Polarimetry Requirements for the GlueX Photon Beam

It has been well demonstrated that having a photon beam with a high degree of linear polarization is an important feature of the GlueX experiment [1,2]. Beam polarization doubles the information provided by the experiment to a partial-wave analysis (PWA) by producing two distinct differential cross sections, one for each polarization state, relative to an unpolarized experiment which measures only the average of the two. Linear polarization is uniquely advantageous because the two initial spin states are eigenstates of parity so that the two contribute to the formation of a given resonance through the exchange of different kinds of particles with the target. Parity conservation alone does not guarantee that the two photon polarizations couple to orthogonal sets of partial waves in the final state, but it is frequently observed that resonances are highly selective of the exchanges to which they couple, in which case it amounts to the same thing. Hence it follows that we need linear polarization, and that more is better. These features are quite well understood, and are not the subject of this discussion. The question being considered is, assuming that we do our best and achieve a good degree of linear polarization,

how well do we need to know the degree p of linear polarization of the beam in order to extract the optimum physics from GlueX?

Meeting Nov. 23, 2005 (A. Afanasev, E. Smith, R. Jones, S. Taylor)

The discussion was focused on the generic example of the 3π system described in [1]. In that paper the authors point to a particular polarization asymmetry as the observable that accents the effects of a small exotic signal. But apart from purposes of illustration, there is no advantage in chosing a single observable over performing a comprehensive partial-wave analysis that takes into account all angular and mass corrlations. Andrei doubted whether the analysis can succeed at all unless the degree p of linear polarization of the beam is provided as an input. Richard suggested that p could be left as a free parameter in the PWA fit, with the nominal polarization provided as a starting value. Andrei expressed his worry in terms of ambiguities that might arise among a number of solutions in this case.

Elton pointed out that the polarization is not a single number, but a function that varies with the energy of the photon. This does not seem to be an essential complication to the problem as originally posed because a complete set of partial-wave amplitudes combined with a suitably parametrized function p(E) completely specifies the PWA likelihood for every event. But we need to keep in mind that a single parameter p may be too restrictive a prescription if we are really going let the polarization float.

There was a general agreement that PWA is an over-determined problem, so additional information such as p might be extracted from the data by letting it float in the fit. There was also agreement that ambiguities are a problem that can hamper the interpretation of results from a PWA, and any extra experimental handles to eliminate ambiguities would be desireable. It was also appreciated that knowing the polarization with an accuracy comparable to the precision of p coming from the PWA fit would be a powerful check on the quality of the fit, something beyond the likelihood itself to give confidence that a chosen set of waves is sufficient.

Phone call Nov. 29, 2005 (C. Meyer, R. Jones)

Curtis reviewed the work done by the GlueX PWA working group on the effects of linear polarization in the extraction of a weak exotic signal. In those studies they looked at the cases with p=0 and p=1 but in both cases they assumed the known value for the polarization when they analyzed the data. This work showed clearly the need for polarization, but did not give any useful criteria for how well it should be known. Curtis pointed to the clear signature of polarization reflected in the Φ(GJ) distribution of the 2π decays of the ρ0.

Richard thought the ρ was not going to offer the best case because of its width and the dependence of the extraction on what is put in for the background under the peak. He proposed the ω as an alternative, which is only 8 MeV wide and has both charged and neutral decay modes. The ω is also better than the ρ at intermediate energies because it couples strongly to π exchange at low t. Helicity conservation holds for π exchange independent of any assumptions regarding high-energy asymptotics. Radphi has a large sample of ω decays at reasonably low |t|=0.1-0.3 GeV2. Helicity conservation can be tested even without polarized beam by looking for the presence of m=0 ω decays in the final state. The Radphi sample provides a good testing ground for this idea.

Regardless of what method is used to measure the polarization, the question of what precision on p is required to extract the most physics from the GlueX data remains an important unanswered question. The only way we know of to answer that question is to repeat some of the PWA exercises that were done earlier on (or carry out new ones) with this specific question in mind. If knowing the polarization at the level of 10% (for example, p=0.40±0.04) is sufficient then vector decays is surely all we need. To do much better than that will require calibrating the reaction, eg. to determine what the analyzing power is for a given set of cuts in mass and t. The general belief is that CBSA (coherent bremsstrahlung spectral analysis) can provide polarization information at the level of 5%, at least before substantial radiation damage has accumulated in the diamond radiator. The essential question to be answered is whether knowledge of the beam polarization substantially more precise than 5% would make any difference in the GlueX data analysis.

Additional comment Nov. 30, 2005 (A. Afanasev)

I agree that repeating the PWA exercises is the right way to specify to what extent the beam polarization needs to be known. I would like see how the PWA excercise is put together. I am concerned that if the model of the reaction mechanism used in such excercises is oversimplified, then full benefits of polarization would not be demonstrated.

R. Jones responds: What guidance can you provide on what assumptions to avoid? My reflex would be to take the model that was used in the double-blind exercise (3π analysis with a1, a2, π2 and an exotic 1-+ resonance at 1800 thrown in) and repeat the analysis assuming several values for the polarization, looking for leakage effects associated with using the wrong p. Do you have something more sophisticated in mind?

References

  1. A.V. Afanasev and A.P. Szczepaniak, ``Charge Exchange rho0 pi+ Photoproduction and Implications for Searches of Exotic Meson'', hep-ph/9910268 and Phys.Rev. D61 (2000) 114008.
  2. C. Meyer, ``A Summary of the Linear Polarization Discussion'', GlueX-doc-384 (Nov. 16, 2004).

This material is based upon work supported by the National Science Foundation under Grant No. 0402151.