From: RL JAFFE 617 253-4858
Date: Tue, 7 Oct 1997 22:33:30 -0400 (EDT)
Subject: Notes on today's discussion
Notes on the Spin Meeting discussion of Transversity on October 7,
1997. Bob Jaffe
Questions and discussion about transversity --
* Can transversity and helicity distributions be related in
model independent ways?
Perhaps transversity, helicity and orbital angular momenta are
all related in some deep way. Recent papers by Soffer and
collaborators use the Melosh transformation to relate them.
Strongly connected to the non-relativistic quark model, it
does not include gluon or qq-bar pairs effects.
* What can be said about antiquark contributions to
transversity, since these are particularly important in the
Drell-Yan process?
Nothing is yet known about antiquark transversities relative
to quark. The transversity distribution is a "valence"
distribution (C-odd) since quarks and antiquarks contribute
with opposite signs.
* Can the pi+pi- asymmetry discussed by Jin, Tang and Jaffe be
adapted to pp-collisions? If so, what should be measured?
Yes! The normal to the plane of two pions observed in a
single jet should be correlated with the transverse spin of
the beam in a single spin asymmetry. The dependence is
cos(phi) * sin (theta), where phi is the angle between the
normal and the spin, and theta is the decay polar angle of the
pi+ in the pi+pi- rest frame. The asymmetry is proportional
to the product of three sines: sin(delta_0) * sin(delta_1) *
sin(delta_0 - delta_1), where delta_0 and delta_1 are pi-pi
s-wave and p-wave phase shifts respectively. Fortunately this
product of sines is not small (its of order 0.4 for m(pi-pi)
around 800-900 MeV).
The denominator in the asymmetry is given by the unpolarized
pi-pi rate. The rho and sigma (called "background") have been
seen in the current fragmentation region in electron
scattering and were roughly comparable. This suggests that
the interference could be of the same order as either. The
crucial unknown is the interference fragmentation function
which could be studied in chiral models with both scalar
(sigma) and vector (rho) resonances in the pi-pi system.
The signal should change sign across the rho. It will depend
in an unknown way on the pi-pi p_T, or z. If this is held
fixed, then the x_1 and x_2 dependence measures the product of
the transversity and some combination of unpolarized quark and
gluon distribution functions.
* How can this signal be seen in the RHIC detectors?
STAR can trigger on electromagnetic energy in the
side jet and then track the charged particles. This gives
sensitivity to both jets in a two jet event. Good, because it
helps to pin down x_1 and x_2.
* Has anyone calculated the pi-pi asymmetry for polarized pp?
No. Not even at tree level.
* What about using heavy qq-bar production to measure
transversity?
Joel Moss discussed using this as a way to measure
longitudinal spin distributions at RHIC. Detection of high
energy muons makes it possible. Moss was optimistic.
Xiangdong Ji looked a this in his paper on measurements of
transversity (Xiang-dong Ji, Phys.Lett.B284:137-143,1992). He
concluded that Drell-Yan was better because the unpolarized
process (that appears in the denominator in the asymmetry) is
smaller in that case.
* Can the interference fragmentation function that enters the
pi-pi asymmetry be measured elsewhere?
Yes, perhaps. It enters the 4-pi correlation between opposite
side jets in e+e- annihilation. Jian Tang has worked this out
and will publish it eventually.
* What about using Lambdas instead of pi-pi to probe
transversity at RHIC?
That will be fine, if there is a significant spin transfer
from a fragmenting u-quark to the Lambda. This will be
studied at HERMES. If it is non-zero, then Lambda's are a
good tool. If not, no.
* Is DIS intrinsically a better place than pp to attempt the pi-pi
measurement of transversity?
No. The first application was made there because it is easier
and because final states in DIS can be studied at existing
facilities (HERMES). In principle pp should be a good place
to look because of the high rates.