# An exact sum rule for transversely polarized DIS

- Authors
- Publication Date
- Jan 01, 1997
- Identifiers
- DOI: 10.1103/PhysRevD.55.4307
- OAI: oai:arXiv.org:hep-ph/9607217
- Source
- CERN Document Server
- Keywords
- Language
- English
- License
- Unknown
- External links

## Abstract

The Operator Product Expansion provides expressions for the n^{th} moments of g_1(x) and g_2(x) in terms of hadronic matrix elements of local operators for n = odd integer. In some cases these matrix elements are expected to be small leading to approximate sum rules for the {\em odd\/} moments of g_{1,2}(x). We have shown how, working in a field-theoretic framework, one can derive expressions for the {\em even\/} moments of the {\em valence\/} parts of g_{1,2}(x). These expressions cannot be written as matrix elements of {\em local\/} operators and do not coincide with the analytic continuation to n= even integer of the OPE results. Just as for the OPE one can in some cases argue that the hadronic matrix elements should be small, leading to approximate sum rules for the moments of the valence parts of g_{1,2}(x). But, most importantly, for the case n=2 we have proved rigorously that the hadronic matrix element vanishes, yielding the exact ELT sum rule \int^1_0 dx\, x\left[g^V_1(x)+2g^V_2(x)\right]=0. We have argued that the convergence properties of this sum rule are good and have discussed how it can be used to get information about g_2(x) and as a further test of QCD.