md5=a24bdb29c3a8ce3a1b112de5f750ff2b" title="Click to view the MathML source">W+W−class="mathContainer hidden">class="mathCode"> at class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000630&_mathId=si3.gif&_user=111111111&_pii=S0370269316000630&_rdoc=1&_issn=03702693&md5=83261383f770ce974d9b03eaaa53f7e9">class="imgLazyJSB inlineImage" height="17" width="40" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316000630-si3.gif">class="mathContainer hidden">class="mathCode">, but, nevertheless, has a sizable impact on the total production rate. We find that the NLO QCD corrections to the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000630&_mathId=si22.gif&_user=111111111&_pii=S0370269316000630&_rdoc=1&_issn=03702693&md5=5409dc73f717fab811200a26fda6dbc2" title="Click to view the MathML source">gg→W+W−class="mathContainer hidden">class="mathCode"> process amount to class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000630&_mathId=si5.gif&_user=111111111&_pii=S0370269316000630&_rdoc=1&_issn=03702693&md5=e925785d0837942bde66ed19249db154" title="Click to view the MathML source">O(50)%class="mathContainer hidden">class="mathCode">, and increase the NNLO QCD cross sections of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000630&_mathId=si6.gif&_user=111111111&_pii=S0370269316000630&_rdoc=1&_issn=03702693&md5=f4e2b0357f003b9db1df1c4993055c7a" title="Click to view the MathML source">pp→W+W−class="mathContainer hidden">class="mathCode"> by approximately two percent, at both the 8 TeV and 13 TeV LHC. We also compute the NLO corrections to gluonic class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000630&_mathId=si2.gif&_user=111111111&_pii=S0370269316000630&_rdoc=1&_issn=03702693&md5=a24bdb29c3a8ce3a1b112de5f750ff2b" title="Click to view the MathML source">W+W−class="mathContainer hidden">class="mathCode"> production within a fiducial volume used by the ATLAS Collaboration in their 8 TeV measurement of the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000630&_mathId=si2.gif&_user=111111111&_pii=S0370269316000630&_rdoc=1&_issn=03702693&md5=a24bdb29c3a8ce3a1b112de5f750ff2b" title="Click to view the MathML source">W+W−class="mathContainer hidden">class="mathCode"> production rate and find that the QCD corrections are significantly smaller than in the inclusive case. While the current experimental uncertainties are still too large to make these differences relevant, the observed strong dependence of perturbative corrections on kinematic cuts underscores that extrapolation from a fiducial measurement to the total cross section is an extremely delicate matter, and calls for the direct comparison of fiducial volume measurements with corresponding theoretical computations.