|
Articles Particle Physics Positivity Constraints on Quark and Gluon Distributions in QCD (1978)
Positivity Constraints on Quark and Gluon Distributions in QCD (1978) |
|
QCD predicts that in the asymptotically free limit 
, if there are 
flavours of quarks,
where
To derive (4) recall that the non-singlet combinations of structure functions are
Writing
one obtains
from which (4) follows.
If we define
then the necessary and sufficient conditions on the 
for 
to be non-negative on [0,1] are
which is Hausdorff's theorem [3]. The necessity of these conditions is obvious since 
(
).
For 
it is necessary and sufficient that 
for all polynomials 
. We can use the fact that
to write
from which the sufficiency of (7) follows.
