Measurement of the $np \to np\pi^0\pi^0$ Reaction in Search for the Recently Observed $d^*(2380)$ Resonance

Exclusive measurements of the quasi-free $np \to np\pi^0\pi^0$ reaction have been performed by means of $dp$ collisions at $T_d$ = 2.27 GeV using the WASA detector setup at COSY. Total and differential cross sections have been obtained covering the energy region $\sqrt s$ = (2.35 - 2.46) GeV, which includes the region of the ABC effect and its associated $d^*(2380)$ resonance. Adding the $d^*$ resonance amplitude to that for the conventional processes leads to a reasonable description of the data. The observed resonance effect in the total cross section is in agreement with the predictions of F\"aldt and Wilkin as well Albadajedo and Oset. The ABC effect, {\it i.e.} the low-mass enhancement in the $\pi^0\pi^0$-invariant mass spectrum, is found to be very modest - if present at all, which might pose a problem to some of its interpretations.


Introduction
Recent data on the basic double-pionic fusion reactions pn → dπ 0 π 0 and pn → dπ + π − demonstrate that the so-called ABC effect is tightly correlated with a narrow resonance structure in the total cross section of these reactions [1,2,3]. The ABC effect denoting a huge low-mass enhancement in the ππ invariant mass spectrum is observed to occur, if the initial nucleons or light nuclei fuse to a bound final nuclear system and if the produced pion pair is isoscalar. The effect has been named after the initials of Abashian, Booth and Crowe, who first observed it in the inclusive measurement of the pd → 3 HeX reaction more than fifty years ago [4].
The resonance structure with I(J P ) = 0(3 + ) [1] observed in the pn → dππ total cross section at √ s ≈ 2. 38 GeV is situated about 80 MeV below √ s = 2m ∆ , the peak position of the conventional t-channel ∆∆ process, which is also observed in this reaction. The resonance structure has a width of only 70 MeV, which is about three times narrower than the conventional process. From the Dalitz plot of the pn → dπ 0 π 0 reaction it is concluded that this resonance nevertheless decays via the intermediate ∆ + ∆ 0 system (at least predominantly) into its final dπ 0 π 0 state. In the pn → ppπ 0 π − reaction the resonance has been sensed, too [5], though in this case there is no ABC effect associated with the resonance. In consequence it has no longer be called ABC resonance, but d * -adopting the notation of the predicted so-called "inevitable dibaryon" [6] with identical quantum numbers.
By subsequent quasifree polarized np scattering measurements it has been demonstrated that there is a resonance pole in the coupled 3 D 3 − 3 G 3 partial waves corresponding to the d * resonance structure in mass, width and quantum numbers [7,8] -supporting thus its s-channel character.
If this scenario is correct, then also the np → npπ 0 π 0 reaction should be affected by this resonance, since this channel may proceed via the same intermediate ∆ 0 ∆ + system as the np → dπ 0 π 0 and pn → ppπ 0 π − reactions do. From a simple isospin point of view we expect the resonance effect in the npπ 0 π 0 system to be identical in size to that in the dπ 0 π 0 system. And from more refined estimates in Refs. [9,10], which account also for the different phase space situations, we expect the resonance effect in the npπ 0 π 0 channel to be about 85% of that in the dπ 0 π 0 system. Since the peak resonance cross section in the latter is 270 µb [3] sitting upon some background due to conventional t-channel Roper and ∆∆ excitations, we estimate the peak resonance contribution in the npπ 0 π 0 system to be in the order of 200 µb.

Experiment
Since there exist no data at all for the np → npπ 0 π 0 channel, we have investigated this reaction experimentally with the WASA detector at COSY (FZ Jülich) by using a deuteron beam with an energy of T d = 2.27 GeV impinging on a hydrogen pellet target [11,12]. By exploiting the quasi-free scattering process d p → npπ 0 π 0 + p spectator , we cover the full energy range of the conjectured resonance. In addition, the quasi-free process in inverse kinematics gives us the opportunity to detect also the fast spectator proton in the forward detector of WASA.
The hardware trigger utilized in this analysis required at least two charged hits in the forward detector as well as two neutral hits in the central detector.
The quasi-free reaction d p → npπ 0 π 0 + p spectator has been selected in the offline analysis by requiring two proton tracks in the forward detector as well as four photon hits in the central detector, which can be traced back to the decay of two π 0 particles. That way the non-measured neutron four-momentum could be reconstructed by a kinematic fit with three over-constraints.
A difficulty emerges from deuterons, which originate from the np → dπ 0 π 0 reaction and which partly also break up while passing the detector. Since in the ∆E − E energy loss plots used for particle identification proton and deuteron bands overlap somewhat, deuterons can not be separated completely from np pairs stemming from the np → npπ 0 π 0 reaction. To suppress such misidentified events we require the angle between emitted neutron and proton to be larger than 5 degrees and also their energies to be in the expected range. Nevertheless a Monte-Carlo (MC) simulation of the np → dπ 0 π 0 reaction, which is known in very detail [1], shows that we have to expect still a contamination of about 5% in the spectra of the np → npπ 0 π 0 reaction. In Figs. 1 -6 the observables are shown with the MC-generated contamination events already subtracted. In the pn invariantmass spectrum M pn , where the contamination shows up most pronounced, this concerns only the first two bins (Fig. 3, bottom).
In Fig. 1 the measured and acceptance corrected spectator momentum distribution is shown in comparison with a Monte-Carlo (MC) simulation of the quasifree d p → npπ 0 π 0 + p spectator process. Due to the beam-pipe ejectiles can only be detected in the WASA forward detector for lab angles larger than three degrees. The good agreement between data and simulation provides confidence that the data indeed reflect a quasifree process. The constraint for the suppression of breakup events (see above) causes the maximum accepted spectator momentum to be < 0.14 GeV/c fulfilling the spectator momentum condition used in previous works [1,3,7] This implies an energy range of 2.35 GeV ≤ √ s ≤ 2.41 GeV being covered due to the Fermi motion of the nucleons in the deuteron. This energy range corresponds to incident lab energies of 1.07 GeV < T n < 1.23 GeV.
In total a sample of about 24000 good events has been selected. The requirement that the two protons have to be in the Efficiency corrected distribution of the spectator proton momenta in the d p → npπ 0 π 0 + p spectator reaction within the WASA acceptance, which allows the detection of the spectator proton only for lab angles larger than three degrees. In addition the constraint for the suppression of breakup events has been applied (see text). Data are given by solid circles. The solid line shows the expected distribution for the quasifree process based on the CD Bonn potential [13] deuteron wavefunction. For comparison the dashed line gives the pure phase-space distribution as expected for a coherent reaction process. angular range covered by the forward detector and that the gammas resulting from π 0 decay have to be in the angular range of the central detector reduces the overall acceptance to about 7%. Efficiency and acceptance corrections of the data have been performed by MC simulations of reaction process and detector setup. For the MC simulations model descriptions have been used, which will be discussed in the next chapter. Since the acceptance is substantially below 100%, the efficiency corrections are not fully model independent. The hatched grey histograms in Figs. 3 -6 give an estimate for systematic uncertainties due to the use of different models with and without d * resonance hypothesis for the efficiency correction. The absolute normalization of the data has been performed by the simultaneous measurement of the quasi-free single pion production process d p → ppπ 0 + n spectator and its comparison to previous bubble-chamber results for the pp → ppπ 0 reaction [14,15]. That way the uncertainty in the absolute normalization of our data is essentially that of the previous pp → ppπ 0 data, i.e. in the order of 20%.

Results and Discussion
In order to determine the energy dependence of the total cross section we have divided our data sample into 10 MeV bins in √ s. The resulting total cross sections together with their statistical and systematic uncertainties are listed in Table 1. Fig. 2 exhibits the energy dependence of the total cross section for the np → npπ 0 π 0 reaction (right) in comparison to that of the pp → ppπ 0 π 0 reaction (left). The previous WASA results [16,17] and the ones of this work are given by the full circles. They are compared to previous bubble-chamber measurements from KEK (open circles) [14] in case of the ppπ 0 π 0 channel. In case of the npπ 0 π 0 channel there exist no dedicated data from previous investigations. However, there are some connected data from the PINOT experiment at Saclay, where the inclusive reactions pp → γγX and pd → γγX were measured at T p = 1.3 and 1.5 GeV [18]. By excluding the two-photon invariant mass regions corresponding to single π 0 or η production the remaining two-photon events populating the combinatorial background are likely to originate from π 0 π 0 production. By using this feature a measure of the ratio of the cross sections pn → pnπ 0 π 0 + dπ 0 π 0 to pp → ppπ 0 π 0 has been obtained. This leads to a crude estimate for the pn → pnπ 0 π 0 cross section to be larger than the pp → ppπ 0 π 0 cross section by roughly a factor of two -in qualitative support of our results from the exclusive measurements [19].
In Fig. 2 we compare the data to theoretical calculations in the framework of the Valencia model [20], which incorporates both non-resonant and resonant t-channel processes for twopion production in NN collisions. The t-channel resonance processes of interest here concern first of all the excitation of the Roper resonance and its subsequent decay either directly into the Nππ system or via the ∆π system as well as the excitation and decay of the ∆∆ system. Deviating from the original Valencia calculations [20] the present calculations have been tuned to describe quantitatively the isovector two-pion production reactions pp → NNππ [16], in particular the ppπ 0 π 0 [21] and nnπ + π + [22] channels by the following modifications: • relativistic corrections for the ∆ propagator as given by Ref. [23], • strongly reduced ρ-exchange contribution in the t-channel ∆∆ process -in agreement with calculations from Ref. [24], • reduction of the N * → ∆π amplitude by a factor of two in agreement with the analysis of photon-and pion-induced pion production on the nucleon [25] and in agreement with pp → ppπ 0 π 0 and pp → ppπ + π − measurements close to threshold [26,27,28,29] as well as readjustment of the total Roper excitation according to the results of the isospin decomposition of the pp → NNππ cross sections [16], • inclusion of the t-channel excitation of the ∆(1600)P 33 resonance.
The latter modification was necessary, in order to account for the unexpectedly large pp → nnπ + π + cross section [22]. The predictive power of these modifications has been demonstrated by its successful applications to the recent pp → ppπ 0 π 0 data at T p = 1.4 GeV [17] and to the pn → ppπ 0 π − reaction [5].
Final state interaction (FSI) in the emitted NN system has been taken into account in the Migdal-Watson [30,31] factorized form.
The NN FSI is by far strongest in the isovector 1 S 0 pn state and less strong in 1 S 0 pp and 3 S 1 pn states as apparent from the scattering lengths in these systems. At energies above 1 GeV the t-channel ∆∆ process is the dominating one. Isospin decomposition of its contribution to the total np → npπ 0 π 0 cross section [32,33,16] shows that in this process the 1 S 0 final state is much less populated than the isoscalar 3 S 1 state. The situation is somewhat different in the near-threshold region, where the Roper excitation process dominates. In this process equal amounts of pn pairs are emitted in 1 S 0 and 3 S 1 states.
Since the modified Valencia calculations have been tuned to the pp → ppπ 0 π 0 reaction, it is no surprise that its total cross section is fairly well described -see Fig. 2, left. For the closely related np → npπ 0 π 0 reaction the calculations predict a similar energy dependence, but an absolute cross section, which is larger by roughly a factor of two -whereas the data are larger by more than an order of magnitude -see Fig. 2, right.
As an independent check of these calculations we may perform an isospin decomposition of cross sections using the formulas given in Refs. [32,33] and the matrix elements deduced from the analysis of the pp induced two-pion production [16]. As an result of such an exercise we get agreement with the modified Valencia calculation within roughly 30%.
As we see from Fig. 2, the experimental cross sections obtained in this work for the np → npπ 0 π 0 reaction are three to four times larger than predicted. This failure points to an important reaction component not included in the t-channel treatment of two-pion production. It is intriguing that we deal here with the energy region, where the d * resonance has been observed both in np scattering [7] and in the isoscalar part of the doublepionic fusion to deuterium [1,3]. Also it has been shown that the description of the pn → ppπ 0 π − cross section improves greatly in this energy region, if this resonance is included [5]. Hence we add also here the amplitude of this resonance to the conventional amplitude. According to the predictions of Fäldt and Wilkin [9] as well as Abaladejo and Oset [10], its contribution at the resonance maximum should be about 200 µb (dotted curve in Fig. 2) as discussed in the introduction. It is amazing, how well the resulting curve (dash-dotted line in Fig.2) describes the data. Of course, it is a pity that there are no data outside the energy region covered by our data. In particular at energies below 1 GeV and above 1.3 GeV, i.e. outside the resonance region, such data would be very helpful to examine experimentally the reliability of the predictions for the t-channel contributions.
When binned into √ s bins of 10 MeV the different distributions do not exhibit any particular energy dependence in their shapes -which is of no surprise, since the energy region covered in this measurement is dominated by the d * resonance as evident from the discussion of the total cross section. Hence we refrain from showing the differential distributions for single √ s bins. We rather show them unbinned, i.e., averaged over the full energy range of the measurement, which has the advantage of better statistics and less systematic uncertainties.
For a four-body final state there are seven independent differential observables. We choose to show in this paper the differential distributions for the invariant masses M π 0 π 0 , M pn , M pπ 0 , M nπ 0 , M nπ 0 π 0 and M ppπ 0 as well as the differential distributions for the center-of-mass (cm) angles for protons and pions, namely Θ c.m. p and Θ c.m. π 0 . These distributions are shown in Figs. 3 -6.
All measured differential distributions are markedly different in shape from pure phase space distributions (shaded areas in Figs. 3 -6), but close to the predictions both with (dashed and dash-dotted lines) and without (solid lines) inclusion of the d * resonance.
The invariant mass spectra for M pπ 0 , M nπ 0 , M nπ 0 π 0 and M pnπ 0 (Figs. 4 -5) are characterized by ∆ and N∆ dynamics as they naturally appear in the deexcitation process of an intermediate ∆∆ system created either by d * decay or via t-channel meson exchange.
The pion angular distribution (Fig. 6) behaves as expected from the p-wave decay of the ∆ resonance. And also the proton angular distribution is similarly curved. Both t-channel meson exchange and the J P = 3 + requirement for d * formation predict comparable shapes in agreement with the data.
The M pn and M π 0 π 0 spectra (Fig. 3) need a more thorough discussion. The data of the M π 0 π 0 spectrum appear to be quite well described by the calculations, which hardly deviate from each other. At small invariant masses though, in the range 0.3 -0.4 GeV/c 2 , there is an indication of a small surplus of strength. Taken the uncertainties inherent in the data and in the theoretical description, these deviations appear not to be particularly significant. Therefore, if this constitutes a sign of the ABC effect, then it is obviously very small in this reaction. Note that contrary to the situation in the pn → ppπ 0 π − reaction, where the pion pair has to be in relative p-wave and hence the ABCeffect is absent, the pion pair here is preferentially in relative s-wave allowing thus, in principle, the occurrence of the ABC effect. Hence, the finding that there is no or nearly no ABC effect comes as a surprise at least for some of its interpretations.  Figure 3: (Color online) Top: distribution of the π 0 π 0 invariant mass M π 0 π 0 for the pn → npπ 0 π 0 reaction at T n = 1.135 GeV. Since the data are shown without separation into √ s bins, they correspond to the average over the energy region covered by the quasifree collision process, which is 2.35 GeV < √ s < 2.41 GeV (1.07 GeV < T n < 1.23 GeV). Filled circles represent the experimental results of this work. The hatched histograms give estimated systematic uncertainties due to the incomplete coverage of the solid angle. The shaded areas denote phase space distributions. The solid lines are calculations with the modified Valencia model. The dashed (dash-dotted) lines shows the result, if the d * resonance amplitude with (without) inclusion of the ∆∆ vertex function [1] is added. All calculations are normalized in area to the data. Bottom: the same as at the top, but for the pn invariant mass M pn .

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nel, but also differential distributions. Of particular interest will be the M pn and M π + π − distributions as discussed in this work.