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Comparison of eta and eta' production in the pp ->pp eta(eta') reactions near threshold

The total cross section of the pp ->pp eta' reaction has been measured at two energies near threshold by detecting the final protons in a magnetic spectrometer. The values obtained are about a factor of 70 less than for the corresponding eta production, in good agreement with the predictions of a one-pion-exchange model.

The production of η mesons in proton-proton collisions near threshold has been measured in recent years using three different techniques. By detecting both final protons in a magnetic spectrometer, the SPESIII group at Saturne [1,2] observed the η meson as a missing mass peak. The PINOT group [3], also working at Saturne, instead identified the η directly through its decay into two photons. Up to at least the threshold for ηπ production this provides a clean measurement of the pp → ppη total cross section. The CELSIUS group used a combination of the two techniques when measuring the γγ decay in coincidence with the directions (but not the energies) of two final charged particles [4]. Each method has its own advantages but it is very reassuring that the total cross sections from the three groups, shown in fig. 1 in terms of the centre-of-mass excess energy Q, present such a consistent picture. In the present letter we report on the first measurement of η ′ production in proton-proton collisions near threshold using the magnetic spectrometer technique, and compare the resulting cross sections with those obtained for the η.
The experiment was carried out at the Laboratoire National SATURNE (LNS) using the SPESIII spectrometer under experimental conditions which were similar to those reported in ref. [1] and so only essential features are reported here. SPESIII is a large acceptance magnetic spectrometer which is well suited to the study of meson production involving both two and three-body final states near threshold.
The detection system consists of three multiwire drift chambers, the first situated on the focal plane, and four planes of scintillators, comprising in total 70 counters.
Under its standard working conditions the spectrometer can analyse particles with momenta p/Z lying between 600 and 1400 MeV/c with a resolution δp/p in the range The maximum opening angles in both the horizontal and vertical directions are ±60 mr and the effective solid angle acceptance is ∆Ω ≈ 10 −2 sr. The momentum resolution can be improved by using one of a series of collimators, though at the expense of reducing the solid angle, and this was done for most of the η measurements reported in ref. [1]. In view of the smaller cross section expected for the η ′ , the collimators were here withdrawn to obtain the maximum solid angle. In such conditions the spectrometer and its detection system covered about 85% and 50% of the total ppη ′ phase space at the two beam energies studied, which were nominally 2416 and 2430 MeV. The liquid hydrogen target had a thickness of 270 mg/cm 2 . The control of the beam intensity and measurement of the number of incident protons was carried out with the help of two scintillator telescopes viewing the target and an ionisation chamber placed in the beam downstream of the target. The absolute calibration of these counters was carried out using the standard carbon activation technique [5].
The missing mass spectra of the pp → ppX reaction shown in figs. 2(a1) and (a2) correspond to measurements a little above the η ′ threshold at T p = 2416 and 2430 MeV respectively. The clear rise near the end of these spectra contains η ′ events but superimposed on a continuum of multipion production and this continuum must be subtracted in order to determine the numbers of η ′ produced. This was carried out using analogous spectra recorded just below threshold at T p = 2400 MeV. The measured momenta p 1 and p 2 for each event were increased by an amount ∆p and the missing mass was evaluated as if the beam energy were either 2416 or 2430 MeV. The values of ∆p were fixed by demanding that the range of proton momenta near the highest missing masses was the same above and below threshold. At the endpoint of the spectra, ∆p = m p (β ′ γ ′ −βγ), where β ′ and β are the incident proton speeds above and below threshold. The predicted backgrounds shown in figs. 2(b1) and 2(b2) still manifest some enhancement near the ends of the spectra arising from the protonproton final state interaction (fsi). The η ′ peaks were obtained by subtracting these background spectra from those of the pp → ppX measured above the η ′ production threshold. The shapes and widths of the η ′ peaks in the resultant pp → ppη ′ spectra, shown in figs. 2(c1) and 2(c2), are in good agreement with the computer simulations discussed later.
In view of the rapid variations of the three-body cross section and the spectrometer acceptance near threshold, it is vital to determine the excess energy Q in the centreof-mass (cm) system with precision. Now the nominal beam energy calculated using the parameters of the SATURNE accelerator is in general slightly greater than the true value. Several previous detailed studies [2,6,7] show that the difference between the real and nominal energies does not depend upon the energy or particle type but rather on the tuning of the accelerator and on the beam extraction. ¿From these measurements we determine an energy correction of dT = 1.1 ± 1.0 MeV which changes a nominal beam energy of 2416 MeV to a 'true' value of T p = 2414.9 MeV.
It is however possible to determine the value of Q directly from the experimental data, as has been done previously at SPESIII for η production [1,6]. Near threshold the width of the proton momentum spectrum is a sensitive function of Q which depends but weakly upon the final masses and the absolute calibrations of the beam and spectrometer. Fig. 3(a) shows such a spectrum for η ′ production, obtained by selecting those events in figs. 2(a1) and 2(b1) in the range 956 MeV/c 2 ≤ M x ≤ 962 MeV/c 2 and performing a subtraction, to be compared with a simulation performed assuming that Q = 4.3 MeV. From the variation of χ 2 for such fits shown in fig. 3(b), we deduce that Q = 4.3 ± 0.9 MeV, corresponding to a value of m η ′ = (957.0 ± 0.9) MeV/c 2 for a beam energy of 2414.9 MeV. This is in good agreement with the World compilation of the η ′ mass [8]. The value of the mid-target value of Q quoted in Table 1  In a one-pion-exchange model, a π 0 is emitted by one proton and converts to an η on the second, leaving the two final protons to be subject to the strong S-wave final state interaction [9]. If the initial pp distortion is neglected, it is straightforward to show in such a model that the S-wave contribution to the total pp → ppη cross section near threshold should have the form (1) with an analogous formula for η ′ production. Here m p , m η and m π are respectively the p, η and π masses. Despite the dominance of the N * (1535) resonance, the spinaverage of the square of the π 0 p → p η amplitude, |f | 2 , varies slowly over the limited range of Q measured in this experiment. It is therefore sufficient to take its value at threshold.
In the short-range limit, which is valid for heavy-meson production, the effect of the proton-proton final state interaction can be modelled by the function [10] F (Q) = ǫ Q ǫ where, including Coulomb distortion, ǫ ≈ 0.45 MeV. Such a function describes accurately the near-threshold energy dependence of the pp → ppπ 0 total cross section down to Q ≈ 1 MeV, when explicit Coulomb suppression becomes important [10].
The overall factor A depends upon the πpp coupling constant and the proton mass etc., but is independent of parameters referring to the η meson, so that its value should be the same for both η and η ′ production.
The dashed curve in fig. 1 shows the prediction of eq.(1) when the value of A is adjusted to fit the lowest energy points of η production. The deviations from this curve of up to a factor of two at higher values of Q have been taken as evidence for an attractive ηpp final state interaction [4]. By using the same value of A, combined with experimental values for the threshold values of |f (π 0 p → p η)| 2 = (365±30) µb/sr and |f (π 0 p → p η ′ )| 2 = (10±1) µb/sr [11], it is possible to make absolute predictions of the pp → ppη ′ total cross section, and the resulting solid line shown in fig. 1, is only about 30% below our two experimental points and in good agreement with the trend in the data. Though the predicted energy dependence is only weakly model dependent, more accurate estimates of the normalisation would require further information on the contributions of ρ and other heavy-meson exchange diagrams [9].
In summary, we have made a first measurement of the pp → ppη ′ total cross section near threshold, determining the mass of the η ′ to better than 0.1%. The relative production rates of the η ′ and η mesons are broadly consistent with expectations based on a meson exchange model. Since the preparation of this letter, we have been informed that measurements by the COSY-11 group closer to threshold have been submitted for publication [12]. It should be noted that there is satisfactory agreement in normalisation where the two experiments meet around Q = 4 MeV.
We wish to thank F. Brochard for much help and advice. The SATURNE machine was closed down on the night of 1/2 December 1997. We should like to express our gratitude to the accelerator crew and support staff for providing us with excellent conditions in which to work on this and previous experiments.