Observation of resonance-like behavior of the pp → { pp } s π 0 reaction around √ s = 2 . 65 GeV

Abstract. The pp → {pp}sπ0 reaction, where {pp}s denotes a diproton, i.e. an unbound interacting proton pair in the 1S 0 state, has been studied in order to obtain the forward differential cross section dσ/dΩ at 11 energy values in the region of 0.8–2.8 GeV. A resonance-like peak with the energy E0 = 2.647 ± 0.005 GeV and the width Γ = 0.26 ± 0.03 GeV has been observed in the energy dependence of the differential cross section dσ/dΩ at zero angle. The slope of the angular dependence for the energies in the peak region is different compared with the energies around it. Possible implications on this phenomenon are discussed.


Introduction
Single pion production in nucleon-nucleon collisions, NN → NNπ, is one of the basic methods to study strong interactions at intermediate energies. While chiral perturbation theory can be employed to describe these processes near the pion production threshold [1], at the energies of Δ(1232)-isobar excitation and above various phenomenological models are used (see e.g. [2] and refs. therein).
The pp → dπ + reaction is a classical example of an NN → NNπ channel that has long been the subject of extensive experimental studies. A way to get more information about the NN → NNπ dynamics is to study together channels with the production of a deuteron and its spin-isospin partner, a diproton. A diproton, {pp} s , is an unbound interacting proton pair in the 1 S 0 final state. The quantum numbers of the {pp} s system are I = 1, S = 0, L = 0 instead of I = 0, S = 1, L = 0, 2 for the deuteron. This difference in quantum numbers of the deuteron and diproton was the main point why the paper [3] suggested to change the deuteron by the {pp} s in the backward elastic scattering pd → dp in the GeV region. A subsequent experimental study of the suggested reaction pd → {pp} s n [4] and its theoretical interpretation [5] allowed one to get more insight into short-range behavior of the NN-interaction potential. After that a set of measurements of the pp → {pp} s π 0 reaction has been carried out at ANKE [6][7][8][9], mostly for the energies in the region of Δ(1232)-isobar excitation. * e-mail: kurbatov@jinr.ru , 0 (201 E Web of Conferences https://doi.org/10.1051/e onf /201920408008 PJ pjc 9) 204 Baldin ISHEPP XXIV 8008 It has long been known that the energy dependence of the forward differential cross section for the pp → dπ + reaction exhibits two peaks: the first one around the proton beam energy T p ≈ 0.55 GeV, and the second one -around T p ≈ 3 GeV [10]. The first peak is caused by three dominant transitions exhibiting a resonance behavior in the intermediate two-baryon system: 1 D 2 p, 3 F 3 d and 3 P 2 d [11]. Here the standard notation 2S +1 L J is used for the state of the initial proton pair with the orbital angular momentum L, spin S , and the total angular momentum J, while the small letters denote the angular momentum of the final pion. The pp → {pp} s π 0 reaction exhibits a similar peak with the maximum slightly shifted towards higher energies, T p ≈ 0.65 GeV. The analysis of this peak indicates that it is caused by two interfering resonance transitions: 3 P 2 d and 3 P 0 s [9]. The transitions responsible for the second peak in the pp → dπ + spectrum remain much less clear. Thus, new data for the spin-isospin partner of this reaction, pp → {pp} s π 0 , might be useful for its understanding.
An earlier ANKE study [7] has revealed that for the pp → {pp} s π 0 reaction the forward differential cross section, after reaching a minimum at T p ≈ 1.4 GeV, rises again at T p ≈ 2.0 GeV, possibly indicating the presence of the second peak similar to that of pp → dπ + . To investigate this phenomenon, measurements of the pp → {pp} s π 0 differential cross section have been performed at 11 energies in the energy range T p = 0.8-2.8 GeV.

Measurements and results
The measurements were carried out using the ANKE spectrometer [12] at the COSY-Jülich storage ring. The experimental setup is shown in Fig. 1. Charged particles produced in the interaction of the stored proton beam with a hydrogen cluster-jet target [13] pass through the analyzing magnet, 3 blocks of track gas chambers and 2 planes of scintillation hodoscopes. The measurements used for earlier studies [6,7,9] have been supplemented with more data at various energies in the energy range 1.0-2.8 GeV. The analysis of the data at 0.8 GeV was repeated because more accurate geometry alignment and kinematic fitting procedures had been developed. ¡ Reconstruction of the three-momenta and trajectories of the particles, identification of the pp → {pp} s π 0 candidates, and their further analysis repeated the procedure described in [6,7,9]. The only significant new feature of the analysis was that we used the kinematic fitting technique [14] based on a widely used FUMILI code [15]. If the event satisfied 3% confidence level after kinematic fitting, it was used for further processing. The two-dimensional registration efficiency for the pp pairs depending on their excitation energy E pp and the polar angle of the pair in the reaction center-of-mass system (CMS) θ cm pp was determined by Monte-Carlo simulations with the uncertainty of about 3%. Systematic errors were estimated to be ≈ 8%. In order to get differential cross section of the reaction dσ/dΩ we used the luminosity estimated using the pp → pp process which ranged from few tens nb −1 to few pb −1 .
The angular range was divided into the bins containing approximately the same number of events. After taking into account all the corrections for every exposition, the differential cross sections dσ/dΩ were obtained, which are presented in Fig. 2. For all the energies we restricted ourselves by the range of the CMS polar angle 0 • ≤ θ cm pp 18 • in order to obtain the evolution of process over the whole energy range, though at the low energies the apparatus acceptance was larger [9].
The cross sections were fitted by either a linear of a quadratic function over sin 2 θ cm pp : depending on the available statistical precision and the resulting χ 2 /ndf value.
p r e l i m i n a r y   [16], circles are the previously published ANKE ones from [7,9], squares stand for current results. The curve is the result of fit of the simple Breit-Wigner distribution (3) to the values from the current measurement. The fit gives the position of the resonance peak E 0 = 2.647 ± 0.005 GeV and the width Γ = 0.26 ± 0.03 GeV It is worth noting that the slope of the angular dependence for the energy range 1.6-2.2 GeV is different compared with all the other energies outside this range measured so far [6,7,9,16] (Figs. 2, 3). The differential cross section at zero angle dσ/dΩ(0) in this 1.6-2.2 GeV range exhibits a pronounced peak surrounded by the minima at ≈ 1.4 GeV and ≈ 2.6 GeV, see Fig. 3.
The differential cross section values allow one to calculate also the integrated cross sections for the analyzed angular range 0 • ≤ θ cm pp < 18 • . It has a peak in the region 1.8-2.0 GeV as well.

Analysis and discussion
The one-pion-exchange mechanism (Fig. 4a) is one of the basic approaches that was used to describe both the pp → dπ + [17][18][19] and pp → {pp} s π 0 [20] reactions. In the work [20] the cross section of the π 0 p → π 0 p scattering, taken from the SAID partial wave analysis program [21], was used for the corresponding vertex of the diagram. This approach qualitatively succeeded to describe the first peak in energy dependence of the differential cross section at zero angle, but failed to reproduce the angular dependence. The triangular diagram in Fig. 4a can be expanded to a box diagram, Fig. 4b, though this approach also did not succeed to describe the experiment well. The reason could be the neglection of interaction between the proton and the excited baryon in the intermediate state. Gal and Garcilazo have shown in series of their works that such an interaction plays an important role in the nucleon-nucleon interactions at intermediate energies (see [22,23] and refs. therein). The chiral constituentquark models [24] are also being used to describe two-baryon interactions in the considered energy range. Thus, the one-pion-exchange mechanism could be considered only as an initial approximation for the underlying dynamics of the pp → {pp} s π 0 reaction. In this work we'd take only first steps towards the analysis of the second pp → {pp} s π 0 peak. We would treat the intermediate state as a "black box" without considering its inner structure. Thus, the process is interpreted as an s-channel excitation of a two-baryon resonance state (see Fig. 4). Due to the position of the peak being far from the threshold, the quantum numbers of the intermediate two-baryon system have little impact on the peak shape. Thus, we would describe the data with the simplest Breit-Wigner form with the fixed width: where N is the normalization, E 0 is the position of the resonance peak, and Γ is its width. Since such Breit-Wigner description is only valid in the region of the peak maximum, we limit the fit to five data points comprising the central part of the peak. The fit gives the following parameters: E 0 = 2.647 ± 0.005 GeV and Γ = 0.26 ± 0.03 GeV (see Fig. 3). It is worth noting that the position of the second pp → dπ + peak is E 0 ≈ 3.0 GeV [10], thus, the pp → {pp}π 0 one is lower by ≈ 350 MeV.

Summary
• Differential cross sections have been measured for the pp → {pp} s π 0 reaction at forward angles for 11 energies in the region T p = 0.8-2.8 GeV; , 0 (201 E Web of Conferences https://doi.org/10.1051/e onf /201920408008 PJ pjc 9) 204 Baldin ISHEPP XXIV 8008 • In addition to the peak around T p ≈ 0.65 GeV that corresponds to the Δ(1232) excitation, the energy dependence of the cross section at zero angle exhibits a peak around T p ≈ 1.85 GeV, similar to the one known for the pp → dπ + reaction; • The slope of the angular dependence for the energy range 1.6-2.2 GeV is different compared with the energies around this range; • The process has been interpreted as s-channel excitation of the two-baryon resonance state, the fit of the simplest Breit-Wigner form to the data provides the following parameters of the peak: the position E 0 = 2.647 ± 0.005 GeV and the width Γ = 0.26 ± 0.03 GeV; • The position of the peak is about 350 MeV lower than that of the pp → dπ + one.