S-wave η′-proton FSI; phenomenological analysis of near-threshold production of π0, η, and η′ mesons in proton-proton collisions

Abstract

We describe a novel technique for comparing total cross sections for the reactions pp → ppπ 0 , pp → ppη, and pp → ppη ′ close to threshold. The initial and final state proton-proton interactions are factored out of the total cross section, and the dependence of this reduced cross section on the volume of phase space is discussed. Different models of the proton-proton interaction are compared. We argue that the scattering length of the S-wave η ′ -proton 1 interaction is of the order of 0.1 fm. PACS: 13.60. Le, 13.85.Lg, 29.20.Dh Typeset using REVT E X 2 New results on η and η ′ meson production in the reaction pp → ppX, measured very recently at the COSY-11 facility [1,2], together with previous data [3,4,5,6,7,8], determine the energy dependence of the near-threshold total cross section with a precision comparable to the measurements of the reaction pp → ppπ 0 [9,10]. These new data encouraged us to perform a phenomenological analysis similar to those of references [11,12,13]. Here we concentrate on π 0 , η, and η ′ meson production, and complete the analysis of these references by taking into account the interaction between the incident protons, and by introducing a new representation of the data. The production rates of π 0 , η, and η ′ mesons will be compared as a function of the available phase space. We will study the phase-space dependence of the quantity |M 0 | which is derived from the total cross section with the ISI and pp-FSI factored out. Consideration of the dependence of |M 0 | on phase space allows us to infer the η-proton and η ′ -proton interactions. To avoid large ambiguities due to differences in pp-FSI models, we normalize the |M 0 | for η and η ′ mesons to the one for the π 0 meson and show that the resulting η ′ -proton interaction is comparable to the π 0 -proton one.In general, the total cross section is presented as a function of the dimensionless parameter η M [9,10,12] 1 , which is defined as the maximum meson momentum in units of meson mass (η M = q max M ), or as a function of the center-of-mass excess energy Q [3,6,8], where nonrelativistically these variables are related by:with m p and M denoting the proton and meson mass, respectively. The above equationshows that the proportionality factor between the variables Q and η 2 M changes for different mesons, since the masses of the π 0 , η, and η ′ are distinct. Hence, depending which variable is selected, the relation between the cross section values changes for different mesons. For example, as shown in reference [4] the η meson production-cross-section exceeds the π 0 cross 1 In order to avoid ambiguities with the abbreviation for the eta-meson, we introduce an additional suffix M for this parameter, which usually is called η.3 section by about a factor of five using η M , whereas the π 0 meson cross section is always larger when employing the Q scale.The total cross section for pp → ppX is in general an integral over phase space, weighted by the square of the transition matrix element and normalized to the incoming fl...

Few-Body Aspects of the Near Threshold Pseudoscalar Meson Production

“…Since the enhancement is similar in η and η case [14], and the strength of proton-η and proton-η interaction seems to be different [12], one can conclude that the observed enhancement is not caused by a proton-meson interaction, especially that calculations assuming a significant contribution of Pwave in the final state [70], and models including energy dependence of the production amplitude [71,72], reproduce the data within error bars. Therefore, the determination of the spin observables and extraction of the contribution from the higher partial waves is mandatory for the understanding of the observed enhancements in the discussed invariant mass spectra.…”

“…Based on the comparison of the shape of the excitation functions for the pp → ppη and pp → ppη reactions it was concluded that the p − η interaction is much stronger than the p − η [12]. At first, the small values of the cross sections for the pp → ppη reaction [47] were even interpreted as an indication of the p − η repulsive interaction [52].…”

“…The reduction of the cross section due to the ISI strongly depends on the meson mass and therefore as it was introduced in reference [12], the strength of the production dynamics is at best expressed as the total cross section normalized to the ISI factor. A natural variable for comparing the production dynamics for different mesons, making it approximately independent of the meson mass, is the volume of the available phase space [12].…”

“…The reduction of the cross section due to the ISI strongly depends on the meson mass and therefore as it was introduced in reference [12], the strength of the production dynamics is at best expressed as the total cross section normalized to the ISI factor. A natural variable for comparing the production dynamics for different mesons, making it approximately independent of the meson mass, is the volume of the available phase space [12]. Such comparison was made for the π 0 , η and η mesons and it was shown that the dynamics for the η meson production is about six time stronger than for the π 0 meson, which again is by further factor of six stronger than that of the η [12].…”

“…A natural variable for comparing the production dynamics for different mesons, making it approximately independent of the meson mass, is the volume of the available phase space [12]. Such comparison was made for the π 0 , η and η mesons and it was shown that the dynamics for the η meson production is about six time stronger than for the π 0 meson, which again is by further factor of six stronger than that of the η [12].…”