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Abstract

The Drell-Hearn-Gerasimov and Bjorken sum rules are special examples of dispersive sum rules for the spin-dependent structure function G1(ν,Q2) at Q2 = 0 and ∞. We generalize these sum rules through studying the virtual-photon Compton amplitudes S1(ν,Q2) and S2(ν,Q2). At small Q2, we calculate the Compton amplitudes at leading order in chiral perturbation theory; the resulting sum rules will be able to be tested against data soon available from the Jefferson Laboratory. For Q2>>ΛQCD2, the standard twist-expansion for the Compton amplitudes leads to the well known deep-inelastic sum rules. Although the situation is still relatively unclear in a small intermediate-Q2 window, we argue that chiral perturbation theory and the twist-expansion alone already provide strong constraints on the Q2-evolution of the G1(ν,Q2) sum rule from Q2 = 0 to ∞.

Gerasimov-Drell-Hearn sum rule and related integrals

“…Recently, Ji et al [21] have extended the calculations to O(p 4 ). They find strong modifications due to the nextorder term, which even change the sign of the slope at the origin to negative values much below the phenomenological analysis.…”

Measurement of the Q2 Dependence of the Deuteron Spin Structure Function g1 and its Moments at Low Q2Adhikari1, Deur2, Fassi3 et al. 2018Phys. Rev. Lett.284320View full textAdd to dashboardCite

“…In the midst of the "spin crisis," it was realized that the GDH integral could be extended to electroproduction to study the transition between the perturbative and nonperturbative domains of QCD [4]. A decade later, the sum rule itself was generalized [21,22]:…”

Effective field theories for muonic hydrogen

“…From the results for the forward virtual Compton tensor [32], we can compute the EFT contribution of the TPE to the hyperfine (HF) splitting in muonic hydrogen allowing for comparison with both previous estimates and experimental data. A detailed account of this analysis can be found in [12].…”