Strange Quark Contribution to the Nucleon Spin from Electroweak Elastic Scattering Data
The total contribution of strange quarks to the intrinsic spin of the nucleon can be determined from a measurement of the strange-quark contribution to the nucleon’s elastic axial form factor. We have studied the strangeness contribution to the elastic vector and axial form factors of the nucleon, using all available elastic electroweak scattering data. Specifically, we combine elastic and scattering cross section data from the Brookhaven E734 experiment with elastic and quasi-elastic and -He scattering parity-violating asymmetry data from the SAMPLE, HAPPEx, G0 and PVA4 experiments. We have not only determined these form factors at individual values of momentum-transfer (), as has been done recently, but also have fit the -dependence of these form factors using simple functional forms. We present the results of these fits using existing data, along with some expectations of how our knowledge of these form factors can be improved with data from the MicroBooNE experiment planned at Fermilab.
Physics Department, New Mexico State University, Las Cruces NM 88003, USA
1 The continuing question of the strange quark contribution to the intrinsic spin of the nucleon
The techniques of inclusive and semi-inclusive polarized deep-inelastic scattering employed at CERN, SLAC, DESY, and Jefferson Lab have provided a wealth of information about the spin structure of the nucleon over the last 25 years. The contributions of the and quarks in the valence region have now been firmly established. As well, data from collisions of polarized protons at RHIC has done much to advance our knowledge of the limitations of the gluon spin contribution to the spin of the nucleon. The strange quark contribution to the spin of the nucleon, however, is still the subject of investigation, and the indications from deep-inelastic scattering are unclear at the moment.
Consider the determination of + from inclusive deep inelastic scattering combined with hyperon -decay data; a good example would be the HERMES measurement [Airapetian:2007mh] of longitudinal spin asymmetries in inclusive positron-proton and positron-deuteron deep-inelastic scattering to determine of the proton, deuteron and neutron. This measurement covered the kinematic range , , with the data evolved to = 5 GeV for analysis. Using SU(3) flavor symmetry, these data are combined with triplet and octet axial charges ( and from hyperon -decay data) in a NNLO analysis to obtain the singlet axial charge and the quark contributions to the proton spin. In doing so, it is necessary to extrapolate the results into the unmeasured regions of to fill the interval . The result for + ,
is inconsistent with 0 to more than 4 standard deviations.
A different technique is used by the same experiment using data from semi-inclusive deep-inelastic scattering, observing asymmetries in the production of charged pions from protons, and in production of charged pions and kaons from deuterons [Airapetian:2004zf]. The goal of this analysis is to determine the polarized parton distribution functions (and their integrals) over the measured -range only; no extrapolations are performed. As a result, this analysis does not rely on SU(3) flavor symmetry for combination with triplet and octet axial charges. However, it is necessary to have some understanding the of the fragmentation functions which relate the fundamental lepton-quark interaction to the particles observed in the final state. The result for is consistent with zero in the measured -range; the integral of ,
is then of course consistent with zero as well.
A similar contrasting picture is illustrated by a recent global QCD fit by de Florian, Sassot, Stratmann and Vogelsang [deFlorian:2009vb] which is able to bring together the hyperon -decay data, the inclusive and semi-inclusive deep-inelastic data from CERN, SLAC, DESY, and Jefferson Lab, and the collision data from RHIC under one roof. Of special interest here is their assumption that the strange and anti-strange polarized distributions are equal; this is supported by recent COMPASS results [Alekseev:2010ub]. Their functional forms allow for a node in the polarized parton distribution functions; this permits a small integral of the strangeness polarized parton distribution function if there is cancelation of positive and negative contributions from different -regions. Also, their functional forms allow for SU(2) and SU(3) symmetry violation; however, the best fit does not support any significant deviation from these symmetries. They determine a “truncated first moment” of the strange quark polarized parton distribution function,
where the uncertainty represents a deviation of the from the minimum of the fit by 2%. This is clearly consistent with 0. On the other hand, when the full -range is used, the effect of SU(3) symmetry and hyperon b-decay data is seen:
which implies . (The authors of Ref. [deFlorian:2009vb] declined to quote an uncertainty for this result because of the uncertainty in the functions required for extrapolation to .)
Additional data, of increased precision, from COMPASS at CERN on semi-inclusive deep-inelastic scattering [Alekseev:2010ub] only deepens the contrast. Compared to HERMES, this experiment uses a rather different polarized beam (muons instead of electrons/positrons), polarized target (solid target instead of a gas target), and detector system, but the conclusion reached is similar:
and its integral are consistent with zero in the measured -range.\@footnotemark\@footnotetextSee also the contribution by Roland Windmolders.