Ž . The reaction ppTMp vv p has been studied at 450 GeVrc and a spin analysis of the vv channel has been performed f s Ž . PC qq for the first time in central production. Evidence is found for the f 1910 in the J s2 wave with spin projection 2 J s2. This is the only state observed in central production with spin projection J s2. Its dP and f dependencies are Z Z T similar to those observed for other glueball candidates. In addition, evidence is found for a state with J s4 consistent Ž . Ž . with the f 2300 . The f 2000 , previously observed in the rr final state, is confirmed. q 2000 Elsevier Science B.V. All 4 0 rights reserved. Ž . E-mail address: andrew.kirk@cern.ch A. Kirk . 0370-2693r00r$ see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0370-2693 00 00622-5 ( ) D. Barberis et al.rPhysics Letters B 484 2000 198–204 199 The vv channel has been studied in several different production mechanisms. In pp interactions the vv final state has been studied by the w x w x NA12 1 and VES 2 collaborations. In both experiments clear signals were observed at 1.6 and 1.9 GeV and were found to have J P C s2, called the Ž . Ž . w x f 1640 and X 1910 3 . In addition, the VES 2 collaboration reported evidence for an vv decay Ž . mode of the f 2050 and, more recently, for a 4 P C qq w x J s4 object in the 2.3 GeV region 4 . In pp annihilations C. Baker et al., using the data from the w x Crystal Barrel experiment 5 , have reported eviŽ . dence for a structure similar to the f 1640 in the 2 vv final state but have shown that this state can be Ž . interpreted as being due to the f 1565 previously 2 w x w x observed in the pp final state 3 . The PDG 3 lists Ž . the X 1910 observed in the vv final state with another J P C s2 resonance with similar mass and width observed in the hh final state. In central production the WA102 experiment did not observe Ž . w x the f 1565 in the pp final state 6 , therefore, the 2 centrally produced vv channel can give information Ž . Ž . on the validity of the f 1565 rf 1640 assignment. 2 2 In addition, in the hh final state of the WA102 w x experiment 7 a peak was observed at 1.9 GeV which was consistent in mass and width with the Ž . X 1910 . A spin analysis showed that this state was consistent with having J P C s1 with spin projection J s1 or J P C s2 with spin projection J s Z Z 2. If the latter hypothesis were true then this was the first time that a state had been observed in central production that was produced with spin projection J s2. Hence, if the states observed in vv and hh Z Ž . P C qq are the same and the X 1910 has J s2 , the Ž . X 1910 should be observed in the J s2 projection Z in the vv final state. In central production, the vv final state was previously observed by the WA76 w x experiment 8 but only 80 events were observed and hence no strong conclusions could be drawn. In this paper, a study is presented of the vv final state formed in the reaction ppTMp vv p 1 Ž . Ž . f s at 450 GeVrc. It represents more than a factor of 60 increase in statistics over previous data on the cenw x trally produced vv final state 8 and, moreover, will present a spin analysis of this channel in central production. The data come from the WA102 experiment which has been performed using the CERN Omega Spectrometer, the layout of which is dew x Ž . scribed in Ref. 9 . Reaction 1 has been isolated using the ppp 0 decay mode of both vs. The reaction ppTMp ppppp p 0 p Ž . f s has been isolated from the sample of events having six outgoing charged tracks and four g s reconstructed in the GAMS-4000 calorimeter, by first imposing the following cuts on the components of < < the missing momentum: missing P -17.0 GeVrc, x < < < < missing P -0.16 GeVrc and missing P -0.12 y z GeVrc, where the x axis is along the beam direction. The two photon mass spectrum, when the mass of the other 2g-pair lies within a band around the p 0 Ž . 0 mass 100–170 MeV , shows a clear p signal with small background. Events containing a fast qqŽ . Ž q. D 1232 were removed if M p p -1.3 GeV, f which left 294 463 centrally produced pp ppp p 0 events. Ž q y 0. Fig. 1a shows a lego plot of M p p p versus Ž q y 0. Ž . M p p p four combinations per event . A clear signal of the vv channel can be observed. Fig. 1b shows the ppp 0 mass spectrum if the other ppp 0 combination is compatible with being an Ž Ž q y 0. . v 0.76FM p p p F0.81 GeV where a clear v signal can be observed. A tight cut has been used around the v signal to increase the signal to background ratio in the selected sample. In order to decrease the background further the parameter l is introduced which describes the v decay on the Dalitz plot and is defined as: < < 2 p =p q y ls 2 3 1 2 2 m ymp ž / 4 9 < < where p =p is proportional to the decay matrix q y element for vTMppp , p is the three momen" tum of the p " in the v rest frame and m is the ppp 0 effective mass squared. Superimposed on Fig. 1b as a shaded histogram is the ppp 0 mass distribution for l)0.3. As can be seen the signal to background ratio in the v region has increased. The vv final state has been selected using the ppp 0 mass cuts described above and by requiring that the l)0.3 for each v candidate. The ( ) D. Barberis et al.rPhysics Letters B 484 2000 198–204 200 Ž . Ž q y 0 . Ž q y 0 . Ž . Ž q y 0 . q y 0 Fig. 1. Selection of the vv final state: a M p p p versus M p p p , b M p p p if the other p p p combination is in Ž Ž q y 0 . . Ž . the v band 0.76FM p p p F0.81 GeV . Superimposed as a shaded histogram is the case for l)0.3. c The vv mass spectrum. Superimposed as a shaded histogram is an estimation of the background contribution. resulting vv mass spectrum is shown in Fig. 1c and consists of 5067 events. As can be seen there is a peak in the 1.9 GeV region. The background below the v signal has several sources including combinatorics and other channels. The combinatorial background is removed, in part, in the selection procedure. The remaining background is approximately 27%. Four methods have been used to determine the effects of this background; studying the side bands around the v signal, studying events that do not balance momentum, studying events that do not pass the l selection cuts and studying events from the pppppp channel. Since the majority of the background is due to other physical Ž . Ž . Ž . channels for example a 1260 a 1260 or v a 1260 1 1 1 production, the two methods that best reproduce the background are the one using events that do not pass the l cut and the other uses events from the pppppp channel. These two methods give a very similar representation of the background. ( ) D. Barberis et al.rPhysics Letters B 484 2000 198–204 201 In the remainder of this paper the method used to determine the background will be the mean of these two methods. Superimposed on the vv mass spectrum in Fig. 1c as a shaded histogram is the estimate of the background. A spin analysis of the centrally produced vv system has been performed using the method dew x scribed in Ref. 10 for the rr final state modified for the vv channel. The z axis is defined by the momentum vector of the exchanged particle with the greatest four-momentum transferred in the vv centre of mass. Assuming that only angular momenta up to 4 contribute, the amplitudes have been calculated Ž . in the spin-orbit LS scheme using spherical harmonics. In order to perform a spin parity analysis the log Ž . likelihood function, L sÝ log P i , is defined by j i j combining the probabilities of all events in 50 MeV vv mass bins from 1.5 to 3.0 GeV. The incoherent sum of various event fractions a is calculated so as j to include more than one wave in the fit, Ls log a P i q 1y a 2 Ž . Ž . Ý Ý Ý j j j ž / ž / i j j Ž . where the term 1yÝ a represents the phase space j j background. The negative log likelihood function Ž . w x yL is then minimised using MINUIT 11 . Coherence between different J P states has been neglected in the fit. Different combinations of waves have been tried and insignificant contributions have been removed from the final fit. It is found necessary to introduce the J P C s2 wave with both J s0 and 2, the J P C s0 wave Z and the J P C s4 wave with J s1. The results of Z the best fit are shown in Fig. 2. The J P C s2 wave with J s2 shows a peak Z at 1.9 GeV. This wave has been fitted using a spin 2 relativistic Breit-Wigner and a linear background and is shown superimposed. The fit gives Ms1897"11 MeV, Gs202 " 32 MeV, parameters consistent Ž . X with those of the X 1910 found from a fit to the hh w x final state 7 . Hence this consistent with the fact that Ž . X the X 1910 has vv and hh decay modes, and we Ž . shall refer to it as the f 1910 hereafter. Correcting 2 for the unseen decay modes and the effects of the X Ž . detector, the branching ratio vvrhh of the f 1910 2 is 2.6 " 0.6. There was no evidence for any wave with J s2 in the hh final state of the WA102 Z w x experiment 12 and hence an upper limit for the X Ž . branching ratio hhrhh of the f 1910 has been 2 Ž . calculated to be 0.2 90% CL . The J P C s2 wave with J s0 shows a broad Z enhancement. Superimposed on the wave is a shaded Ž . histogram representing the f 1640 . As can be seen 2 the J P C s2 wave with J s0 is not compatible Z Ž . with the f 1640 observed by other experiments. 2 This non observation does not contradict the claim Ž . that the f 1640 is an vv decay mode of the 2 Ž . f 1565 since this state is also not observed in 2 central production. The J P C s0 wave shows some activity near threshold and a broad enhancement around 2 GeV. In a previous analysis of the 4p channel, the WA102 experiment observed a similar structure in the J P C s0 rr wave which was identified with the Ž . f 2000 . Superimposed on the wave is a shaded 0 Ž . histogram representing the f 2000 assuming that 0 the branching ratio rrrvv s 3 as expected for a isoscalar resonance. This well represents the wave in the 2 GeV region. The J P C s4 wave with

A study of the vv channel produced in central pp interactions at 450