xF3 Structure Function Research Articles

The Jacobi polynomials QCD analysis of the CCFR data for xF3 and the Q2-dependence of the Gross-Llewellyn Smith sum rule

We present the results of our QCD analysis of the recent CCFR data for the structure function xF3(x,Q2) of the deep-inelastic neutrino-nucleon scattering. The analysis is based on the Jacobi polynomials expansion of the structure functions. The concrete results for the parameter Λ(4)MS and the shape of quark distributions are determined. At the reference scale |Q02|; = 3GeV2 our results are in satisfactory agreement with the ones obtained by the CCFR group with the help of another method. The Q02-dependence of the Gross-Llewellyn Smith sum rule is extracted in the wide region of high-momentum transfer. Within systematical uncertainties the results obtained are consistent with the perturbative QCD predictions. We reveal the effect of the discrepancy between our results and the analysed perturbative QCD predictions at the level of the statistical error bars. The importance of taking account, in our procedure, of the next-next-to-leading approximation of the moments of the structure function xF3(x,Q2) is stressed.

A measurement of the Gross-Llewellyn Smith sum rule from the CCFR xF3 structure function

We report a measurement of the Gross-Llewellyn Smith sum rule: ∫( 1 x ) dx xF 3(x, Q 2=3 GeV 2)=2.50±0.018( stat.) ±0.078( syst.) .

Analysis ofx F 3: QCD and higher twist

We have analysed all available data on the non-singlet neutrino structure functionxF3 taking into account systematic errors and EMC corrections. A good fit to all data withQ2≧5 (GeV/c)2,W2≧10 (GeV/c)2 is obtained neglecting higher twist contributions, with Λ=0.18±0.07 GeV, corresponding toα s (Q2=25(GeV/c)2)=0.18±0.02. On lowering the cuts toQ2≧3 (GeV/c)2,W2≧3 (GeV/c)2, we find evidence for a small negative higher-twist term. Incorporating such a term in a simple parametrisation yields an increased Λ value of 0.27±0.05 GeV, corresponding toα s (Q2=25(GeV/c)2)=0.20±0.01.

OddC gluonic regge singularities of perturbative QCD and their decoupling from deep inelastic neutrino scattering

The QCD motivated integral equation for three reggeised gluons in the oddC colour singlet channel is solved for large external masses of gluons. It generates a Regge singularity forj≅1. Possible contribution of this singularity to the “non-singlet” structure functionxF3 is examined atx≅0, where in principle it should give a constant term and dominate over the valence quark contribution. The coupling of the three gluon system to currents is, however, shown to vanish in the lowest order and in higher orders in the multi-Regge approximation.

Bounds for the ratio of anomalous dimensions

Without demanding that the functions f(q2) and g(q2) in the structure function xF3(x,q2)=Cx1mf/(1-x)ng be slowly varying, upper and lower bounds are obtained for the slope of the graph for 1g MN against 1g MN', where MN is the Nth moment of xF3(x,q2). The bounds obtained here also include the predictions of scalar gluon theories which is not the case for Harari's bounds (1979). Further, it is observed that the bounds are sensitive to the way in which the q2 dependence is introduced in xF3(x,q2).

Bounds for the ratio of anomalous dimensions

Without demanding that the functions f(q2) and g(q2) in the structure function xF3(x,q2)=Cx1mf/(1-x)ng be slowly varying, upper and lower bounds are obtained for the slope of the graph for 1g MN against 1g MN', where MN is the Nth moment of xF3(x,q2). The bounds obtained here also include the predictions of scalar gluon theories which is not the case for Harari's bounds (1979). Further, it is observed that the bounds are sensitive to the way in which the q2 dependence is introduced in xF3(x,q2).

Can moments of structure functions be predicted by general assumptions alone?

One of the major successes of QCD has been the prediction of the q 2 behaviour of the structure function xF 3( x, q 2). It has recently been claimed that the experimental results can be predicted from general assumptions alone, so they do not test QCD. We show this is false.

Moments of structure functions and experimental tests of QCD

Simple assumptions which have little or no connection to quantum chromodynamics, lead to upper and lower bounds for the slope of the graph for log M N ′ versus log M N , where M N is the Nth moment of the deep inelastic structure function xF 3( x, q 2). The published results of the CDHS and BEBC collaborations cover the entire range allowed by our bounds and therefore cannot be considered as evidence for the validity of QCD.