Probing the Pion's Structure

In research carried out at the Thomas Jefferson National Accelerator Facility (Jefferson Lab), the F_π Collaboration has provided significant new data on the structure of the pion, the lightest particle built of quarks. The pion, arguably the most important of the mesons due to its unusually small mass, can be naively pictured as consisting of one each of the lightest quarks and anti-quarks. As with all quark-based particles, however, a more realistic description of the pion also includes the quark-gluon sea: a strong-force driven bevy of quarks, anti-quarks and gluons popping into and out of existence and providing the foundation of the pion's structure. This structure is mapped out by a single quantity (known as a "form factor" F_π), which provides information about the distribution of electric charge inside the pion. By measuring F_π at ever shorter distances, it is possible to study the pion's transition from a particle in whose structure the quark-gluon sea plays a significant role, to one that behaves like a simple quark-antiquark system.

The importance of the measurement is to be seen in the context of understanding in detail the mechanisms that bind quarks, which do not exist as free particles in nature, into nucleons (three-quark objects such as protons and neutrons) and mesons (quark-antiquark pairs such as pions). These two families of bound quark objects are collectively called hadrons. The underlying theory describing the quarks and gluons is Quantum Chromo-Dynamics (QCD), which has been successfully applied to high energy processes which are able to resolve hadron structure in fine detail. However, a peculiar property of the strong nuclear force is that it grows stronger when the energy involved in the interaction between quarks and gluons gets smaller. In this case, precision calculations with perturbative theoretical methods (known as perturbative QCD) break down, and theorists resort to ``effective'' models of hadron structure. While these models are well constrained at very low energies, corresponding to low-resolution in the hadronic structure, their predictions differ significantly at higher energies, where their range of validity should give way to that of perturbative QCD. It is this breakdown of precision calculations that the Jefferson Lab experiment set out to probe, significantly increasing the range of precision data for the pion form factor.

The pion is not an easy target to have experimentally, since it is unstable with a life-time of only 26 billionths of a second. To get around this difficulty, the scientists involved in the experiment used a proton target, since the proton sometimes fluctuates into an intermediate state of a pion and a neutron. The process of interest is therefore the scattering of a multi-giga-electron volt (GeV) electron from the virtual pion inside the proton (Fig. 1). A snapshot of the pion at the moment of scattering was taken by measuring the scattered pions and electrons within a set energy range and at a set angle in the Jefferson Lab Hall C magnetic spectrometers.

The new data shows that the pion form factor remains high in the the resolution range probed (up to Q²=2.45 GeV²), with no sign of turning around to levels predicted by perturbative QCD [Fig. 2]. Thus, the highest Q²=2.45 GeV² probed by the experiment is still far from the resolution region where the pion behaves like a simple quark-antiquark pair. These new high-precision data provide a stringent test for models that attempt to incorporate the important ``softer'' quark-gluon sea contributions, serving as a benchmark for understanding the strong interaction at its most basic level. It remains unclear at what energies the pion actually behaves as its simplistic picture implies, and plans are now being made to study the pion with the higher-energy electron beam proposed for the 12 GeV upgrade at Jefferson Lab. The upgrade will allow an extension of the F_π measurement to Q²=6 GeV², which will probe the pion at double the resolution.

Figure 1. The t-channel diagram of interest in this experiment, where the electron scatters off the virtual π⁺ inside the proton, knocking it on shell. The scattered electron and the pion are detected in coincidence, providing a snapshot of the pion at the moment of scattering.

Figure 2. Pion form factor results from the two JLab Hall C experiments. Also shown are e-π elastic data from CERN and earlier pion electroproduction data from DESY. The curves are from a Dyson-Schwinger equation (Maris and Tandy, 2000), QCD sum rule (Nesterenko, 1982), constituent quark model (Hwang, 2001), and a pQCD calculation (Bakulev, 2004).

References

[1] T. Horn, et. al., Phys. Rev. Lett. 97 (2006) 192001.
[2] V. Tadevosyan, et al., Phys. Rev. C 75 (2007) 055205.
[3] J. Volmer, et al., Phys. Rev. Lett. 86 (2001) 1713.