ABC Effect in Double-Pionic Fusion – a New Resonance ?

The ABC effect, an intriguing low-mass enhancement in the ππ invariant mass spectrum — known since more than 50 years from inclusive measu rements of double-pionic fusion reactions — is reexamined. To this end exclusive an d kinematically complete high-statistics experiments of the fusion reactions to d, 3He and4He have been carried out with WASA at COSY. These measurements cover the full ene rgy r gion, where the ABC effect has been observed previously. They also complement the systema tic me surements of nucleon-nucleon induced two-pion production. An isospin decomposition of all three basic double-pionic fusion reactions leading to the deuteron un iquely shows that solely the isoscalar reaction part exhibits the ABC e ffect tightly correlated with a narrow resonance structure in the total cross section. The peak energ y of the resonance structure is about 90 MeV below the nominal ∆∆ threshold of 2m∆ and its width of only 70 MeV is much less than the 2 Γ∆ expected from the conventional t-channel∆∆ process. Based on angular distributions the quantum numbers I(JP) = 0(3) have been assigned. In the double-pionic fusion reaction dd →4Heπ0π0 again the ABC e ffect is observed to be correlated with the appearance of a resonance-like structure in the tota l cross section at the same excess energy. From this we conclude that this resonance stru cture obviously is strong enough to survive even in nuclei.


Introduction
The ABC effect, an intriguing low-mass enhancement in the ππ invariant mass spectrum, has first been observed in inclusive measurements of the pd → 3 He X reaction by Abashian, Booth and Crowe [1].Subsequent bubble-chamber [2,3] and single-arm magnetic spectrometer measurements [4][5][6][7][8][9][10][11] suggested this enhancement to be correlated with the production of an isoscalar pion pair in fusion reactions to light nuclei.Its explanation has been a puzzle since more than 50 years.Therefore it has been named just after the initials of those authors, who first observed this effect.
In recent exclusive and kinematically complete measurements of the pn → dπ 0 π 0 reaction it has been demonstrated [12][13][14] that the ABC effect in this basic double-pionic fusion reaction is correlated with a narrow structure in the total cross section with quantum numbers I(J P ) = 0(3 + ), a mass of 2.37 GeV and a width of about 70 MeV.The mass is about 90 MeV below 2 m ∆ , the mass of a ∆∆ system and the width is three times narrower than expected from a conventional t-channel ∆∆ process.
The bulk of these experiments has been performed with the WASA detector featuring a solid angle coverage of nearly 4π, windowless hydrogen and deuterium pellet target systems [33,34] as well as a reliable particle identification for γ, π, p, n, d, 3 He and 4 He ejectiles.
Measurements at WASA have been performed by detection of all ejectiles of an event (with the exception of spectator nucleons) allowing thus kinematic fits with several overconstraints in the data analysis.The pn initiated reactions have been studied via the quasifree pd process with a spectator proton resulting from the target deuteron.By use of the Fermi motion of the active nucleon in the deuteron target the energy dependence of pn and pp initiated reactions could be measured over a range of more than 100 MeV with just a single beam energy.

Discussion of Results
From these measurements total as well as differential cross sections have been obtained over the full energy region, where the ABC effect has been found previously.
As an example we show in Fig. 1 the distribution of the π 0 π 0 invariant mass for the double pionic fusions to d and 4 He.In both cases we observe a pronounced ABC effect, i.e. low-mass enhancement -similar to the situation in the pd → 3 Heπ 0 π 0 reaction [28].This experimental finding strongly contravenes conventional calculations based on the mutual excitation of the two colliding nucleons to their ∆(1232) state by t-channel meson exchange, which rather predict a gentle two-hump structure relative to phase space (dotted lines in Fig. 1) [12,22,31].Such conventional calculations give a good account for the data for pp initiated two-pion production [15,22,26].Hence it comes as a surprise that they obviously do not work for pn initiated two-pion production -in particular fusion processes.
They are connected by the following isospin relation [35] for their total cross sections: which allows for a cross check on the internal consistency of measurements.Based on our measurements of all three reactions we have carried out an isospin decomposition of the isospin-mixed pn → dπ + π − reaction by use of both the isovector pp → dπ + π 0 and the isoscalar pn → dπ 0 π 0 channel.We find internal consistency of the measurements within their uncertainties.The result of the isospin decomposition is shown in Fig. 2 [14,36].

Isovector Double-Pionic Fusion
The purely isovector pp → dπ + π 0 reaction exhibits no ABC effect in the π + π 0 invariant mass distribution, which is plausible, since the isovector π + π 0 pair needs to be in relative p-wave due to Bose symmetry.Accordingly the low mass region appears to be suppressed relative to phase space rather than enhanced.This is borne out in the data and properly reproduced by conventional calculations of the t-channel ∆∆ process [14,15].In the energy region of interest the total cross section rises smoothly (black filled circles in Fig. 2) -again in accord with the conventional calculations. [GeV]

Isoscalar Double-Pionic Fusion
In contrast, the purely isoscalar fusion reaction pn → dπ 0 π 0 does not behave as expected from conventional reaction dynamics.It rather exhibits a narrow resonance structure in the total cross section (blue filled circles in Fig. 2), which is correlated with the appearance of the ABC effect in the π 0 π 0 invariant mass spectrum (Fig. 1) [12][13][14].Its peak energy is about 90 MeV below the nominal ∆∆ threshold of 2 m ∆ and its width of only 70 MeV is much less than the width of 2 Γ ∆ expected from the conventional t-channel ∆∆ process.From the angular distributions the quantum numbers I(J P ) = 0(3 + ) have been assigned to this structure [12].From Dalitz plots we may deduce that this state decays first into a ∆∆ system before it reaches the dπ 0 π 0 final system.Such a kind of a dibaryonic state has actually been predicted in some theoretical models, see e.g.[37,38].At present no conventional process is known, which could at least qualitatively explain this phenomenon.
Note that this reaction constitutes the only two-pion production channel in NN collisions, which is purely isoscalar.Hence exotic processes in the isoscalar channel are likely to be seen best in this particular reaction without being buried underneath large isovector contributions.
In the double-pionic fusion reaction dd → 4 Heπ 0 π 0 again the ABC effect is observed to be correlated with the appearance of a resonance-like structure in the total cross section at the same excess energy, however, with an increased width due to Fermi motion in initial and final nuclei as well as due to collision damping, see Fig. 3 [31,32].From this we conclude that this resonance structure obviously is strong enough to survive even in light nuclei.
The energy dependence of the reaction pd → 3 Heππ is under investigation.Preliminary results [39,40] indicate a similar trend as observed for the 4 He case.

Conclusions and Outlook
Based on the large amount of meanwhile available data we observe a scenario, which is surprisingly different, whether the two-pion production is initiated by isovector or isoscalar NN collisions.Whereas all pp, i.e. isovector initiated reaction channels may be well understood by conventional t-channel processes, the two-pion production initiated by isoscalar pn collisions is not understood by such processes alone.The outstanding finding here is that the ABC effect known for more than fifty years is strictly P r e l i m i n a r y Fig. 2. Preliminary results for the total cross sections of the basic double-pionic fusion reactions pN → dππ of different isospin systems in dependence of the center-of-mass energy √ s from threshold ( √ s = 2.15 GeV) up to 2.6 GeV.The data for the isospin mixed reaction pn → dπ + π − are shown by the red full circles.The data for its isovector part given by half the cross section of the pp → dπ + π 0 reaction are plotted by the black filled circles, whereas the data for its isoscalar part given by twice the cross section of the pn → dπ 0 π 0 reaction are shown by the blue filled circles.From Ref. [36].correlated with a narrow resonance-like structure in the total cross section.For the purely isoscalar pn → dπ 0 π 0 reaction this phenomenon -interpreted as s-channel resonance with I(J P ) = 0(3 + )comprises most of the measured cross section.The same situation is found for the double-pionic fusion to the nuclei 3 He and 4 He.If true then this isoscalar pn resonance structure is obviously strong enough to survive even in nuclei.
In forthcoming investigations signals of such a resonance will be searched for in the reaction channels pn → pnπ 0 π 0 [41] and especially in pn elastic scattering.The pn → ppπ 0 π − reaction, where also the resonance should show up in principle, is currently under investigation [16].Also singlepion production channels could in principle contain effects from this resonance.However, the large conventional cross sections in these channels make it very difficult to search for the resonance there.Total cross sections of the pn → dπ 0 π 0 (black symbols) and dd → 4 Heπ 0 π 0 reactions (colored symbols) in dependence of the excess energy above threshold.Both cross sections are given in relative units and scaled such as to have comparable heights in the peak cross section.The WASA-at-COSY results (solid circles) are compared to results from a previous exclusive measurement at CELSIUS/WASA [29] (square) as well as inclusive measurements at CELSIUS [42] (star), Birmingham [43] (inverted triangle) and Saclay [7] (triangle).The dotted line shows the energy dependence of the conventional t-channel ∆∆ process, arbitrarily scaled in height.
Fig.3.Total cross sections of the pn → dπ 0 π 0 (black symbols) and dd → 4 Heπ 0 π 0 reactions (colored symbols) in dependence of the excess energy above threshold.Both cross sections are given in relative units and scaled such as to have comparable heights in the peak cross section.The WASA-at-COSY results (solid circles) are compared to results from a previous exclusive measurement at CELSIUS/WASA[29] (square) as well as inclusive measurements at CELSIUS[42] (star), Birmingham[43] (inverted triangle) and Saclay[7] (triangle).The dotted line shows the energy dependence of the conventional t-channel ∆∆ process, arbitrarily scaled in height.