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Scattering that resolves the constituents of a hadron at large spacelike momentum transfer, with an inclusive sum over final hadron states.

In Electron scattering from a proton, write the reaction as $e^{-}p\to e^{-}X$: the outgoing Electron is measured, while $X$ denotes all allowed final hadron states. Large momentum transfer supplies a short-distance probe; a large final invariant mass separates the deep continuum from elastic scattering and individual particle resonances. The useful surprise is that an extended proton can have a response characteristic of much smaller constituents. Deep inelastic scattering turns measurements outside the proton into constraints on its internal parton distribution functions.

The SLAC-MIT deep inelastic electron scattering experiment connects this definition to an actual measurement. Its evidence came from distributions of outgoing Electron energies and scattering angles, rather than a photograph of a quark. Bjorken scaling concerns deep-inelastic structure functions after known scattering factors have been accounted for; it does not say that the raw differential scattering cross-section is constant.

The 1969 SLAC-MIT deep inelastic electron scattering experiment found approximate Bjorken scaling: an estimated deep-inelastic structure function depended mainly on a ratio of kinematic variables. Its restricted angular coverage did not separately determine both deep-inelastic structure functions, and the extraction assumed transverse virtual photons. This was motivation for a microscopic theory, not already a measurement of the QCD coupling.^[ref]

The 1973 David Gross–Frank Wilczek calculation supplied a quantum field theory explanation of approximately free partons with calculable logarithmic corrections. Asymptotic freedom therefore permits approximate Bjorken scaling without requiring exact scale independence. The QCD coupling governs the corrections, while parton distribution functions and their evolution connect the short-distance calculation to a proton.^[ref]

In a later direct test, H1 collided Positrons and protons at HERA and selected deep inelastic scattering events. A liquid-argon particle calorimeter identified the outgoing Positron with an associated track; calorimeter deposits and charged tracks reconstructed particle jets in the Breit frame. Vertex, timing and longitudinal energy-balance cuts suppressed backgrounds; two simulations checked detector corrections. Fits of particle jet cross sections to next-to-leading-order QCD extracted ${\alpha }_s(E_T)$ in transverse-energy bins, consistent with decreasing QCD coupling. Hadronization, parton distribution functions and renormalization scale choices limited the inference. This measures rates and fits a coupling, rather than directly reading a force meter.^[ref]