A coupled channel analysis of the centrally produced K q K y and p q p y final states in pp interactions at 450 GeVrc

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1 16 September 1999 Physics Letters B A coupled channel analysis of the centrally produced K q K y and p q p y final states in pp interactions at 45 GeVrc WA1 Collaboration D. Barberis d, F.G. Binon f, F.E. Close c,d, K.M. Danielsen k, S.V. Donskov e, B.C. Earl c, D. Evans c, B.R. French d, T. Hino l, S. Inaba h, A. Jacholkowski d, T. Jacobsen k, G.V. Khaustov e, J.B. Kinson c, A. Kirk c, A.A. Kondashov e, A.A. Lednev e, V. Lenti d, I. Minashvili g, J.P. Peigneux a, V. Romanovsky g, N. Russakovich g, A. Semenov g, P.M. Shagin e, H. Shimizu j, A.V. Singovsky a,e, A. Sobol e, M. Stassinaki b, J.P. Stroot f, K. Takamatsu i, T. Tsuru h, O. Villalobos Baillie c, M.F. Votruba c, Y. Yasu h a LAPP-INP3, Annecy, France b Athens UniÕersity, Physics Department, Athens, Greece c School of Physics and Astronomy, UniÕersity of Birmingham, Birmingham, UK d CERN - European Organization for Nuclear Research, GeneÕa, Switzerland e IHEP, ProtÕino, Russia f IISN, Belgium g JINR, Dubna, Russia h High Energy Accelerator Research Organization KEK, Tsukuba, Ibaraki 35-81, Japan i l Faculty of Engineering, Miyazaki UniÕersity, Miyazaki , Japan j RCNP, Osaka UniÕersity, Ibaraki, Osaka , Japan k Oslo UniÕersity, Oslo, Norway Faculty of Science, Tohoku UniÕersity, Aoba-ku, Sendai , Japan Received 7 July 1999; accepted 9 July 1999 Editor: L. Montanet Abstract A coupled channel analysis of the centrally produced K q K y and p q p y final states has been performed in pp collisions at an incident beam momentum of 45 GeVrc. The pole positions and branching ratios to pp and KK of the f Ž 98., f Ž 137., f Ž 15. and f Ž 171. have been determined. A systematic study of the production properties of all the resonances observed in the p q p y and K q K y channels has been performed. q 1999 Elsevier Science B.V. All rights reserved r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S

2 D. Barberis et al.rphysics Letters B Recently the WA1 collaboration has published the results of partial wave analyses of the centrally wx wx produced K K, KSKS 1, p p and pp wx 3 channels. A striking feature of these analyses was the result that the f Ž 171. has Js Ž J we shall refer to it as the f Ž 171. hereafter.. In these papers the S-wave from each channel was fitted independently using interfering Breit-Wigners and a background. In this present paper we will first show how the resulting parameters change if a different method of fitting is used, namely, a T-Matrix analysis and a K-Matrix analysis using the methods described in Ref. wx 4. Next we will perform a coupled channel fit to the K q K y and p q p y final states in order to determine the pole positions and branching ratios of the observed mesons. Finally we will present information on the production kinematics of these resonances. In our previous publication a fit has been performed to the p q p y S-wave using a coherent sum of relativistic Breit-Wigner functions and a background of the form: N res iu A M sbgd M q a e n pp pp Ý n BWn Mpp ns1 where the background has been parameterised as BgdŽ M. sa Ž M ym. e b yg Mppyd Mpp pp pp p where an and un are the amplitude and the phase of the n-th resonance respectively, a, b, g and d are real parameters, BWŽ M. pp is the relativistic Breit- Wigner function for a spin zero resonance. In order to describe the centrally produced p q p y mass spectrum the function < AM < pp has been multiplied by the kinematical factor Ž M y 4 m. 1r rm 3 wx pp p pp 5. The resulting function is then convoluted with a Gaussian to account for the experimental mass resolution. In this present paper we use the Flatte formula wx 6 to describe the f Ž 98., this is referred to as Method I. For the p q p y channel the Breit-Wigner has the form: ( ( m Gi Gp BW Ž Mpp. s m ym yim Ž G qg. p K and in the K q K y channel the Breit-Wigner has the form: ( ( m Gi GK BW Ž MKK. s m ym yim Ž G qg. p K where Gi is absorbed into the intensity of the reso- nance. Gp and GK describe the partial widths of the resonance to decay to pp and KK and are given by 1r p pž m r4ymp. G sg 1r 1r K k Ž K. q K G sg r m r4ym q m r4ym where gp and gk are the squares of the coupling constants of the resonance to the pp and KK systems. The resulting fit is shown in Fig. 1a. for the entire mass spectrum and in Fig. 1b. for masses above 1 GeV. The sheet II pole positions wx 7 for the resonances are Ø f Ž 98. MsŽ 983"8. yiž 58"11. Ø f Ž 137. Ms Ž 136"18. yi Ž 111"3. Ø f Ž 15. Ms Ž 15"1. yi Ž 65"1. Ø f Ž 171. Ms Ž 1748". yi Ž 73". These parameters are consistent with the PDG wx 8 values for these resonances. To test the sensitivity of these results on the fitting method used we have also performed a fit to the p q p y mass spectrum using the T-Matrix paramewx 4. The invariant ampli- terisation of Zou and Bugg tude for p q p y central production can be expressed as Asa1Ž s. T11qa Ž s. T1 Ž 1. where T and T are the invariant amplitudes for 11 1 elastic pp pp and KK pp scattering and are parameterised by e if y1 g1e if T11 s q Ž. ir M ysyiž r g qr g. 1 R 1 1 ( g g e if 1 T1 s Ž 3. M ysyiž r g qr g. R 1 1 Ž where r s 1 y 4 m rs. 1r and r s Ž 1 p 1 y 4 m. Krs 1r are phase space factors and s is the invariant mass squared of the p q p y channel. The

3 464 D. Barberis et al.rphysics Letters B Fig. 1. The p p mass spectrum with a. and b. fit using interfering Breit-Wigners. Fit using the T-Matrix parameterisation c. and d. the original fit and e. including two extra poles. Fit using the K-Matrix parameterisation f. and g. the original fit and h. including another two poles. background term is presumed to be coupled only to the pp channel and has the form e if y1 1 Tb s s ir AŽ s. yir 1 1 which satisfies the unitarity condition. As is an arbitrary real function which has been taken to be of the form 1qa1sqas AŽ s. s b sym r qb s 1 p The real functions a Ž s. in Eq. Ž 1. i describe the coupling of the initial state to the channel i. These functions are approximated by the power expression wx 5: n s aiž s. s Ý ai ½ n 4m K 5 ns where the factor 4m K is introduced as a convenient scaling. It has been found that ns3 is sufficient to describe the S-wave distribution. In order to describe the centrally produced p p mass spectrum, the function < AM < pp has been multiplied by the kinematical factor Ž Mpp y 4 m. 1r rm 3 wx 5 and the resulting function is then p pp

4 D. Barberis et al.rphysics Letters B convoluted with a Gaussian to account for the experimental mass resolution. The resulting fit is shown in Fig. 1c. for the entire mass spectrum and in Fig. 1d. for masses above 1 GeV. As can be seen the fit does not describe well the region above 1. GeV. The sheet II pole corresponding to the f Ž 98. is Ø MsŽ 993"8. yiž 38"9. There are two poles from the background term with Ø M sž 388"55. yiž 3"8. 1 Ø M sž 1541"3. yiž 143"1. The first pole may be associated with the low mass S-wave. The NA1r collaboration wx 9 have previously shown that this region may be interpreted as being due to the s particle. The second pole would appear to be in the region of the f Ž 15. but the width is very broad. This is due to the fact that the fit is not able to properly describe the region around 1.3 GeV. Adding one more term to Eqs. Ž. and Ž. 3 to describe the 13 mass region improves the fit considerably but still does not describe the region around 17. In order to produce a satisfactory fit two terms have to be added to Eqs. Ž. and Ž. 3 to account for the f Ž 137. and f Ž 171. which results in the fit shown in Fig. 1e. for masses above 1 GeV. The new sheet II pole positions are Ø f Ž 98. MsŽ 99"6. yiž 5"9. Ø f Ž 137. Ms Ž 131"3. yi Ž 134"3. Ø f Ž 15. Ms Ž 1497"17. yi Ž 8"1. Ø f Ž 171. Ms Ž 175"15. yi Ž 53"1. These parameters are consistent with the values from the fit using interfering Breit-Wigners and with the PDG wx 8 values for these resonances. An alternative parameterisation is to use the K- Matrix formalism. In this case the Lorentz invariant T-Matrix is expressed as In the K-Matrix formalism the background is assumed to couple to both the pp and KK channels. In order to describe the centrally produced p p mass spectrum, the function < AM < pp has been multiplied by the kinematical factor Ž Mpp y 4 m. 1r rm 3 wx p pp 5 and the resulting function is then convoluted with a Gaussian to account for the experimental mass resolution. Two coupled channel resonances are found from the fit shown in Fig. 1f. for the entire mass spectrum and in Fig. 1g. for masses above 1 GeV with their sheet II T-Matrix poles at Ø M sž 988"18. yiž 39"1. 1 Ø M sž 156". yiž 191"53. As in the case of the T-Matrix analysis the fit fails in the 1.3 GeV region. Adding one additional pole improves the fit. However, in order to to obtain a TsK ˆ ˆ 1yirK ˆ ˆ y1 where for the case of pp and KK final states ˆ r is a dimensional diagonal matrix and Kˆ is a real symmetric dimensional matrix of the form aa i j bb i j K ijs q qg M ys s ys R b ij Fig.. A coupled channel fit to the p q p y and K q K y S-wave distributions.

5 466 D. Barberis et al.rphysics Letters B satisfactory fit it is found necessary to include two extra poles. The fit shown is in Fig. 1h. for masses above 1 GeV and results in sheet II pole positions of Ø f Ž 98. MsŽ 98"9. yiž 38"16. Ø f Ž 137. Ms Ž 19"3. yi Ž 14"5. Ø f Ž 15. Ms Ž 151"1. yi Ž 56"15. Ø f Ž 171. Ms Ž 179"15. yi Ž 75"18. These parameters are consistent with the values from the two previous fits. Finally, in order to perform a coupled channel fit to the p q p y and K q K y final states a correct normalisation of the two data sets has to be performed. The fit has been modified to take into account the relative differences in geometrical acceptance, event reconstruction and event selection. The fit also includes corrections for the unseen decay modes so that the branching ratio pp to KK can be calculated. In addition to the resonances discussed above, the a Ž 98. can also contribute to the KK S-wave mass spectrum. The contribution from a 98 K K has been calculated from the observed decay a Ž 98. hp and the measured branching ratio of the a Ž 98. w1 x. The calculated contribution Ž 5" 1 events. has been included in the fit as a histogram. There is no evidence for any a Ž 145. contribution in the hp channel and hence it has not been included in the fit to the KK S-wave. The coupled channel fit has been performed using the three methods described above. The following pole positions and branching ratios quoted for the resonances are a mean from the three methods. The statistical error is the largest error from the three fits and the systematic error quoted represents the spread of the values from the three methods. The results of Fig. 3. The p q p y S-wave and D-wave in three dp T intervals.

6 D. Barberis et al.rphysics Letters B Table 1 Production of the resonances as a function of dp expressed as a percentage of their total contribution and the ratio Ž R. T of events produced at dpt F. GeV to the events produced at dpt G.5 GeV. dp F. GeV.FdP F.5 GeV dp G.5 GeV Rs dp T F. GeV T T T dp T G.5 GeV f Ž ". 5.6".7 6.".7.88".1 f Ž "4. 3.". 49.9".9.36".8 f Ž " "5..3"3. 1.5".18 f Ž " "1. 7.8"1.1.95".6 rž " "4. 5.5"3..1".5 f Ž " ".6 6.9" 1.7.1". f Ž " " 3. 6." 4..7".4 f Ž 15..6" " "3..6".8 the combined fit are shown in Fig.. The sheet II pole positions are Ø f Ž 98. MsŽ 987"6"6. yiž 48"1"8. Ø f Ž 137. M s Ž 131 " 5 " 1. y iž 19 " "15. Ø f Ž 15. MsŽ 15"1"1. yiž 49"9"8. Ø f Ž 171. MsŽ 177"1"11. yiž 63"8"9. These parameters are consistent with the PDG wx 8 values for these resonances. For the f Ž 98. the Fig. 4. The f distributions of the resonances observed in the p q p y and K q K y channels.

7 468 D. Barberis et al.rphysics Letters B Fig. 5. The four momentum transfer squared Ž< t<. from one of the proton vertices for the resonances observed in the p p and K q K y channels. couplings were determined to be gps.19".3 ".4 and gk s.4".4".4. The branching ratios for the f Ž 137., f Ž 15. and f Ž 171. have been calculated to be: fž 137. KK s.46".15".11 fž 137. pp fž 15. KK s.33".3".7 fž 15. pp fž 171. KK s5.".6".9 fž 171. pp These values are to be compared with the PDG wx 8 values of 1.35".68 for the f Ž 137. and.19".7 for the f Ž 15., which comes from the Crystal Barrel experiment w11 x. The value for the f Ž 171. is consistent with the value of.56".9 which comes from the WA76 experiment which assumed J s for the f Ž 171. w1 x J. In our previous publications a study has been performed of resonance production rate as a function of the difference in the transverse momentum vectors Ž dp. T between the particles exchanged from the fast and slow vertices w13,14 x. It has been observed w15x that all the undisputed qq states Ži.e. h, h, f Ž etc.. are suppressed as dpt goes to zero, whereas the glueball candidates f Ž 15. and f Ž 195. survive. In order to calculate the contribution of each resonance as a function of dp T, the partial waves have Table The slope parameter b from a single exponential fit to the < t< distributions. f 98 f 137 f 15 f 171 r 77 y brgev 5.3". 6.7".5 5.".5 6.5".8 5.8".1

8 D. Barberis et al.rphysics Letters B Table 3 ds < < yb1t ybt The slope parameters from a fit to the t distributions of the form sae qb te. dt a b1 b b y GeV GeV f Ž 17..5".4 8.3" " ".4 f Ž ".3 8.3" " " 3.3 y been fitted in three dpt intervals with the parameters of the resonances fixed to those obtained from the fits to the total data using method I. As an example of how the mass spectra change as a function of dp T, Fig. 3 shows the p q p y S-wave and D-wave in three dpt intervals. The S-wave clearly shows that the region around 1.3 GeV is more enhanced at large dpt in contrast to the low mass part of the spectrum. This is not due to feed through from the D-wave which has been estimated to be less than 3 % in this mass region. In the D-wave the f Ž 17. is suppressed at small dpt in contrast to the behaviour of the low mass part of the D-wave. Table 1 gives the percentage of each resonance in three dpt intervals together with the ratio of the number of events for dpt -. GeV to the number of events for dp T ).5 GeV for each resonance considered. As can be seen from Table 1, the r Ž 77., f Ž 17. and f Ž 155. are suppressed at small dp in contrast to the f Ž 98., f Ž 15. T and f Ž The azimuthal angle Ž f. is defined as the angle between the pt vectors of the two protons. In order to determine the f dependence for the resonances observed, the partial waves have been fitted in 3 degree bins of f with the parameters of the resonances fixed to those obtained from the fits to the total data. The fraction of each resonance as a function of f is plotted in Fig. 4. The f dependences are clearly not flat and considerable variation is observed between the different resonances. In order to determine the four momentum transfer dependence Ž. t of the resonances observed in the p q p y and K q K y channels the partial waves have been fitted in.1 GeV bins of t with the parameters of the resonances fixed to those obtained from the fits to the total data. Fig. 5 shows the four momentum transfer from one of the proton vertices for these resonances. The distributions for the f Ž 98., f Ž 137., f Ž 15., f Ž 171. and rž 77. have been fitted with a single exponential of the form expž yb< t<. and the values of b found are given in Table. The distributions for the f Ž 17. and f Ž 155. cannot be fitted with a single exponential. Instead they have been fitted to the form ds sae dt qb te yb1t ybt The parameters resulting from the fit are given in Table 3. In a previous publication by the WA76 collaboraw16x the ratios of the production cross sections tion for the rž 77., f Ž 98. and f Ž 17. were calculated at ' s s1.7 and 3.8 GeV. However, the experiment at 3 GeV Ž ' s s3.8 GeV. was only sensitive to f angles less than 9 degrees and the acceptance program that had been used assumed a flat f distribution. Hence the cross sections at 3 GeV were underestimated for the rž 77. and f Ž 17. and overestimated for the f Ž 98.. After correcting for geometrical acceptances, detector efficiencies, losses due to cuts, and unseen Table 4 The ratio of the cross sections at ' ' s s s9.1 s s s1.7 ' s s9.1 and 1.7 GeV. r 77 f 98 f 17 f 15.36".5 1.8".1.98" ".14

9 47 D. Barberis et al.rphysics Letters B decay modes, the ratios of the cross-sections for the rž 77., f Ž 98., f Ž 17. and in addition, the f Ž 15. at ' s s 9.1 and 1.7 GeV are given in Table 4. The cross sections for the f Ž 98., f Ž 17. and f Ž 15. are compatible with being independent of energy which is consistent with them being produced via double Pomeron exchange w17 x. In summary, a coupled channel fit has been performed to the centrally produced p q p y and K q K y - mass spectra. The pole positions and branching ratios of the f Ž 98., f Ž 137., f Ž 15. and f Ž 171. have been determined using three different methods which give consistent results. An analysis of the dp T dependence of the resonances observed shows that the undisputed qq mesons are suppressed at small dp in contrast to the enigmatic f Ž 98., f Ž 15. T and f Ž Considerable variation is observed in the f distributions of the produced mesons. Acknowledgements This work is supported, in part, by grants from the British Particle Physics and Astronomy Research Council, the British Royal Society, the Ministry of Education, Science, Sports and Culture of Japan Ž grants no and , the French Programme International de Cooperation Scientifique Ž grant no and the Russian Foundation for Basic Research Žgrants and References wx 1 D. Barberis, Phys. Lett. B453 Ž wx D. Barberis, Phys. Lett. B453 Ž wx 3 D. Barberis, Phys. Lett. B453 Ž wx 4 B.S. Zou, D.V. Bugg, Phys. Rev. D48 Ž R3948. wx 5 K.L. Au, D. Morgan, M.R. Pennington, Phys. Rev. D35 Ž wx 6 S.M. Flatte, Phys. Lett. B 38 Ž wx 7 D. Morgan, Phys. Lett. B 51 Ž wx 8 Particle Data Group, European Physical Journal C 3 Ž wx 9 D. Alde, Phys. Lett. B397 Ž w1x D. Barberis, Phys. Lett. B44 Ž w11x A. Abele, Phys. Rev. D57 Ž w1x T.A. Armstrong, Zeit. Phys. C 51 Ž w13x D. Barberis, Phys. Lett. B397 Ž w14x F.E. Close, A. Kirk, Phys. Lett. B397 Ž w15x A. Kirk, Yad. Fiz. 6 Ž w16x T.A. Armstrong, Zeit. Phys. C51 Ž w17x S.N. Ganguli, D.P. Roy, Phys. Rep. 67 Ž