This paper reexamines the “sea” of light anti‑quarks inside the proton and finds that anti‑up quarks (ū) outnumber anti‑down quarks (d̄) over a wide range of momentum fractions x. The authors reach this conclusion by performing two next‑to‑next‑to‑leading order (NNLO) global fits to modern proton data. One fit uses only the combined HERA electron–proton deep‑inelastic scattering measurements (called HERAshape). The second adds ATLAS measurements of W± and Z boson production in 7 TeV proton–proton collisions (called ATLASshape). The ATLAS dataset has an integrated luminosity of 4.6 fb−1 and helps pin down flavor differences in the proton sea.

What the researchers did, in plain terms, is take high‑precision measurements that are sensitive to which types of quarks are present and at what fraction x of the proton momentum they carry. The HERA data cover an especially wide kinematic range (for neutral current interactions x from about 6×10−7 to 0.65 and Q2 from 0.045 to 50 000 GeV2; for charged current interactions x ≳ 1.3×10−2). Charged current processes at HERA, where a W boson changes a quark’s flavor, are directly sensitive to the light anti‑quark content. The authors ran NNLO QCD fits using standard tools (xFitter, QCDNUM, APPLgrid, and MINUIT) and allowed more freedom in the parametrization of ū and d̄ than in some earlier fits. They also used a strange‑to‑down ratio implied by ATLAS measurements, which corresponds to a strange fraction fs ≃ 0.54 in their setup.

The two fits agree that the anti‑up distribution is larger than the anti‑down distribution for x roughly between 10−2 and 1. Including the ATLAS W/Z data reduces the uncertainties and changes the detailed shape: the authors report two crossings of the difference x(d̄−ū) near x ≈ 10−3 and x ≈ 2×10−2, and overall a suppression of d̄ relative to ū at higher x. They also find a noticeably larger strange quark contribution than in some older proton fits; the ATLAS data in particular push the strange component upward.