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Virtual photons see hard scattering processes

E.S. Smith and J.M. Laget
March 2, 2005

The interaction between particles made up of quarks is an effective residual interaction of the strong force between the quarks mediated by gluons. At low energies quarks are confined inside composite particles and their bare couplings are hidden within the particles that bind them together. To identify the quark structure of the interaction, it is necessary to measure very small interaction rates in kinematic regimes that have been previously inaccessible. This requires simultaneous access to two scales of observation, which has been achieved for the first time at Jefferson Lab using the exclusive electro-production of vector mesons [1] in the CLAS detector [2].

Evidence for quarks was first demonstrated using deep inelastic scattering at SLAC [3]. The sensitivity to structure inside the proton was achieved by scattering photons of adjustable mass off a target proton. These virtual photons were created with an electron beam and their mass was determined by carefully selecting the energy and angle of the scattered electron. The transverse size, or de Broglie wavelength ( λ ≅ 1/Q), of these photons determined the observation scale to be about the size of λ. The measured cross section is almost independent of Q2 (Fig. 1) which shows that the photons were scattered off point-like objects inside the proton. In this inclusive experiment, only the scattered electron was detected which sums over all possible final state particles [4].

Additional information about the constituents inside the target is obtained by measuring exclusive reactions, especially when the scattered particles are emitted at large angles. The emission of particles to large angles requires that the interaction occur with large momentum transfer -t and therefore small impact parameter b ≅ 1√-t which determines the size of the interaction region. Independently tuning these two scales, λ and b, provides original insight into the space-time structure of the interaction between constituents in the incident photon with the constituents in the target proton [5]. Due to the very low probability for producing specific outgoing particles, the measurement of these reactions are only now possible with the large acceptance detectors, such as CLAS, operating at high luminosity. Since these experiments force the scattered quarks to recombine into specific particles in the final state, they extend the original SLAC experiments to new frontiers.

Fig1 Figure 1: Evidence for quarks was demonstrated using deep inelastic scattering. The size of the incident photons was reduced by increasing the momentum transfer Q2 in order to become sensitive to the substructure in the target. The relatively constant cross section as a function of Q2 demonstrated that the electrons were scattering off of point-like partons.

Some of the data on exclusive ω electro-production are summarized in Figure 2. At low momentum transfer -t (large impact parameter), the cross sections fall very quickly as a function of Q2. This is expected from the scattering of the incoming electron off the pion which is exchanged between the target and the outgoing $\omega$ mesons. On the other hand, at large -t (small impact parameter), the cross section is almost constant with Q2. This indicates that the virtual photon is scattering off point-like constituents in the target. The curves quantify the transition from the effective coupling of the photon to a pion to the bare coupling of the photon to point-like partons.

Fig2 Figure 2: When the impact parameter is large (top), the cross section for ω meson production falls quickly as a function of Q2. But when the experiment selects the kinematics corresponding to small impact parameter (bottom), the cross section becomes constant with Q2 indicating that the interaction takes place between quarks.

The effect of changing the kinematics of the reaction by selecting small photons (i.e. large Q2) and small impact parameters (i.e. large -t), is illustrated in Fig. 3. When both the virtuality Q2 of the photon and the momentum transfer -t are small (3a), the vector meson and the nucleon target interact at a distance (large impact parameter). The partons which are exchanged have enough time to combine into composite mesons, whose effective interactions drive the cross section. On the other hand, at high -t (3b), the small impact parameter b prevents the exchanged partons from forming composite particles during the short interaction time.

When Q2 is large, the wavelength of the virtual photon decreases ( λ ≅ 1/Q), and consequently its resolving power increases. It begins to probe processes which occur at shorter and shorter distances and can couple to the constituents of the exchanged particles. When Q2 is large but -t is small (3c), the photon "sees" only the quarks inside the pion which is exchanged between the proton and the outgoing meson. When -t and Q2 are both large (3d) the quarks inside the photon are able to couple directly to the quarks inside the target because the wavelength λ becomes comparable to the impact parameter b. The virtual photon "sees" the partons which are exchanged during the hard scattering [5].

Figure 3: These diagrams depict the effective interaction at low energies of composite particles (green bars) and how the substructure is revealed by selected kinematics. The substructure of the incoming photon beam is revealed at high Q2, and the constituents of the target are uncovered using large-angle scattering, or high -t reactions.

For the first time, the large acceptance of CLAS operating at high luminosity has been able to probe the exclusive production in kinematic regions of intense interest. The measurements are helping us to understand how the interaction of composite particles comes about from the bare interactions of their constituents.

The Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility for the U.S. Department of Energy under contract DE-AC05-84ER40150.


  1. L. Morand, Ph.D. Thesis, University of Paris 2003; L. Morand et. al, Eur. Phys. J. A 24, 445 (2005).
  2. B.A. Mecking et al., Nucl. Instr. Meth. A 503, 513 (2003).
  3. J.I. Friedman, H.W. Kendall, and R.E. Taylor, Nobel Prize in Physics 1990. See
  4. F. Halzen and A. Martin Quarks and Leptons: An Introductory Course in Modern Particle Physics (New York: John Wiley & Sons, 1985); D.H. Perkins Introduction to High Energy Physics (Cambridge: Cambridge University Press, 2000).
  5. J.M. Laget, Phys Rev. D 70 (2004) 054023.

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