Parton density lab

Choose Q (1–1000 GeV) and the probe x. The preview and valid edits update immediately. Number fields accept exact values; sliders move in logarithmic steps. Enable Q′ to compare scales using dashed curves and a separate density column. Reset restores a live default view. Only exact input text and the comparison choice are retained, including unfinished entries; curves and results are rebuilt. Legacy logarithmic slider settings migrate to the corresponding physical values.

x is the fraction of longitudinal proton momentum carried by a parton. The vertical axis shows x f(x), not the number density f(x). The x axis is logarithmic. The four displayed contributions are up valence, down valence, gluons and the combined sea-quark plus antiquark contribution. Here “sea” is one aggregated, symmetric q/q̄ pair, not a flavor-resolved PDF set.

Local share divides a component’s x f(x) by the total at the selected x. It is neither its share of all proton momentum nor a measured probability. Open Momentum shares to see the integrals ∫₀¹ x f(x) dx instead. The plot starts at x=0.001; the analytic integrals include the entire interval 0–1.

Heuristic teaching model. Each density has the form N xᵃ(1−x)ᵇ. Shape exponents change smoothly with s=log₁₀(Q/GeV)/3 across the whole slider range. The amplitudes keep ∫uᵥ dx=2 and ∫dᵥ dx=1. The remaining momentum is assigned 80% to gluons and 20% to the combined sea. Those proportions and shape changes are arbitrary teaching choices. The sea curve and its table row both include q+q̄=2 sea.

The full momentum sum is 1 by construction, not an independent validation of QCD. These are not experimental PDF fits, do not solve DGLAP equations and do not predict cross sections, uncertainties or heavy-flavor thresholds.

PDG Structure Functions (2025): Definitions and QCD evolution.

Click inside the plot to place the probe. Solid component dots use Q and hollow dots use Q′. The x field is the exact and keyboard-accessible alternative. Clicks and slider moves set eight significant digits; typed text is not rounded. The supported probe range is 0.001 ≤ x < 1. The final slider position uses the nearest representable value below 1, because local fractions at the exact endpoint are undefined. Changing x moves the probe and updates local readings without rebuilding the curves.