Near-threshold pion production in diproton reactions with polarised beams and target at ANKE-COSY

An extensive experimental study of near-threshold pion production in d iproton reactions is underway at the ANKE-COSY spectrometer (J ülich). The programme is aimed at isolating the four-nucleon-pion contact interaction term appearin g in theχPT expansions of these processes. This will establish links between pion produ ction and other low energy phenomena within the χPT approach. The first step in the programme was to measure the di fferential cross-section and the proton analysing power in the ~pp→ {pp}s π0and ~pn→ {pp}s πreactions over the full angular range. Here {pp}s denotes a diproton, i.e., a two-proton system in a1S 0 state. These data allow a partial wave analysis to be carried out provided that simplifying assumptions are made when applying the Wats on theorem. To make the analysis more robust, and independent of the uncertainties in he relative normalization, the spin-correlation coe fficientsAx,x andAy,y in the~n~p → {pp}s π reaction were measured in a follow-up experiment. The first results of the data analysis are presented and future developments of the programme are outlined. 1 The physics case for near-threshold single pion production The ANKE [1] experimental programme on the near-threshold p ion roduction aims to measure the cross sections and spin observables in the pp→ {pp}s π0 andnp→ {pp}s π reactions [2,3]. The symbol {pp}s here denotes a diproton, that is, an unbound proton pair with a very low excitation energy, Epp < 3 MeV. The selection of a low excitation energy ensures the do minance of the1S 0 state of the diproton, which simplifies significantly the theoretical an alysis. A full data set of all observables at low beam energies would allow us to determine the partial wave am plitudes which, in turn, would provide a non-trivial test of chiral perturbation theory [4] and als o ead to the determination of the value of the parameterd, which represents the important contact term that a ffects the pionp-wave amplitudes. The short range physics in chiral e ff ctive field theories, which provide a model-independent un derstanding of Nature, is encoded in the so-called low energ y constants (LEC). These LECs, once determined from one process, can be applied to predict many o thers. For example, the LECs c1–c4 extracted fromπN analysis on the basis of chiral perturbation theory are now w idely used to parameterise the short range physics in the NN-interaction, few-nucleon systems, single (and multi-) pi on production inNN collisionsetc. Analogously, by studying the p-wave pion production amplitudes we get access to the 4 Nπ contact operator, the strength of which is controlled by the low energy constant d. This LEC enters also in electroweak processes, such as pp→ deν and tritonβ decay, in few-body operators ( e.g. in pd → pd), pion photoproductionγd → nnπ and its inverseπd → γNN. It therefore plays a very important role in connecting di fferent low-energy reactions. On the practical side, the pp→ {pp}s π0 andnp→ {pp}s π reactions have the big advantage for COSY that both the pion and diproton have spin-zero, which me ans that the only spin degrees of freea e-mail:s.dymov@fz-juelich.de EPJ Web of Conferences dom are connected with the initial state. There are therefor e n non-trivial spin-transfer observables, which means that rescattering experiments are not required . Four types of experiments are possible for both π0 andπ production. These are the measurement of the unpolarised di fferential cross section dσ/dΩ, the beam or target analysing power Ay, the in-plane spin-correlationAx,x, and the mixed correlation parameter Ax,z. Knowing these one can determine the magnitudes and the relative phase of the two scalar amplitud es as functions of the pion production angle for either thepp or pn experiment. At low energies it is reasonable to assume that data can be ana lysed by truncating the partial wave expansion at orbital angular momentum l = 2. It is shown in [5] that the magnitude of one of the pwave amplitudes is then fixed completely by the measurement o f (1−Ax,x) · dσ/dΩ for np→ {pp}s π and that the magnitude of the other p-wave amplitude and its relative phase can be deduced from a combined analysis of this with our cross section and analys ing power data forpp→ {pp}s π0and np→ {pp}s π. These data will provide two determinations of the LEC d. Measurements of the mixed spin-correlation parameters Az,x are not required for the extraction of the p-wave amplitudes, though such information is vital in order to identify the d-wave terms. 2 Measurement of cross section and analysing power As first steps in the programme, measurements with a polarise d proton beam incident on unpolarised hydrogen and deuterium cluster targets were performed at a b eam energy of Tp = 353 MeV [2,3]. 2.1 The ~pp→ {pp}s π0 process The polarised proton COSY beam and the ANKE hydrogen cluster target were used in this measurement. The final proton pair was recorded in the ANKE forward de tector and identified with the use of the time-of-flight di fference between the two protons. After the selection of the pr oton pairs, the ~pp→ {pp}s π0events were identified by the missing-mass criterion. The be am polarisation and luminosity were determined by detecting simultaneously the ~pp→ dπ and~pp→ pp processes, for which the cross sections and analysing powers are known with high p recision at this energy. cm π θ cos -1 -0.5 0 0.5 1 [n b/ sr ]

dom are connected with the initial state.There are therefore no non-trivial spin-transfer observables, which means that rescattering experiments are not required.
Four types of experiments are possible for both π 0 and π − production.These are the measurement of the unpolarised differential cross section dσ/dΩ, the beam or target analysing power A y , the in-plane spin-correlation A x,x , and the mixed correlation parameter A x,z .Knowing these one can determine the magnitudes and the relative phase of the two scalar amplitudes as functions of the pion production angle for either the pp or pn experiment.
At low energies it is reasonable to assume that data can be analysed by truncating the partial wave expansion at orbital angular momentum ℓ = 2.It is shown in [5] that the magnitude of one of the pwave amplitudes is then fixed completely by the measurement of (1 − A x,x ) • dσ/dΩ for np → {pp} s π − and that the magnitude of the other p-wave amplitude and its relative phase can be deduced from a combined analysis of this with our cross section and analysing power data for pp → {pp} s π 0 and np → {pp} s π − .These data will provide two determinations of the LEC d.Measurements of the mixed spin-correlation parameters A z,x are not required for the extraction of the p-wave amplitudes, though such information is vital in order to identify the d-wave terms.

Measurement of cross section and analysing power
As first steps in the programme, measurements with a polarised proton beam incident on unpolarised hydrogen and deuterium cluster targets were performed at a beam energy of T p = 353 MeV [2,3].

The pp → { pp} s π 0 process
The polarised proton COSY beam and the ANKE hydrogen cluster target were used in this measurement.The final proton pair was recorded in the ANKE forward detector and identified with the use of the time-of-flight difference between the two protons.After the selection of the proton pairs, the pp → {pp} s π 0 events were identified by the missing-mass criterion.The beam polarisation and luminosity were determined by detecting simultaneously the pp → dπ + and pp → pp processes, for which the cross sections and analysing powers are known with high precision at this energy.[6].Open (red) circles are CELSIUS data obtained at 360 MeV [7].The curve is a linear fit in cos 2 θ π to our data.
The ANKE results for the differential cross section and the vector analysing power are shown in Figs. 1 and 2. For a spin-singlet diproton, the spin structure of the pp → {pp} s π 0 or np → {pp} s π − reaction is that of 1 2 + 1 2 + → 0 + 0 − .Parity and angular momentum conservation require the initial nucleonnucleon pair to have spin S = 1.The pion orbital angular momentum ℓ and the initial nucleon-nucleon isospin I are then linked by ℓ + I = odd so that, for the pp → {pp} s π 0 reaction, only even pion partial waves are allowed.As a consequence, the unpolarised cross section for π 0 production, and this times 01020-p.2 MESON2012 -12th International Workshop on Meson Production, Properties and Interaction the proton analysing power A y , must be of the form where θ π is the pion c.m. production angle with respect to the direction of the polarised proton beam.
Here p is the incident c.m. momentum and k that of the produced pion which, at 353 MeV, have values p = 407 MeV/c and k ≈ 94 MeV/c.If one considers only pion waves with l ≤ 2, a non-zero value of the analysing power in this process must arise from the interference between the s and d waves.The strong A y signal demonstrates the importance of this interference.

The pn → { pp} s π − process
The ANKE deuterium cluster target was used in the experiment.Low energies of the spectator proton, T spec < 6 MeV, were selected to ensure the validity of the quasi-free approximation.The diproton was recorded in either the Forward or Positive side ANKE detectors.In addition, either the π − was recorded at large c.m. angles in the Negative side Detector, or the spectator proton was measured in the Silicon Tracking Telescope (STT).Particle identification was made on the basis of the time-offlight information except for the spectator proton, which was recognised through its energy loss in the STT.The process was then isolated via the missing mass value built for the three observed final state particles.The polarisation of the proton beam and the reaction luminosity were both estimated from the quasi-free pn → dπ 0 data that were taken in parallel.
The unpolarised cross section for π − production, and this times the proton analysing power A y , are of the form where θ π is the pion c.m. production angle, p is the incident c.m. momentum, and k that of the produced pion.
Whereas the TRIUMF results only cover the central region of pion angles [9], the ANKE data [8] in Fig. 3 extend over the whole angular domain.The two data sets are consistent in the backward hemisphere but the TRIUMF measurements show no indication of the rise at forward angles that is seen at ANKE.Some confirmation of the ANKE angular shape is offered by pion absorption data, π −3 He → pnp spec , where the unobserved slow proton is assumed to be a spectator [10].In this case the reaction can be interpreted as being π − {pp} s → pn, though the internal structure of the bound diproton is very different to that in the production data.The forward/backward peaking is in complete contrast to the results found for π 0 production [7] and is an indication of the dominance of the I = 0 p-wave amplitudes in this reaction.Fig. 3. Unpolarised differential cross section for the pn → {pp} s π − reaction at ≈ 353 MeV.The ANKE data [8] are shown by red circles and the TRIUMF results [9] by green triangles.The arbitrarily scaled TRIUMF cross sections extracted from π −3 He → pnp spec data [10] are also included (blue stars).The curve is a cubic fit to the ANKE data.[8] and TRIUMF data [11] (triangles).The line represent the quotient of the fit in panel (a) and that to the cross section in Fig. 3.
The results for the analysing power of the pn → {pp} s π − reaction [8] are displayed in Fig. 4, with A y (dσ/dΩ) being shown in panel (a) and A y in panel (b).The agreement with the TRIUMF A y data [11] is good in the backward hemisphere and both show a strong and rather asymmetric fluctuation in the central angular region.

Partial wave analysis
The spin structure of the pn → {pp} s π − and of pp → {pp} s π 0 reactions are identical.The cross section and analysing power can be written in terms of two scalar amplitudes A and B; Keeping terms up to pion d waves, the pp → {pp} s π 0 data at 353 MeV [6] can be parameterised in terms of the three partial wave amplitudes M P s , M P d , and M F d , corresponding to the transitions, 3 P 0 → 1 S 0 s, 3 P 2 → 1 S 0 d, and 3 F 2 → 1 S 0 d, respectively.In proton-neutron collisions there are also the two p-wave transitions, 3 S 1 → 1 S 0 p and 3 D 1 → 1 S 0 p that arise in the isospin I = 0 case, and for these we introduce amplitudes M S p and M D p , respectively.It is clear from the very different behaviour of the angular distributions for π 0 and π − production that the extra p-wave amplitudes are very large and that it will not be justified to discard their interference with M P d .By neglecting the small coupling between the 3 P 2 and 3 F 2 partial waves, and imposing the Watson theorem to determine the phases, it was possible to extract values for the complex amplitudes M P s , M P d , and M F d from the analysis of the pp → {pp} s π 0 reaction [6].Such an approach is not valid for the two 01020-p.4 MESON2012 -12th International Workshop on Meson Production, Properties and Interaction p-wave terms because of the very strong coupling between the incident 3 S 1 and 3 D 1 waves.Although there is a significant overall relative uncertainty between the π − and π 0 production data, associated with luminosity and other systematic effects, the combined system is actually over determined [8].As a consequence, if an acceptable solution is achieved it would support the approximations made in our analysis, such as the neglect of higher partial waves, d-d interference, and the effect of coupling between the 3 P 2 and 3 F 2 partial waves.The best fit to the combined pp → {pp} s π 0 and pn → {pp} s π − data sets is obtained with Since this solution has χ 2 /NDF = 89/82, it shows that our truncated expansions can give a very good description of the data.The contribution from the 3 F 2 → 1 S 0 d transition is clearly very small and, if one eliminated M F d completely, it would give only a marginally poorer fit with χ 2 /NDF = 94/82.It should be noted that, whereas the phases of M P s , M P d and M F d were imposed (see above), the phases of M S p and M D p were extracted from the production data.
3 Measurement of A x,x and A y,y in n p → {pp} s π − The spin-correlation coefficients A x,x and A y,y of the quasi-free n p → {pp} s π − reaction were measured at ANKE in 2011 by using the vector polarised deuteron beam and the hydrogen Polarised Internal Target (PIT) [12], equipped with a long storage cell.The main source of background is the interaction of a beam particle with the aluminum storage cell walls.In order to obtain the shape of the background in the missing mass spectra, a dedicated measurement was made with the N 2 gas in the storage cell.
As shown in Ref. [5], the experiment is essentially self-analysing.The values of A x,x and A y,y depend on the product of the beam and target polarisations.However, this product can be controlled by demanding that A y,y = 1 for all angles and A x,x = 1 in the forward and backward directions.This property of the experiment gives us also a powerful tool to study the systematic uncertainties of the measurement.Nevertheless, the beam and target polarisation values can be determined independently through the simultaneous detection of processes for which the analysing powers are known.For the beam energy of interest, T n = 353 MeV per nucleon, the most suitable reaction for the ANKE conditions is quasi-free pn → dπ 0 .
The observed experimental asymmetry can be written as: where Σ 1 = N ↑↑ + N ↓↓ and Σ 2 = N ↑↓ + N ↓↑ , with N being the number of events collected with the directions of the beam and target spins indicated by the arrows.PQ is the product of the beam and target polarisations.The value of PQ = 0.35, extracted from the polarimetry reaction data, was used in the preliminary analysis.The data were divided into five bins in the pion emission angle and ξ/PQ was fitted as a function of cos 2 ϕ in each bin.The acceptance of the apparatus was significantly higher for events with large cos 2 ϕ so that the value of A y,y could be determined with smaller uncertainty than that of A x,x .The A y,y results are shown in Fig. 5 in terms of of the pion emission angle.As expected, A y,y is consistent with unity over the whole angular range.To reduce the uncertainty in the extraction of A x,x , it was assumed that A y,y = 1 and the cos 2 ϕ fit repeated, leading to the results shown in Fig. 6.

Outlook
The theoretical uncertainties inherent in the assumptions made in the partial wave analysis [8] are hard to estimate.These can be tested by studying additional observables but the only non-trivial unmeasured one is the mixed spin-correlation coefficient A z,x .Its measurement in the p n → {pp} s π − reaction is proposed as the next step in the ANKE pion production programme [13].This result will provide new constrains on the partial wave analysis and therefore make the analysis more robust.The experiment will require a longitudinally polarised proton beam at the ANKE target position and this can be accomplished with the use of a Siberian snake.The installation of such a snake is foreseen for late 2012.
The results presented here would not have been possible without the efforts of the COSY machine crew and other members of the ANKE collaboration.The work was partially supported by the COSY-FFE programme and by grants from the DFG (436 RUS 113/965/0-1) and GNSF (ST09-1024-4-200).

Fig. 1 .
Fig.1.Differential cross section for the pp → {pp} s π 0 reaction at 353 MeV as a function of the cosine of the pion centre-of-mass angle.Solid (black) circles represent ANKE measurements[6].Open (red) circles are CELSIUS data obtained at 360 MeV[7].The curve is a linear fit in cos 2 θ π to our data.

Fig. 2 .
Fig. 2. (a) The product of the measured analysing power and differential cross section for the pp → {pp} s π 0 reaction.The curve represents the best fit of Eq. (1), keeping terms up to b 2 .(b)Measured values of A y for the pp → {pp} s π 0 reaction[6].The line represents the quotient of the best fit to the data in panel (a) and the fit to the cross section of Fig.1.

Fig. 4 .
Fig. 4. (a) The product of the measured analysing power and differential cross section for the pn → {pp} s π − reaction at 353 MeV.The curve represents the best fit of Eq. (2) with b 1 , b 2 , and b 3 terms.(b) Measured values of A y for the pn → {pp} s π − reaction showing both the ANKE (circles)[8] and TRIUMF data[11] (triangles).The line represent the quotient of the fit in panel (a) and that to the cross section in Fig.3.