From: kamal@wind.phy.bnl.gov (Basim Kamal)
Date: Wed, 5 Nov 1997 22:14:32 -0500
Subject: notes on spin discussion
Hi,
Here's a summary of Tuesday's spin discussion:
(1) A general 101 intro to renormalization was given, using DREG
as the regulator.
(2) The connection between parton distributions defined in
different factorization (i.e. renormalization) schemes was
given.
(3) Using this connection, we were able to show that certain
factorization schemes not respecting various symmetries could
lead to unphysical parton distributions. It was pointed out,
however, that even unphysical parton distributions can be used
in making physical predictions on cross sections, since the
physcial predictions are scheme independent, order by order.
Hence all scheme ambiguities are higher order in alpha_s.
The details can be found in BK, hep-ph/9710374, BNL-64853.
In practical terms however, certain schemes (i.e. DIS) make
it difficult to define some distributions (i.e. the gluon dist.)
as George Sterman reminded us.
(4) An issue raised (Samios) was whether our choice of factorization
scheme could in any way influence how we extrapolate our
distributions to large and small x, where experiment is not
sensitive. No conclusion was reached on this issue, although
Jianwei Qiu and Bob Jaffe seemed to think this was a possibility.
(5) Finally, as Gerry mentioned in his e-mail, one might wonder
about whether fitting g_1 in different schemes could have
consequences for asymmetries at RHIC. This question should be
addressed in the context of (3) and (4).
- Basim