Proton--induced deuteron breakup at GeV energies with forward emission of a fast proton pair

A study of the deuteron breakup reaction $pd \to (pp)n$ with forward emission of a fast proton pair with small excitation energy $E_{pp}<$ 3 MeV has been performed at the ANKE spectrometer at COSY--J\"ulich. An exclusive measurement was carried out at six proton--beam energies $T_p=$~0.6,~0.7,~0.8,~0.95,~1.35, and 1.9 GeV by reconstructing the momenta of the two protons. The differential cross section of the breakup reaction, averaged up to $8^{\circ}$ over the cm polar angle of the total momentum of the $pp$ pairs, has been obtained. Since the kinematics of this process is quite similar to that of backward elastic $pd \to dp$ scattering, the results are compared to calculations based on a theoretical model previously applied to the $pd \to dp$ process.


Introduction
Backward elastic pd → dp scattering at energies of several hundred MeV is one of the simplest hadron-nucleus processes with high transferred momentum. It has been studied for more than 30 years both experimentally and theoretically with the aim of extracting information about the short-range structure of the NN interaction and the dynamics of high-momentum transfer in few-nucleon systems. Besides the one-nucleon-exchange (ONE) mechanism ( Fig. 1), a number of concepts have been discussed in this context, e.g. the presence of nucleon resonances (N * ) inside the deuteron [1], the importance of virtual pions [2], and three-baryon resonances [3] (for a review see Ref. [4]). Only at low energies, where ONE dominates, are the data on differen- tial cross section, tensor analyzing power T 20 , and spin transfer coefficient κ, reasonably well described [4][5][6][7][8]. At higher energies, where internal momenta above 0.3 GeV/c are probed in the deuteron, the dynamics becomes more complicated, because of a possible excitation of N * and ∆ resonances in the intermediate states. These effects are taken into account to some extent in the one-pion-exchange model, but when adding the ONE amplitude, the problem of double counting arises [2,9,10]. The excitation of the ∆(1232) resonance in the intermediate state (∆ mechanism) is explicitly included in a model [3,5], which also takes into account coherently ONE and single pN scattering (SS) in a consistent way (Fig. 1). This model, improved in Ref. [11] with respect to the ∆ contribution through the analysis of pp → pnπ + data [12], describes the gross features of the pd → dp spin-averaged differential cross section. After further refinement also the tensor analyzing power at beam energies below 0.5 GeV is qualitatively reproduced [5]. Above the region, where the ∆(1232) dominates, the role of intermediate excitations of heavier baryon resonances is expected to increase and this makes the theoretical interpretation of this process much more ambiguous.
In view of the above complications, it would be very important to study a similar pd process, where contributions from the N * and ∆ resonance excitation are suppressed. For that purpose, an appropriate reaction is the deuteron breakup p + d → (pp) + n with emission of the two protons in forward direction (θ pp ≈ 0 • ) at low excitation energy E pp < 3 MeV. With the neutron emitted backward, the kinematics of this reaction is quite close to that of pd backward elastic scattering. Therefore, the same mechanisms can be applied in the analysis of the process as well. According to the ONE+SS+∆ model calculations [13,14], which implicitly include the pp final-state interaction (fsi), the pp pair is expected to be mainly in a 1 S 0 state. Due to isospin invariance, the isovector nature of the pp pair leads to a suppression of the amplitude of the ∆ mechanism by a factor three in comparison to the ONE amplitude for all partial waves of the pp system [13]. The same suppression factor also applies for a broad class of diagrams with isovector meson-nucleon rescattering in the intermediate state, including excitation of N * resonances [15]. As a result, the contribution of the ONE mechanism, which is sensitive to the NN potential at short distances, becomes more pronounced than in pd → dp scattering. Furthermore, the node in the half-off-shell pp scattering amplitude in the 1 S 0 state at an off-shell momentum of about 0.4 GeV/c leads to a dip of the differential cross section of the deuteron breakup at 0.7-0.8 GeV beam energy [13,16]. At higher energies of 1-3 GeV, the cross section is dominated by the ONE mechanism and decreases rather smoothly.
Another attractive feature of the process is the simplicity of its phenomenological description, since at zero degrees it requires only two spin amplitudes. Therefore, a model-independent amplitude analysis becomes possible through the measurement of a few polarization observables. As a first step, we have measured the differential cross section at six beam energies in the interval 0.6-1.9 GeV, which covers the region of the dip predicted by the ONE+SS+∆ model, thereby probing a wide range of high internal momenta of the NN system (q N N ∼ 0.3-0.6 GeV/c).

Experiment
The experiment was performed at incident proton beam energies of 0.6, 0.7, 0.8, 0.95, 1.35, and 1.9 GeV with the spectrometer ANKE [17] at the internal beam of the COoler SYnchrotron COSY-Jülich [18]. In Fig. 2 those parts of the spectrometer are shown that are of concern for the present experiment. The protons stored in the COSY ring (∼ 3 · 10 10 ) impinged on a deuterium cluster-jet target [19], which provided a target thickness of about 1.3 · 10 13 atoms/cm 2 . The produced charged particles, after passing the magnetic field of the dipole D2, were registered by a set of three multiwire proportional chambers (MWPC) and a scintillation-counter hodoscope. Each wire chamber contains a horizontal and a vertical anode-wire plane (1 mm wire spacing), and two planes of inclined strips, that allowed us to obtain the re-  the pp → dπ + reaction. Events with two registered particles contributed little to the total trigger rate and were selected off-line. Protons from the breakup process pd → ppn with an excitation energy E pp < 3 MeV could be detected with the experimental setup for laboratory polar angles between 0 and 7 • at all energies.
Among those events with two registered particles, breakup events are identified by the determination of the missing-mass value, calculated under the assumption that these particles are protons. At all energies the missing-mass spectra reveal a well defined peak at the neutron mass with an rms value of about 20 MeV (Fig. 4). The peak is clearly separated from the one at 1.1- 1.2 GeV/c 2 , caused by proton pairs from the pd → ppπ 0 n or pd → ppπ − p reactions. A direct identification of the particle type is possible for those events for which the two particles hit different counters in the hodoscope.
These amount to about 60% of all events in the peak at the neutron mass. For E pp < 3 MeV, the fraction varies from 60 to 22% for T p = 0.6 to 1.9 GeV. The time-of-flight difference ∆t measured in the hodoscope was compared to the difference ∆t(p 1 , p 2 ) obtained from the reconstructed particle momenta p 1 and p 2 , again assuming that the two particles are protons. Applying a 2σ cut to the peak of the ∆t − ∆t(p 1 , p 2 ) distribution, proton pairs could be selected such that the contribution from other pairs was less than 1%. When both tracks hit the same counter, the energy loss distributions were analyzed and found to be in agreement with the assumption that both registered particles were protons. However, the energy loss cut was not used, since the proton separation from other particles was not quite perfect. In this case we relied on the fact that misidentified pairs (pπ + , dπ + , dp or 3 Hπ + ) show up only at substantially higher missing mass values and therefore cannot contribute to the peak at the neutron mass. For background subtraction, the spectra in the vicinity of the The integrated luminosity L int was obtained by counting protons, elastically and quasi-elastically scattered at small laboratory angles between 5 and 10 • .
It is not possible to distinguish these processes experimentally at ANKE, but the achieved momentum resolution makes possible a clean separation from the meson production continuum. The number of counts obtained was related to a simulation using the calculated small angle pd → pX cross section.
The calculation takes into account the sum of elastic and inelastic terms in closure approximation of the Glauber-Franco theory [20], which includes the sum over the complete set of final pn states. In order to estimate the obtained accuracy, the cross sections, calculated for elastic and quasielastic pd scattering within the same framework, were compared with the experimental data of Refs. [21,22,23,24,25] and [26]  The total errors of the luminosities of Table 1 take into account this uncertainty and other systematic errors of 5%, resulting from a small variation of the derived luminosity with the polar angle, caused by the position-dependent efficiency of the MWPC.

Results and discussion
The data allowed us to deduce the three-fold differential cross sections of the proton pair and its total momentum is nearly isotropic, but would allow a few percent of nonisotropic contamination to the differential cross section.
The counting rates at high energies (1.35 and 1.9 GeV) were rather low.
Therefore, in order to present the energy dependence of the process for all measured beam energies, the three-fold cross section was integrated over the interval 0 < E pp < 3 MeV and averaged over the angular range 0 < θ cm ( Table 1). Here N cor = N i=1 1/(A i · ε i ), N is the number of selected proton pairs, A i and ε i correspond to acceptance and detector efficiency for registration of the i-th pair. The correction factor f , close to unity, accounts for several soft cuts applied during data processing. The acceptance was calculated as a function of E pp and θ cm pp assuming a uniform distribution in φ cm pp and isotropy in the two proton system. The average detector efficiency was ε ≈ 90%.
The differential cross section obtained as a function of beam energy is shown in Fig. 6. The energy dependence of the measured cross section is similar to that of the pd → dp process, but its absolute value is smaller by about two or- note that the ONE+SS+∆ model underestimates the pd → dp cross section Table 1 Summary of the experimental results. T p denotes the beam energy, L int the integrated luminosity, N the number of events with E pp < 3 MeV and pair emission angle θ cm pp < 8 • , N cor gives the number of events N , corrected for acceptance and detector efficiency, N sig /(N sig + N bg ) is the background correction, and dσ/dΩ cm pp denotes the cross section (see Eq. (1)). in the dip region (T p ∼ 0.8 GeV) as well [33]. A possible explanation for this discrepancy is discussed in Ref. [4], where the contributions of NN * compo-

Conclusion
We report here the first measurement of the cross section of the pd → (pp)n reaction with a fast singlet pp pair emitted in forward direction at beam energies between 0.6 and 1.9 GeV. The measurement was carried out in collinear kinematics close to those of pd backward elastic scattering. The known mechanisms of the pd → dp process describe reasonably well the measured breakup cross section at low energies (0.6-0.7 GeV). At higher energies the calculations depend on the NN interaction potential at short distances and disagree with the data. Possible shortcomings of the model may be attributed at present to an inappropriate choice of the reaction dynamics or inadequate assumptions about the short-range structure of the deuteron. The latter could be remedied by more detailed calculations using modern NN potentials, which are in progress.
We would like to emphasize that a study of the pd → (pp)n reaction with detection of pp 1 S 0 pairs provides a new tool to investigate the short-range NN interaction. For further insight, additional data, in particular polarization measurements, are needed to provide a complete set of observables. These experiments are foreseen at ANKE.