Data on pbar-p -> etaprime-pizero-pizero for masses 1960 to 2410 MeV/c^2
A.V. Anisovich, C.A. Baker, C.J. Batty, D.V. Bugg, C. Hodd, V.A. Nikonov, A.V. Sarantsev, V.V. Sarantsev, B.S. Zou
aa r X i v : . [ h e p - e x ] S e p Data on ¯ pp → η ′ π π for masses 1960 to 2410 MeV/c A.V. Anisovich c , C.A. Baker b , C.J. Batty b , D.V. Bugg a , C. Hodd a , V.A. Nikonov c , A.V.Sarantsev c , V.V. Sarantsev c , B.S. Zou a a Queen Mary and Westfield College, London E1 4NS, UK b Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX,UK c PNPI, Gatchina, St. Petersburg district, 188350, Russia
Abstract
Data on ¯ pp → η ′ (958) π π are presented at nine ¯ p momenta from 600 to 1940 MeV/c.Strong S-wave production of f (1270) η ′ is observed, requiring a J P C = 2 − + resonance withmass M = 2248 ±
20 MeV, Γ = 280 ±
20 MeV.
The first data are presented on ¯ pp → η ′ π π in flight. These data were taken with the CrystalBarrel detector at LEAR. They are part of an extensive study of the I = 0, C = +1 system inseveral channels. Data have been reported earlier on π π [1], ηη and ηη ′ [2], and ηπ π [3]. Acomparison will be made here specifically with the ηπ π data, and with a combined amplitudeanalysis of all the earlier data [4].The experimental set-up has been reported in detail [5]. A ¯ p beam from LEAR interactsin a liquid hydrogen target 4.4 cm long at the centre of the detector. Incident ¯ p are countedby a coincidence between a scintillator of 5 mm diameter and a small multiwire proportionalchamber, both positioned ∼ p beam of ∼ × /s, the trigger rate is ∼ γ events, where η ′ → ηπ π , η → γγ . Photons aredetected with high efficiency down to 20 MeV in a barrel of 1380 CsI crystals covering 98% ofthe solid angle; the geometry is such that crystals point towards the target. The crystals havea length of 16 radiation lengths and provide an angular resolution of ±
20 mrad in azimuth andpolar angle. The energy resolution is given by ∆
E/E = 2 . /E (GeV) / .The general procedures for event reconstruction and selection have been described in severalearlier publications, of which the most detailed concern the study of π π , ηη and ηη ′ final states[1,2]. A Monte Carlo simulation of the detector is used to assess the efficiency for reconstructionof the π π η ′ final state and the levels of background from competing channels.Events are first submitted to a kinematic fit to ¯ pp → γ , requiring a confidence level > pp → η π is then selected, again with confidence level > η π comes from 5 π events. This background is suppressedstrongly by rejecting any event passing a kinematic fit to 5 π with confidence level >
1% (or0.1% at 600 MeV/c, where the background is more severe). Finally, those few events are rejectedwhich fit ηη π with confidence level better than η π .Fig. 1 illustrates at four beam momenta the ηππ mass distribution of surviving events inthe mass range around the η ′ . There is a clear η ′ signal, agreeing in mass within ≤ π events, (ii) ω π , ( ω → π γ ) Now at IHEP, Beijing 100039, China M ( ηππ ) at four beam momenta indicated by numerical values inMeV/c. The shaded areas show selected signal events in the η ′ peak and those used for sidebandsubtraction.after losing one photon, and (iii) η π without an η ′ . The predicted background agrees with thatobserved (within 10% of the prediction). Tighter cuts do not improve the signal/backgroundratio significantly, but simply cause loss of events.Signal events are selected from the peak region of the η ′ by adjusting a mass cut around thepeak at every individual momentum so as to optimise the signal/background ratio. Very rarely,two events fall within the window; in this case the one closer to the η ′ is accepted. Statisticsof the data selection are shown in Table 1. In the maximum likelihood fit used for amplitudeanalysis, sidebins events shown shaded in Fig. 1 are used to subtract the background. Theareas of sidebins are chosen so that each covers twice the range of mass squared which is usedto select η ′ events; in this way, statistical errors on the background are small. A technicality isthat the width of the mass cut is varied according to the accuracy with which the η ′ mass isreconstructed. This is the reason that sidebands have diffuse edges: the width of the sidebinlikewise varies with the width of the η ′ mass cut. Technically, the way the subtraction is madeis to include sidebin events into the fit with a weight − .
25 times that of events selected in thesignal region. Amplitudes are constructed with tensor expressions using the measured mass ofeach η ′ .Fig. 2 shows the Dalitz plots at all momenta for events from the signal region. Thereis an obvious contribution due to f (1270) η ′ , appearing at momenta ≥ f (1270) peak is nearly uniform within the availablestatistics. At 1940 MeV/c, there is also some weak f (1270) in the background; we have checkedthat this is not due to η ′ π π signal spilling into the mass ranges used for the sidebins.2igure 2: Dalitz plots at all beam momenta for events from the signal region of Fig. 1. Numericalvalues indicate beam momenta in Mev/c.Figure 3: Dalitz plots for events from the sidebin regions of Fig. 1.3omentum Data BG Signal ǫ (MeV/c) (%)600 180 61 119 2.90900 1017 399 618 4.611050 831 257 574 5.761200 2770 852 1918 6.331350 2296 595 1701 5.921525 1416 381 1035 5.061642 1530 330 1200 4.721800 1503 325 1178 4.571940 1063 240 823 4.34Table 1: Numbers of selected events, estimated background (BG), true signal, and reconstrucionefficiency ǫ as a function of beam momentum.There is no indication for the presence of a (1320) → η ′ π . The expected contribution maybe predicted from fits which have been made to a (1320) π in ηπ π data [3]. The predictedcontribution is only ∼
3% of η ′ π π , because of the small (0.53%) branching fraction of a (1320)to η ′ π . This contribution is included in the amplitude analysis using amplitudes fitted to the ηππ data, but is so small as to have negligible effect on conclusions. Fig. 4 shows projections attwo beam momenta on to masses of ππ and πη ; the latter is featureless. The histograms showresults of the maximum likelihood fit described below.Figure 4: Projections on to M ( ππ ) and M ( η ′ π ) at beam momenta of 1050 and 1800 MeV/c; inall cases, a background subtraction is made using sidebins. Histograms show the fit comparedwith data.We now turn to physics results. Data points on Fig. 5(a) show the integrated η ′ π π crosssection after background subtraction and after scaling to allow for all other unobserved decay4odes of η ′ , η and π . There is a peak around 2230 MeV, which is the nominal threshold for f (1270) η ′ (958). The absolute normalisation is obtained using beam counts, target length anddensity, and correcting the observed number of signal events for the reconstruction efficiencyshown in Table 1. A correction is applied for observed dependence of the cross section on beamrate, as described in detail in Ref. [1].The amplitude analysis is made using (a) S and P-waves for ση ′ , where σ stands for the ππ S-wave amplitude, for which we use the parametrisation of Zou and Bugg [6], (b) S and P-wavesfor f (1270) η ′ , and (c) a small, almost negligible contribution from P → f (975) η ′ , whichhelps marginally in fitting the ππ mass distribution at the lowest three beam momenta. It isto be expected that higher partial waves for f η ′ will be suppressed strongly by the centrifugalbarrier in the final states. Contributions from f η ′ D-waves have been tried in the fit, but arenot required; indeed, the P-wave contribution is quite small. Likewise, ση ′ contributions with L ≥ f (1270) η ′ in partial waves D ( J P C = 2 − + ), P and F (2 ++ ), P (1 ++ ) and F (3 ++ ); they will be compared with f (1270) η observed in ηππ data[3,4]. These two channels are related by the composition of the η ′ and η in terms of strange andnon-strange quarks: | η > ≃ . u ¯ u + d ¯ d √ − . s ¯ s, (1) | η ′ > ≃ . u ¯ u + d ¯ d √ . s ¯ s. (2)The coefficients 0.8 and 0.6 are derived from the well known pseudo-scalar mixing angle [7]. Ourearlier analysis of ¯ pp → π − π + , π π , ηη and ηη ′ [8] finds that almost all s -channel resonancesproduced in ¯ pp interactions are consistent with small mixing angles ≤ ◦ between ( u ¯ u + d ¯ d ) / √ s ¯ s . The naive prediction is therefore that amplitudes a for ¯ pp → f (1270) η ′ and ¯ pp → f (1270) η will be related by a ( f η ′ ) ≃ . a ( f η ) . (3)The peak in the full curve of Fig. 5(a) requires a resonance in f η ′ close to the mass of thepeak. However, the mass spectrum from a simple resonance will be pushed upwards by therapidly increasing phase space for the final state f η ′ . This effect is visible in the dotted curveof Fig. 5(c), which shows the resonance contribution to f η ′ fitted to η (2248); this curve peaksabove 2300 MeV because of the increasing phase space. In order to reproduce the integrated crosssection of Fig. 5(a), the amplitude analysis requires a strong interfering background peakingbelow threshold. The interference is constructive at low masses, and is required to give a large f η ′ cross section there, despite the limited phase space. Above the peak at 2230 MeV, theinterference becomes destructive, and cuts off the f η ′ cross section on the upper side of theresonance.The motivation for including this background contribution at low f η ′ masses arises fromthe new combined analysis [4] of ηππ data, together with those on ¯ pp → π − π + , π π , ηη and ηη ′ . Results for ηππ from that analysis are shown in Fig. 5(b). That analysis requires a 2 − + resonance at 2267 ±
14 MeV. It appears there most clearly in f (1270) η with L = 2 in the finalstate, shown by the chain curve in Fig.5(b). However, for the dominant f η L = 0 channel,what one observes is a strong peak near 2 GeV, shown by the full curve. This comes mostlyfrom η (1860), but partly from η (2030) reported in an analysis of data on ¯ pp → ηπ π π [9].5 Figure 5: (a) Points with errors show the integrated cross sections for the final state η ′ π π ,after correction for backgrounds and for all decay modes of η ′ , η and π ; the full curve showsthe fit from the amplitude analysis; the dashed curve shows the ηππ cross section from Ref.[3], multiplied by the SU(3) factor (0 . ; the dotted curve shows the ση ′ contribution; (b)the full curve shows the cross section for f η fitted to ηππ data; the dotted curve shows thecontribution to ηππ from η (2248) alone and the dashed curve that from η (1860) + η (2030);the chain curve shows the intensity fitted to f (1270) η with L = 2 in Ref. [4]; (c) as (b) for f η ′ ;(d) Argand diagram for the f η ′ S-wave amplitude; crosses mark beam momenta; (e) Intensitiesof contributions to f η ′ from P (full curve), P (chain curve), F (dotted) and F (dashed);(f) intensities of contributions to ση ′ from 0 − (full curve), 1 + (dashed) and 1 + → f (975) η ′ (dotted). 6he intensities of contributions to the f η channel are shown in Fig. 5(b) from (i) all η (2248)contributions (dotted curve) and (ii) the coherent sum of η (1860) and η (2030) (dashed curve);the latter two resonances are not well resolved by the ηππ data, because they lie close togethernear the ¯ pp threshold. The contribution from η (2248) interferes destructively with η (1860)and η (2030), so as to cut off the full curve at high masses.In present data, the width of the η (2248) is well determined by the width of the peak in Fig.5(a): Γ = 280 ±
20 MeV. This determination is superior to that in ηππ data: 290 ±
50 MeV.The mass is somewhat less well determined, since the interference with the tails of the lowerresonances may shift the peak by an amount which is sensitive to their widths. Using the bestestimates for the widths from Ref. [8], the mass from the present data is M = 2248 ±
20 MeV,in reasonable agreement with the value derived from ηππ data: 2267 ±
14 MeV. The Arganddiagram for the f η ′ S-wave amplitude is shown in Fig. 5(d).A striking feature of the f η ′ signal is its large magnitude. The dashed curve on Fig. 5(a)shows the complete integrated ηπ π cross section, multiplied by (0 . to allow for the expectedinhibition of η ′ with respect to η . It is surprising that the f η ′ signal is nearly as strong as thedashed curve, bearing in mind the difference in available phase space for f η ′ and f η . The peakin the η ′ ππ cross section (full curve) is much larger than the small peak observed at the samemass in the ηππ cross section. Likewise, the S-wave peak due to η (2248) → f η ′ , shown by thedotted curve in Fig. 5(c), is considerably stronger than that in f η in Fig. 5(b). If one takes intoaccount the available phase space for f η ′ and f η , the coupling constant for η (2248) → f η ′ relative to that in f η is stronger than predicted by equn. (3) by a factor 5 . pp annihilation usually favours high mass final states [10].This may be understood as a form factor effect, arising from the sizes of the participatingstates. In present data, the final state f η ′ has very low momentum. However, in the process η (2248) → f η , the momentum q in the final state is ∼
635 MeV/c. The factor 5.2 wouldrequire a form factor exp − (4 . q ) in amplitude, with q in GeV/c; if this arises from a sourcehaving a Gaussian distribution in r , the form factor takes the well known form exp − ( q R / R = 0 .
98 fm. Such a form factor is surprisingly strong. Forcomparison, the Vandermeulen form factor approximates to exp − (1 . q ).A possibility is that η (2248) is an s ¯ s state. However, strong production from ¯ pp is unlikelyand in disagreement with results for ππ , ηη and ηη ′ [4].The strong sub-threshold contribution to the f η ′ S-wave is intriguing. A variety of explana-tions are possible, of which we mention one. In Ref. [9], evidence has been presented for three η resonances in a mass range where only two are likely to be q ¯ q . Of these, η (1860) is a candidatefor a hybrid, because of its strong decay to f η , despite limited phase space. If that conjecture iscorrect, it should be accompanied by an s ¯ sg partner at about 2100 MeV. Such an s ¯ sg hybrid isexpected to decay strongly to f (1525) η ′ and f (1270) η ′ . If it mixes into neighbouring q ¯ q states,it could help to explain the anomalously strong f η ′ signal observed here.We now consider other partial waves. The present data require a small but significant P-wave f η ′ contribution. This could arise from initial ¯ pp states P , P , F or F . The amplitudeanalysis of Ref. [4] requires all of these contributions in ηππ data with a 3 + resonance at 2303MeV, a 1 + resonance at 2310 ±
60 MeV and 2 + resonances at 2240 and 2293 MeV. A good fit topresent data may be obtained by fixing the relative magnitudes and phases of these partial wavesfrom the fit to ηπ π data. The absolute magnitude of the P-wave contribution is sensitive tothe radius chosen for the Blatt-Weisskopf centrifugal barrier. This radius is therefore adjustedto give the best fit to the data, with the reasonable result 0 . f η ′ at (a) 1525 and (b) 1940 MeV/c for M ( ππ ) > . ση ′ at (c) 900 and (d) 1800 MeV/c for M ( ππ ) < F , 3 .
2% for P , 3 .
2% for the 2 + resonance at 2240 MeV and 1.0% for the 2 + resonance at 2293 MeV; in the latter two, the ratiosof amplitudes for P and F are taken from Ref. [4]. Without these amplitudes, log likelihoodof the fit to η ′ π π is worse by 142 for only one parameter fitted to the overall magnitude; sothe P-wave contribution is highly significant. [Our definition of log likelihood is such that ita change of 0.5 corresponds to one standard deviation change in one variable]. If instead themagnitudes and phases of these amplitudes are fitted freely, the fit changes very little. It is notpossible from the present data to separate P and F , which need to be constrained in relativemagnitude as determined in Ref. [4]. With this constraint, the freely fitted intensities are 3 . F , 4 .
7% for P and 3 .
9% for 2 + , close to the contrained fit.Figs. 6(a) and (b) show angular distributions for production of η ′ f (1270) in the mass range > . θ of the η ′ The distributions are uncorrected foracceptance, which is included in the maximum likelihood fit shown by the histograms. At highbeam momenta, the acceptance for η ′ falls in the forward direction, where the separation of itsdecay products becomes less efficient. A check on the reconstruction procedure is that angulardistributions are symmetric forward-backward in the centre of mass system within errors, aftercorrection for acceptance; this symmetry is required by charge conjugation invariance.We now turn to the contributions from the broad ση ′ channel. From present data, the onlyfirm conclusion which may be drawn is that contributions from both S and P initial statesare required. At all momenta from 900 MeV/c upwards, the data require angular distributionsof the form A + B cos θ η ′ , as shown in Figs. 6(c) and (d). The ηππ data have been fittedincluding 0 − and 1 + resonances. Present data are fitted well by the same resonances. However,statistics are not sufficient to provide clear evidence of these resonances in present data. Fig. 6shows that the fit to data is adequate. 8n summary, the main feature of the η ′ π π data is a peak at 2230 MeV, requring a dominantcontribution from the f (1270) η ′ S-wave. The data require a 2 − + resonance with mass 2248 ± ±
20 MeV; this result is closely consistent with an η (2267) resonanceobserved in ηππ data. The f η ′ S-wave amplitude is surprisingly strong compared with that for f η , even allowing for a form factor in the latter. Contributions from f (1270) η ′ P-states areconsistent with the amplitude analysis of the ηππ data.
We thank the Crystal Barrel Collaboration for allowing use of the data. We wish to thankthe technical staff of the LEAR machine group and of all participating institutes for theirinvaluable contributions to the successful running of the experiment. We acknowledge financialsupport from the British Particle Physics and Astronomy Research Council (PPARC). The St.Petersburg group wishes to acknowledge financial support from PPARC and INTAS grant RFBR95-0267.
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