By Janet Seger and Yuri Gorbunov
STAR has recently completed and published an extensive analysis of rho-meson production in 200-GeV ultraperipheral Au-Au collisions at RHIC .
Ultraperipheral “collisions”—where the gold nuclei pass in close proximity to each other but don’t actually overlap—are ubiquitous at RHIC.
In these collisions, the nuclei interact via the long-range electromagnetic force, exchanging virtual photons from the clouds surrounding each nucleus. This “equivalent photon” model of the electromagnetic interaction was originally developed by Fermi in 1924, and extended to relativistic particles by Weizsäcker and Williams. The number of virtual photons in the clouds surrounding the nuclei grows like Z2, so for heavy ions the number of photons is much larger than for electrons or protons. Often there is more than one photon exchanged in a single Au-Au “collision”.
Most of the previous studies of photonuclear interactions  have been done at HERA, an electron-proton collider. In that case, the nucleus is the simplest possible—the proton. At RHIC, we not only have higher photon fluxes, we also have a more complex “target” for the exchanged photon—a heavy nucleus such as gold.
In contrast to central collisions, that can produce thousands of tracks in the STAR detector, ultraperipheral collisions typically produce only a handful of tracks. The system that is produced generally has a small net momentum component transverse to the beam line. Because of these differences, ultraperipheral collisions can be fairly easily separated from the “background” of hadronic events produced when the nuclei actually overlap. The greatest experimental challenge is triggering on these events with a good efficiency.
The most frequently observed product in an ultraperipheral collision is a single vector meson. In this case, the exchanged photon fluctuates into a quark-antiquark pair, scatters off the other nucleus and emerges as a real vector meson. As the lightest vector meson, the rho is the most copiously produced and therefore the easiest to study. The rho decays into two oppositely charged pions that are almost back-to-back in the transverse plane.
In addition to fluctuating into a quark-antiquark pair and emerging as a rho meson, the exchanged photon can alternatively fluctuate directly into two pions. In either case, a pair of back-to-back, oppositely-charged pions is observed; there is no way to determine if a particular pair of observed pions spent some part of their former life as a rho meson. Therefore, these two possible “paths”-- from photon to observed pion pair-- interfere with each other quantum mechanically. However, the mass spectra for the two paths are dramatically different. For the rho meson, the mass spectrum features a wide peak centered around 770 MeV/c2. For the directly-produced pion pairs, the mass spectrum is approximately flat in the region of interest. By fitting our observed mass spectrum to a function that accounts for this quantum mechanical interference, we can measure the relative amplitudes of the two interfering paths. This mass fit is shown in Fig. 2. We find the ratio of the amplitude of direct pion production to resonant rho production is consistent with that observed at HERA . Our finding that the rho retains the helicity of the emitted photon is also consistent with measurements at HERA .
Finally, we have measured the rho-zero production cross section, giving us the opportunity to distinguish between three different theoretical models of vector meson production in ultraperipheral collisions. The Klein and Nystrand model combines a vector dominance model with a classical mechanical approach for scattering, based on gamma-proton experimental results. The Frankfurt, Strikman, Zhalov model combines a generalized vector dominance model with a Gribov-Glauber approach to the scattering. The Goncalves and Machado model uses a QCD dipole approach with nuclear effects and parton saturation phenomenon. (The interested reader can find references to these models in ). The models differ most significantly in how they model the nuclear interaction, which is also where RHIC collisions differ most significantly from HERA collisions. A comparison of our data with three published model predictions is shown in Fig. 3.
Our theoretical understanding of ultraperipheral collisions can be further tested by measuring the energy and Z-dependence of the photonuclear cross section. An analysis of rho-meson production in Au-Au collisions at 130 GeV has been published, and a study of rho-meson production in Au-Au collisions at 62 GeV/nucleon is underway. An analysis of rho-meson production in asymmetric d-Au collisions has also been completed . As we continue to analyze RHIC data taken at different energies and with different species, we will be able to determine whether the rho production cross section varies in accordance with theoretical models.
Data from ultraperipheral collisions at RHIC also gives us the opportunity to answer some open questions about excited mesons. For example, the existence of the states rho(1450) and rho (1700) is fairly well-established; these states are assumed to be radial excitations of the rho meson. There remains some disagreement on the masses and widths of these states; in particular, the question remains whether the rho(1450) and rho(1700) are two distinct particles, or one broad resonance. If they are two distinct particles, they may have different absorption cross sections in nuclei; STAR can test the coupling to the nucleus to resolve this issue. This analysis is currently underway.
We anticipate a continued vibrant physics program as we collect higher-statistics ultraperipheral collisions datasets. Of particular interest is the production cross section for the J/psi meson, which is predicted to give insight into the gluon distribution function. Some predictions indicate a 50% reduction in the production cross section at mid-rapidity due to the effects of gluon shadowing. PHENIX has reported an observation of J/psi production in ultraperipheral collisions at RHIC, but the statistics are too low to distinguish between different theoretical predictions 
RHIC is a very fruitful place to study ultraperipheral
collisions. This study will continue at the LHC  where
photon energies will be even larger, allowing the measurement of
heavier states, such as the upsilon. In this setting, it may be
even easier to extract good information about the distribution
of gluons in the nucleus from ultraperipheral collisions.
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