slides PDF - Theory Group

Moments of parton distributions
Parton distributions measured in deep inelastic scattering
Forward matrix elements:
< N(p, s) | O { µ 1 ...µ n}
| N(p, s) >~ dx
q
C. Alexandrou, University of Cyprus PSI, December 18th 2007
! x n-1 q(x)
< x n > = dx x q n q(x) + (-1) n+1 1
% !
"
q(x) #
$
q = q + q & '
-1
< x n > = dx x (q n
1
% (q(x) + (-1)
-1
n !
"
(q(x) #
$ (q = q& - q' < x n > = dx x )q n
! ! µ unpolarized moment
1 ...µ n µ 1 µ µ
O = q "
2 ! i D ...i D n} $
q #
%
polarized moment
transversity
1
%
-1
q
µµ 1 ...µ n O = q ! ! 5q
5 µ i ! D µ ! µ "
1 ...i D n} $
#
% q
µ&µ 1 ...µ n O = q ! ' Tq
5 µ& i ! D µ ! µ "
2 ...i D n} $
#
% q
!
D = 1
2 ( " D ( # Moments of parton distributions
3 types of operators:
D)
)q(x) + (-1) n+1 !
"
)q(x) #
$ )q = qT + q *