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.