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| Bjorken sum rule | |
|---|---|
| Name | Bjorken sum rule |
| Field | Particle physics |
| Discovered | 1966 |
| Discoverer | James Bjorken |
| Related | Quantum chromodynamics, deep inelastic scattering, spin structure functions |
Bjorken sum rule The Bjorken sum rule relates the difference of proton and neutron spin-dependent structure functions to the axial charge measured in beta decay, providing a fundamental constraint in particle physics and quantum chromodynamics. Proposed by James Bjorken in 1966 during the development of current algebra and parton models, it connects deep inelastic scattering experiments at facilities such as SLAC National Accelerator Laboratory and CERN to weak interaction measurements like neutron beta decay studied at Los Alamos National Laboratory and Institut Laue-Langevin. The sum rule has guided experimental programs at DESY, Jefferson Lab, Brookhaven National Laboratory, and COMPASS and remains central to precision tests of Quantum chromodynamics and the Standard Model.
The Bjorken sum rule emerged from arguments in the context of the parton model, current algebra, and approximate symmetries of isospin in the 1960s, bridging observables in polarized deep inelastic scattering at SLAC and theoretical quantities like the axial-vector coupling g_A measured in neutron decay at Harvard University-affiliated experiments. It provided an early quantitative test for the emerging picture of constituents inside the proton and neutron and helped motivate polarized beam and target programs at CERN, DESY, RHIC, and Jefferson Lab.
The derivation uses operator product expansion concepts developed by researchers at Stanford University, current algebra techniques associated with Murray Gell-Mann and Geoffrey Chew, and the parton interpretation championed by Richard Feynman. It connects the integral over Bjorken-x of the difference between proton and neutron polarized structure functions g1^p and g1^n to the axial charge g_A extracted from neutron beta decay and the Cabibbo-symmetric axial current, relying on isovector current conservation analogous to ideas from Noether's theorem and symmetry considerations used by Murray Gell-Mann and Steven Weinberg. Subsequent formalization employed the operator product expansion and renormalization group concepts elaborated by Kenneth Wilson and John C. Collins.
Experimental verification began with polarized deep inelastic scattering at SLAC National Accelerator Laboratory using polarized electron beams and polarized targets studied by collaborations linked to MIT, Columbia University, and Princeton University. Later precision measurements were carried out by experiments at CERN (EMC, SMC), DESY (HERMES), Jefferson Lab (CLAS, Hall A, Hall B), and COMPASS at CERN. Measurements compare integrals of g1^p − g1^n over x with axial-charge values from beta decay experiments at Los Alamos National Laboratory and precision weak-interaction studies at Institut Laue-Langevin and TRIUMF. Results involve global analyses by groups associated with Particle Data Group, involving theorists from MIT, Caltech, Yale University, and University of Cambridge to assess systematic uncertainties and extrapolations to unmeasured small-x regions.
Perturbative Quantum Chromodynamics corrections to the sum rule were computed using techniques developed by Gross and Wilczek and David Gross and Frank Wilczek and later higher-order calculations by teams including Gorishnii, Larin, and Vermaseren. The QCD radiative corrections introduce a calculable series in the strong coupling alpha_s, requiring renormalization group evolution formulated by Nicola Cabibbo-related weak phenomenology and by renormalization formalism from Kenneth Wilson and John C. Collins. Nonperturbative power-suppressed corrections (higher-twist) were modeled and constrained using methods from QCD sum rules developed by Shifman, Vainshtein, and Zakharov, lattice gauge theory computations by collaborations at CERN, Brookhaven National Laboratory, and Fermilab, and phenomenological fits influenced by groups at Saclay and Bonn.
The Bjorken sum rule serves as a benchmark for tests of Quantum chromodynamics and for determinations of the strong coupling constant alpha_s in polarized processes, influencing analyses at LEP, RHIC, and Jefferson Lab. It constrains polarized parton distribution functions used in global fits by collaborations such as NNPDF, CTEQ, and MSTW, and informs spin decomposition studies of the proton spin crisis that engaged groups at EMC, SLAC, and Brookhaven National Laboratory (RHIC spin program). The sum rule also interfaces with electroweak precision tests relevant to CERN collider programs and theoretical frameworks connected to chiral perturbation theory developed by Steven Weinberg and Gasser and Leutwyler.
Generalizations include flavor-singlet and nonsinglet sum rules related to the Ellis–Jaffe sum rule measured by the European Muon Collaboration and extensions to transverse-momentum-dependent distributions explored by researchers at DESY, Jefferson Lab, and BNL. The formalism extends to moments of structure functions analyzed with lattice QCD collaborations at Riken BNL Research Center, Fermilab, and CERN and to higher-spin and higher-twist operator matrix elements studied by theorists at Princeton University, University of Oxford, and IPN Orsay. Modern developments connect the Bjorken framework to generalized parton distributions probed at Jefferson Lab and planned at the Electron-Ion Collider.
Category:Quantum chromodynamics Category:Particle physics Category:Deep inelastic scattering