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Polarized Deep Inelastic ScatteringEdit

Polarized deep inelastic scattering (PDIS) is a key tool for peering into the spin structure of the nucleon. In this process, a high-energy lepton beam is scattered off a polarized nucleon target, allowing experimenters to access spin-dependent information that is encoded in structure functions such as g1(x, Q^2) and g2(x, Q^2). By comparing how the scattering rate changes with the relative orientation of the lepton and nucleon spins, physicists extract details about how the constituents of the nucleon—quarks and gluons—contribute to its overall spin. This field sits at the intersection of the parton model, Quantum Chromodynamics (QCD), and precise experimental technique, and it has driven interpretations of how the spin of a proton or neutron emerges from its internal dynamics. See for example structure function and deep inelastic scattering to place PDIS in the broader context of high-energy physics.

From a practical standpoint, PDIS experiments have evolved from early fixed-target studies to modern, high-luminosity programs. They test how the spin-dependent parton distributions evolve with momentum transfer Q^2, how quark helicities sum to the nucleon spin, and how gluons and orbital angular momentum enter the picture. The data underpin a detailed, testable narrative in which the spin of the nucleon is not a single, monolithic quantity but the result of several competing contributions that vary with x (the fraction of the nucleon’s momentum carried by a parton) and with Q^2. See quantum chromodynamics and parton distribution functions for the theoretical framework behind the interpretation of PDIS results.

Theoretical framework

  • Polarization and cross sections: In polarized deep inelastic scattering, the differential cross section contains spin-dependent terms that isolate g1 and g2. These structure functions are related to the helicity distributions of quarks and to more subtle quark-gluon correlations. For a concise introduction, see g1 structure function and g2 structure function.

  • Parton model and QCD: In the naive parton model, the proton’s spin is carried by the spins of its quarks. In the QCD framework, the spin content is decomposed into quark helicities (ΔΣ), gluon polarization (ΔG), and orbital angular momentum (Lq +Lg). The decomposition is constrained by fundamental sum rules such as the Bjorken sum rule and, under certain assumptions, the Ellis–Jaffe sum rule for flavor-separated contributions.

  • Evolution and global analyses: The q^2-dependence of spin-dependent parton distributions is governed by QCD evolution equations. Modern analyses combine PDIS data with semi-inclusive DIS and other measurements to extract Δq(x, Q^2) and Δg(x, Q^2) across a wide kinematic range, as seen in contemporary fits like those from DSSV or JAM.

  • Experimental observables: The asymmetries measured in PDIS experiments, such as A1 and A2, connect directly to the ratio of polarized to unpolarized structure functions and to the underlying helicity distributions. See spin asymmetry for a broader discussion of these observables.

Experimental program and key results

  • Early SLAC and CERN programs: Initial polarized DIS experiments established the feasibility of measuring spin-dependent cross sections and opened the door to quantifying the spin content of the nucleon. See SLAC and CERN programs for historical context.

  • The EMC moment and the spin crisis: The European Muon Collaboration (EMC) reported results that suggested quark spins account for only a small fraction of the proton’s spin, triggering intense theoretical and experimental activity. This “spin crisis” stimulated a re-examination of how spin is distributed among quarks, gluons, and orbital motion. See spin crisis and the ensuing literature.

  • Mid–career refinements: Experiments at HERMES and COMPASS refined measurements of polarized quark distributions and contributed to the growing consensus that gluon polarization and orbital angular momentum play nontrivial roles. The Jefferson Laboratory program provided high-precision data at intermediate Q^2, complementing the high-energy program.

  • Semi-inclusive DIS and flavor separation: By detecting specific hadrons in the final state, SIDIS experiments provide flavor-sensitive information about quark helicities, improving the separation of up, down, and strange quark contributions. See semi-inclusive deep inelastic scattering for details.

  • Lattice and global analyses: Lattice QCD calculations offer ab initio estimates of components of the spin decomposition, while global fits that combine DIS and SIDIS data, together with theoretical evolution, yield a quantitative picture of ΔΣ, ΔG, and orbital contributions. See lattice QCD and global analysis.

Spin structure of the nucleon

  • Quark helicity contributions (ΔΣ): The total spin carried by quark helicities is a central quantity in PDIS studies. While initial measurements suggested a surprisingly small quark contribution, more recent analyses indicate that quarks contribute a substantial but incomplete portion of the nucleon spin, with the remainder supplied by gluons and orbital motion. See quark helicity distribution and nucleon spin for a broader synthesis.

  • Gluon polarization (ΔG): The spin carried by gluons is probed both indirectly through QCD evolution and directly in certain processes sensitive to gluon spin. Evidence supports a nonzero ΔG, but the size and x-dependence are still actively constrained by data and theory. See gluon polarization for details.

  • Orbital angular momentum (Lq + Lg): A growing portion of the nucleon spin is attributed to the orbital motion of quarks and gluons inside the nucleon. This aspect is more challenging to access experimentally, but it is essential for a complete spin budget. See orbital angular momentum for a relevant discussion.

  • Sum rules and consistency checks: The Bjorken sum rule provides a robust, model-independent test of QCD and the isovector part of the spin structure. The validity of this and related relations across Q^2 is a central consistency check for the whole framework. See sum rule.

Controversies and debates

  • The spin decomposition and its interpretation: A central debate concerns how to interpret the decomposition ΔΣ + ΔG + Lq + Lg into a physical, gauge-invariant picture of the nucleon’s spin. Critics of overly simplistic narratives emphasize that orbital angular momentum and gluon dynamics can be as important as quark spins, while others argue for a practical, testable partition that guides experiment and theory alike. See nucleon spin decomposition.

  • Assumptions behind the Ellis–Jaffe sum rule: The Ellis–Jaffe prediction relies on SU(3) flavor symmetry and vanishing strange-quark polarization. In light of data, these assumptions come under scrutiny, and many researchers prefer to treat the sum rule as a guiding constraint rather than a strict test. See Ellis–Jaffe sum rule.

  • Semi-inclusive DIS and fragmentation uncertainties: Extracting flavor-separated helicities from SIDIS depends on fragmentation functions, which carry their own uncertainties. This complicates the interpretation of SIDIS results and motivates cross-checks with other measurements and theory. See semi-inclusive deep inelastic scattering and fragmentation function.

  • The role of woke or identity-centered critiques versus the science: In public discourse, debates sometimes mix scientific interpretation with broader social critiques about how science is funded, communicated, or prioritized. In the PDIS context, the robust, repeatable nature of spin measurements—rooted in cross-sections, asymmetries, and QCD evolution—remains the core standard of evaluation. Proponents of careful, data-driven analysis note that physics should advance by tightening uncertainties and testing predictions, not by importing social narratives into the interpretation of experimental results. See discussions around scientific method and funder policies for related considerations.

  • The future path: Many within the field advocate for more precise measurements of g1 and g2 across broader x and Q^2, improved fragmentation functions, and continued advances in lattice QCD to pin down the spin budget. These programs aim to resolve remaining ambiguities about ΔG(x) and the distribution of orbital angular momentum, offering a clearer, more complete picture of how the nucleon’s spin emerges from QCD dynamics. See future experiments.

See also