Antinuclei

The rates for antimatter production in high energy nucleus-nucleus collisions are of fundamental interest for several reasons. The yield of antiprotons ( 's) is a sensitive probe of the space-time evolution of the baryon density, since 's, once created, can be strongly absorbed when they encounter a baryon, due to the annihilation reaction mesons. There is now considerable data on production from AGS experiments E802, E814 and E858 [48, 11, 22]. However, there is as yet no quantitative theoretical understanding of these data. In fact, there is considerable uncertainty concerning the mechanism for antimatter production. Gavin et al. argue that the ratio is suppressed in heavy ion collisions, relative to the ratio seen in p-p collisions [49], whereas Ellis et al. suggest a enhancement [50], based on a Skyrme-type model where the nucleon is identified as a topological soliton. In the approach of Gavin et al., the suppression arises due to annihilation with co-moving baryons, and for high energy central collisions, we have

where is a formation time for 's, is the freezeout time, and are the densities of and p in the central region at , and

Here is the averaged annihilation cross section, is the projectile radius and is the rapidity density of baryonic charge. The degree of suppression of the ratio thus depends strongly on the formation time . If a quark-gluon plasma is formed, an hadronic picture based on absorption in a medium no longer applies. Ellis et al. regard the hadronization of a plasma droplet in terms of the formation of domains in which the quark-antiquark condensate assumes independent values. If the orientations of in adjacent domains are mismatched, ``topological defects'' may form, which are interpreted as baryons or antibaryons. This approach can lead to strong deviations from chemical equilibrium as the hadronization process unfolds, and an enhanced production of 's at levels which exceed the rate expected from an equilibrium Boltzmann distribution.

We mentioned the approaches of Gavin et al. and Ellis et al. to illustrate the diversity of theoretical predictions regarding production. In fact, in heavy ion central collisions, the is produced in a dense hadronic environment, not in a free space N-N collision, and a central theoretical challenge is how to include the effects of the medium on the production and propagation of antimatter.

The high sensitivity of E864 will permit us to extend the study of antimatter production beyond 's, to antideuterons and probably also and . The measurement of composite antinuclear systems will shed light on a new set of theoretical questions. For instance, the production rates for the and heavier antinuclei will be extremely sensitive to the space-time evolution of hadron densities during the collision process, through reactions like and , by which 's are created and destroyed. The free space rates for these processes are identical to measured cross sections for and , as follows from the CPT theorem. Will one be able to explain cross sections in a hadronic cascade picture at AGS energies, with the above free space cross sections as input? Does one need to include additional effects of the dense medium, say by using density and temperature dependent effective cross sections ? Does a simple coalescence model apply to production? What is the influence of formation time on the rate for antinucleus production? If the 's do not form until they are in a region of low density, one might expect a suppression of the rate.

In p-p and p-nucleus collisions at high energies, production seems to be consistent with a coalescence model. However, preliminary results from E858 [22], based on two events, indicate that the ratio in Si-Au collisions at 14.6 GeV/A is an order of magnitude less than expected based on the coalescence model (with a coalescence probability obtained by fitting the observed d/p ratio). However, one should recall that deuteron production is the result of coalescence of pre-existing nucleons, while formation requires that two antinucleons be produced in the collision, so the space-time dynamics of d and formation are likely to be quite different.

In the coalescence model, the rate of production is proportional to the Ath power of the yield. This rule works for light nucleus cross sections at BEVALAC energies [21], and will soon be tested for d, t, and possibly formation at AGS energies. However, it is not at all clear that this simple power law applies to yields, since other dynamical mechanisms come into play, for instance formation time and strong annihilation. It has also been suggested that enhanced rates for formation may provide a signature that the system evolved through an intermediate quark-gluon phase [51]. This results from an increased antiquark content in the plasma.

We now provide some rough estimates of the yields for antinucleus production. In the thermal coalescence model [25] discussed earlier in connection with strangelet production, we find

where is the proton density at freezeout and is the thermal wavelength. Adjusting the penalty factor P to reproduce the E858 preliminary value of order for the ratio in Si-Au collisions, and extrapolating from Si-Au to the Au-Au case, assuming increases by a factor of 3 (based on FRITIOF estimates), we estimate

per interaction. This is at the limit of sensitivity of E864. One could also assume that antinuclei are produced from a hadronic fireball in thermal and chemical equilibrium [52]; this gives yields per interaction in the range

This is presumably an upper limit, since it is unlikely that can be considered to be in chemical equilibrium. Thus it is clear that the high sensitivity of E864 is necessary in order to explore antinuclei heavier than the . Based on these crude estimates, the rate for will be too small to measure in E864 (or any other proposed experiment). However, there may be dramatic surprises (an enhancement due to formation of plasma droplets?) so a search is warranted.