Burkhardt-Cottingham sum rule and forward spin polarizabilities in heavy baryon chiral perturbation theory

Abstract

We study spin-dependent sum rules for forward virtual Compton scattering (VVCS) off the nucleon in heavy baryon chiral perturbation theory (HBChPT) at order O(p 4 ). We show how these sum rules can be evaluated from low energy expansions (in the virtual photon energy) of the forward VVCS amplitude. We study in particular the Burkhardt-Cottingham sum rule in HBChPT and the higher terms in the low energy expansion, which can be related to generalized forward spin polarizabilities of the nucleon. The dependence of these observables on the photon virtuality Q 2 can be accessed, at small and intermediate Q 2 values, from existing and forthcoming data at Jefferson Lab.

Higher moments of nucleon spin structure functions in heavy baryon chiral perturbation theory and in a resonance model

“…(16) has also been calculated in HBChPT [7] (see Ref. [9] for the corresponding calculation within the framework of relativistic baryon ChPT).…”

“…Following the notations of Refs. [6,7], we use the VVCS amplitudes g T T (ν, Q 2 ) and g LT (ν, Q 2 ), where ν is the lab energy and Q 2 the virtuality of the virtual photon, and T (L) denotes the transverse (longitudinal) virtual photon polarization.…”

“…[6]). Using the calculation of these spin polarizabilities within HBChPT [7] (see also Refs. [8,9]), and within a unitary isobar model [10], we evaluate d 2 .…”

Neutron spin sum rules and spin polarizabilities at low Q2

“…For γ 0 , the RBChPT [13] calculation with resonance contributions is in good agreement with the experimental data at 0.1 GeV 2 . However, the HBChPT [14] calculation shows a large discrepancy, which might indicate the importance of the resonances. Compared to MAID, the data is again significantly more negative for the lowest-Q 2 point.…”

Jefferson Lab Physics Overview: Recent Results

“…Consequently, g 2 provides a direct probe of the quark-gluon correlations in the nucleon wave function. In particular the piece of interesting physics is contained in the second moment in x of a linear combination of g 1 and g 2 , [34] while the dashed line is a HBχPT calculation [35] valid only at very low Q 2 . The lattice prediction [36] at Q 2 = 5 GeV 2 for the neutron d 2 reduced matrix element is negative but close to zero.…”