October 23, 2007 Edition
 

Issue Summary / Events List

Direct Photons at PHENIX

The Equation of State that Controls the Expansion of Matter Created at RHIC

Diffractive Deep Inelastic Scattering Probes the QCD Vacuum

Diffractive Deep Inelastic Scattering Probes the QCD Vacuum

By Raju Venugopalan

Consider the following scenario: An electron slams into a proton at rest with an energy 50,000 times the proton rest energy and in about 1 in 7 such scatterings, nothing happens to the proton. In contrast, the virtual photon emitted by the scattered electron showers into a spray of hadrons separated in angle (or an equivalent unit called rapidity) from the proton. These striking diffractive events (see Fig. 1a) were observed in Deep Inelastic Scattering (DIS) experiments with the HERA collider at DESY, Germany.

The phenomenon of diffraction is familiar to us from many areas of physics and is generally understood to arise from the constructive or destructive interference of waves. One such example, a plane wave impinging on a single slit is shown in Fig. 1b. In analogy to the familiar example of wave diffraction around a solid object, strong interaction diffractive events have long been interpreted as resulting from the scattering of waves from the incoming hadron, that impinge on a "black disc" hadron target, bend around it, and are reconstituted into various waveforms on the other side.

In the process of scattering, the hadrons exchange an object called the Pomeron (named after the Russian physicist Isaac Pomeranchuk) that carries the quantum numbers of the vacuum. Indeed, much of the strong interaction phenomena of multi-particle production can be interpreted in terms of these Pomeron exchanges.

In the modern strong interaction theory of Quantum ChromoDynamics (QCD), the simplest model of Pomeron exchange is that of a colorless combination of two gluons, each of which individually carries color charge. In general, diffractive events probe the complex structure of the QCD vacuum that contains colorless gluon and quark condensates. Hard diffractive events at collider energies, allow one to study hadron final states with energies much larger that the fundamental QCD momentum scale of ~ 200 MeV. By the uncertainty principle of quantum mechanics, these events therefore provide considerable insight into the short distance structure of the QCD vacuum.

Fig. 1a: Hard diffractive event at HERA (ZEUS collaboration). A 27.5 GeV electron enters the beam pipe from left; a 920 GeV proton from right. The two scatter in the center; the scattered electron goes top left, the emitted virtual photon fragments go bottom right and the proton exits right down the beam pipe. A “lego” plot of energy distribution in the rapidity-azimuth plane, and the azimuthal distribution around the beam pipe are also shown.

Fig. 1b: Single slit diffraction of a plane wave. An interference pattern of a large central peak, phase cancellations and secondary peaks is visible.

A QCD diagram of a diffractive event is shown in Fig. 2a. It can be visualized in the proton rest frame as the electron emitting a photon with virtuality Q² and energy ω, that subsequently splits into a quark--anti-quark+gluon “dipole”; other “wave packet” dipole configurations are also feasible. These dipoles interact coherently with the hadron target via the exchange of a colorless gluon ladder. Because the spread in rapidity between the dipole and the target is large, gluon bremsstrahlung radiation could have filled up the gap; indeed, the naive expectation in QCD is that such gaps in rapidity are exponentially suppressed. It was therefore a surprise to see the large fraction of rapidity gap events at HERA. Another surprising feature of the data is that the fraction of diffractive events is roughly constant with variations in the energy of the photon+proton system; again, the expectation was that it would grow rapidly with energy.

Fig. 2a: Sketch of a diffractive event. The virtual photon fragments into a quark-anti-quark +gluon dipole that interacts with the proton (or nucleus) by exchanging a colorless combination of gluons.

Fig.2b: Fraction of diffractive events in nuclei relative to fraction for the proton vs. atomic number ~ 15% of proton events are diffractive. Filled symbols: (see text) Q²=8 GeV²; ω = 4*(10² – 10⁴) GeV, (bottom to top). Open symbols: Q²=1GeV² ; ω = 0.5*(10²-10⁴) GeV (bottom to top).

This data is simply explained if dipole cross-sections quickly rise, with increasing dipole size, to become as large as hadron cross-sections. The dynamical origin of the saturation of dipole cross-sections can be understood as follows. In QCD, the stability of the QCD vacuum requires that the strength of Chromo-Electric and Chromo-Magnetic fields be no larger than the inverse of the QCD coupling. This bound is evaded dynamically by strong multi-gluon correlations that arise with increasing gluon density. The characteristic momentum scale of these correlations (and corresponding inverse dipole sizes) is called the saturation scale Q_S. At high energies or atomic numbers, it can be much larger than the QCD momentum scale of ~ 200 MeV. This dense gluon state at high energies is called the Color Glass Condensate (CGC) and hints of its existence, besides the HERA experiments, have been seen in the RHIC deuteron+gold and gold+gold experiments.

The CGC predicts the growth of Q_S with both the energy and the atomic number. As discussed previously by Thomas Ullrich in the Aug. 14th issue of this newsletter, the tremendous “nuclear oomph” generated by the growth of the saturation scale with atomic number provides a strong motivation for studying this novel physics regime with an Electron Ion Collider (EIC).

Diffractive Deep Inelastic Scattering (DDIS) off nuclei provides a promising probe of the physics of high parton densities. A simple model prediction (see Fig.2b) incorporating this physics predicts that as many as 1 in 4 e+A scattering events off large nuclei will be large rapidity gap events, where the nucleus remains intact. This result is a dramatic illustration of the quantum world when one considers that the force binding nucleons in the nucleus is ~10⁵ times weaker than the incoming electron’s energy.

DDIS studies of the large number of diffractive final states may provide definitive answers to several outstanding questions in QCD. One of these, to refer to our prior discussion, is the relation between the Pomeron interpretation of diffractive scattering and those of saturated, strongly correlated gluons. These studies will therefore provide key insights into the appropriate “quasi-particle” constituents of QCD at high energies. They may also throw light on Pomeron exchange in 3+1-dimensional QCD like theories that, remarkably, are speculated to be “holograms” of gravity in a 10 dimensional world.

DDIS provides a stringent test of our understanding of the universality of QCD interactions. The factorization of QCD computations into “universal” parameterizations of quark and gluon distributions and process-dependent scattering probabilities underlies much of the success and predictive power of QCD. However, this factorization is only applicable for a limited range of processes. It fails hugely for diffractive processes; diffractive distributions extracted from HERA data lead to a vast overprediction of the magnitude of diffractive proton+anti-proton cross-sections at Fermilab.

Diffractive measurements of the incoming and outgoing momenta of the nucleus, in coincidence with hadronic final states, will generate novel studies of the spatial “tomography” of gluon and quark distributions. Mapping this spatial clumping is, for example, of considerable importance in quantitative interpretations of the behavior of jet quenching measurements at RHIC. Finally, understanding the QCD diffractive background is important to isolate channels for new physics at the LHC that rely on missing energy. When nothing is seen, could it be because of a QCD rapidity gap?

This discussion suggests that diffractive studies will be an important feature of experiments at a future Electron Ion Collider. Detailed simulations of such events are required for machine and detector planning.