Hard Processes in Nuelcar/Particle Physics

Abstract

Since submission of second annual report to the PSF, substantial progress towards the goals of the Project has been made. First, the paper dealing with relativistic and binding energy corrections to direct photon production in upsilon decay was revised and submitted to Physical review D. The revised copy is enclosed, and the paper will be published in Phys Rev D54, 1, (1996). Second, a new piece of research was initiated on a subject of great topical interest at major acceleration of the world – the photoproduction of J/Ψ mesons off protons in the non-forward direction. The third part on heavy quark fragmentation functions has also been completed and has already been accepted for publication in Phys. REV D. The three major achievements of the Project are briefly described below; a more detailed exposition will follow thereafter. First, we have computed the rate for 3S^1→ℽ+X taking into account the bound state structure of the decaying quarkonium state. Previous authors have described the relevant hadron dynamics in this decay process by just Φ(0) but this is correct only if one assume that Q and Ǭ are exactly on the on-shell and at rest relative to each other. This assumption is only approximately true – heavy quarkonia are weakly bound QǬ composites and V^2/C^2 is a small parameter. Improvement requires introduction of additional hadronic quantities, which we identify within the context of a systematically improvable gauge -invariant theory for quarkonium decays. Here we apply the method developed by the Particle-Nuclear group at Quaid e Azam University to more complicated three particle case and obtain the photon spectrum for the process ϒ→ℽ + 2g. We find that inclusion of binding and relativistic effect via the two additional parameters, ∈B/AI and ▽^2Φ(0)/AI^2 Φ(0), makes the computed spectrum softer for large z, (z< 0.9). For still larger z, 0.9> z > 1, there are non-perturbative effects due to final-stage gluon interactions which cannot be reliably computed and which, therefore, we don’t address in the above mentioned paper. In the second piece of research, we showed that the important of forward J/Ψ photoproduction can be understood in term of a simple, parameter free, model which yield a microscopic explanation of the parameter ⦵ which characterized this process. The model is the following: the incident photon, considered to be nearly real here, fuses with a gluon for the target photon to form a colour octet QǬ pair in the 3s^0,3p^0,and 3p^2 states. The size of the octet is of Φ(m^(-1)) where m, the dark mass, is assumed to be much larger then the QCD scale A. Subsequently, the octet propagates and increases its size. Since the quark are assumed heavy, the repulsive force between the quark is coulombic and the non-relativistic propagator can be exactly calculated. The system is still small when it finally absorbs, or emits, a low momentum gluon from the ambient QCD vacuum and converts into the final 1—state. We assume that, viewed from protons rest frame, produced QǬ octet moves rapidly away from the hadron from which it was formed. The octet’s interaction with low momentum gluons is calculated by means of the QCD multipole expansion technique, where the small parameter is the size of the QǬ system. To leading order, two multipoles contribute: the colour E1 interaction, and the magnetic M1 interaction. Surprisingly the M1 dominates the E1 for the system under consideration. The third area of research considered in this project concerns fragmentation. There are many situations in high-energy physics, such as Z^0 decay or electron-positron collisions, where a highly virtual heavy c or b quark is produced which moves out rapidly from the production region. Since this is a coloured object it cannot exist in isolation and must necessarily hadronized. The mechanism for this are various. Anti-quarks, both light and heavy, can be pulled out of the vacuum and reconstituted to form mesons or baryons. In general these will be long distance non-perturbative processes and therefore very difficult to analyse. However, the production of heavy quarkonium states occurs over a small distance scale and one may therefore apply perturbation theory to such processes. The problem with all existing treatments of fragmentation is that colour gauge invariance is not properly accounted for. Effectively, all authors have implicitly assumed the size of the produced mesons to be so small that the guage-link between the colour source is a unit operator. This is valid only in the limit of infinitely massive quarks. But certainly this cannot be true for c or b quarks – even for that t quark this would be true for only few percent. To find corrections is not, however, a trivail task. The relativistic bound-state problem is a very hard one. Inspite of efforts over the last few decades, the full solution for even a simple system like positronium has not been obtained. Of course, for this simple electromagnetic system, the hydrogen atom provides an excellent starting point and so one can systematically add in corrections. However, the strong interaction problem is very different – at distance greater then one fermi the interaction is exceedingly complicated and all sorts of non-perturbative effects enter. The Fock space of the consist of multiple quark and gluon states interwoven in a very complex way. In order to deal with the heavy-quark bound state, we have developed a technique which start from the point that the speed of quarks in a QǬ system is much smaller then c, the speed of light. This is assumption which should be reasonably good in the cȼ, system, but better for bƀ