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Coupled-channel analysis of πππ and KKπ final states from pp annihilation at rest in hydrogen targets at three densities
@ ELSEVIER
NUCLEAR PHYSICS A Nuclear PhysicsA655 (1999) 82c-88c www.elscvier.nl/locate/npe
Coupled-channel analysis of 7rTr~r and Kr~'Tr final states from /Sp annihilation at rest in hydrogen targets at three densities N. Semprini Cesari ~ * a Dip. di Fisica, Univ. di Bologna and INFN, Sez. di Bologna, Bologna, Italy The spin-parity analysis of the reactions pp ~ 7r+Tr-Tr°,K+K-Tr °, K * K % r ~ is performed in the context of an approach which solves the problems connected to the complexity of K + K - T r ° dynamics and to the number of partial waves involved in pp annihilation at rest. The preliminary results are presented. 1. I N T R O D U C T I O N Actually, the main interest of coupled channel analysis of lrTrTr and K/~Tr final states, is related to the problem of establishing the nature of f0(1500). Following [1], the quark or ghon content of this state can be determined by comparing the branching ratios (b.r.) in 7r+Tr- and K + K - final states. Up to now, the coherent realization of this program has been obstructed by the necessity of accounting the large number of partial waves (p.w.) of annihilating /~p system and by the complexity of K + K - ~ r ° dynamics. Our approach is conceived to solve both these problems, nevertheless, in our opinion, the uncertainty introduced by the currently used resonance b.r. definition turns out to be the most relevant. I think that, to give a solid foundation to the interpretation of exotic states, this problem must be solved. 2. T H E G E N E R A L A P P R O A C H One of the fundamental advantages given by/Sp annihilation at rest is represented by the fact that only S and P waves are involved. Nevertheless, due to the large number of produced resonaces, the five p.w. of protonium system (zP0 p.w. is forbidden by selection rules) bring in the problem too many parameters. To overcome the difficulty liquid hydrogen targets are used, with the additional hypothesis that only S-wave annihilation contributes. As known, in liquid hydrogen P-wave annihilation is suppressed [2], but its exclusion clearly contradicts the experimental data (as we shall see) and introduces a dangerous and incontrollable source of systematic errors. An alternative solution consists in collecting the same final state in different hydrogen densities, which means, different relative contribution of S and P waves [2]. This tecnique was developed and systematically employed, for the first time, by the Obelix experiment which collected data in liquid (LH) and low pressure hydrogen (LP, corresponding to 5 m b a r ) , dominated by S and P wave *For the Obelix Collaboration 0375-9474/99/$ see front matter © 1999 ElsevierScience B.V. All rights reserved. PII S0375-9474(99)00184-0
N. Semprini Cesari /Nuclear Physics A655 (1999) 82c-88c
83c
annihilation respectively and normal pressure hydrogen (NTP), where their contribution is comparable. A second fundamental aspect is related to the intrinsic complexity of K + K-Tr ° dynamics. From the point view of strong interactions, i@ system, in each p.w., is a mixing of I=0,1 isospin eigenstates with opposite G-parity, so, in general, G=+1,-1 and mixed resonances can be produced (all SU(3) nonet states). ~rTr~rdynamics remains simple because only G = - I ~p sources are involved and only G = + I resonances can be formed. On the contrary, K+K-Tr ° final state can be produced by G=+1,-1 and mixed intermediate states and all these can be excited by ~p system. Remarkable is the case of K* which is produced, in each p.w., by two isospin eigenstates. To get control over the dynamics we introduce in the game also K+K%r ~ final state: the involved physics is the same (no additional parameters are needed), moreover, only isovector resonances can be formed. In this way, by using K+K-Tr ° and K±K%r ~: channels, an isospin decomposition, at the level of experimental data, is performed. Summarizing, the data corresponding to i@ --+ lr+~r-lr°, K+K-lr°, K±K%r~: final states, each one collected at three different hydrogen densities, are analyzed in the same formalism frame (fig. 1). To constraint the difficult low energy behaviour of S-wave dimeson system, ~r~r [3] and ~rK [4] S-wave phase-shift data are included. To handle the large amount of experimental data and to perform the fits in a acceptable time, a parallel processes code was written (PVM package) and a HP multiprocessor (HP 9000/800/K250), equipped with 4 Risc-processor (64 bit PA-RISC 8000), is used. 3. T H E F O R M A L I S M
To take out the relevant physical information from experimental data (masses, partial and total widths of the produced resonances), it is necessary to give an acceptable description of the annihilation process, which involves QCD in the difficult low energy limit. As known, no explicit calculation are possible, nevertheless, it is widely believed that in this limit QCD looks like the so called Skyrme-Model, which sketchs annihilation as a fast process which produces a burst of mesons in a volume of about 1.5 fm [5]. The mutual interact!ions among mesons form the resonances observed in the experimental spectra. It is easy to recognize in this picture the physical basis of Final State Interaction hypothesis. If only binary interactions are considered (Isobar Model hypothesis), unitarity and analicity require real and smooth energy functions/3 to describe resonance production. Usually, isobar model approximations are avoided by taking these functions complex, but no theoretical motivations justify this choice. Mesonic interactions are described by means of resonances of mass m , coupled to dimeson systems in a universal fashion, independently of the production process (g). The explicit expression of the amplitude, written in the frame of K-matrix and P-vector formalism, which incorporate the dynamics so far discussed, can be found elsewhere [6]. Here we report only the expression of the probability density D(p) corresponding to a given point of the Dalitz plot (D.p.) and to a given target density p : D(p) =: ~
f2s+,L.,(p ) IA=,+,L,I ~
The coefficients
f2s+tLs(p),
(I)
which represent the weights of the five p.w. involved in i6p
84c
N. Semprini Ce~'arilNuclear Physics A655 (1999) 82c-88c
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iV.. Semprini Cesari /Nuclear Physics A655 (1999) 82c-88c
85c
annihilation at rest, are the only pressure depending terms. If l, j and p label the final state, the p.w. and the density respectively, their expression is:
f~t = NPt W~ i/3j[2
(2)
N pt is the number of collected/Sp events, W f the hyperfine level population and flj the arbitrary normalization of the production parameters. Let me now consider the following ratios: __
f]tlSo
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f~"~
J3~l
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f[~a - N[~s~Wrs,
(3)
Due to the fact that Stark oscillations and dipolar transitions preserve the spin, the first ratio is density independent. Since NOl are known, the second ratio is fixed in each density. The third ratio can be directly compared to the ratio of two meson b.r., measured at the same densities, that proceed from the same initial states. Usually, these constraints are not imposed but we require they would be fulfilled by the found fit solution, obtaining in this way a strong consistency check. 4. F I T R E S U L T S The solution up to now obtained is preliminary and gives a normalized X2 of about two units (fig.2). In t a b l e l the b.r. and the p.w. percentages are listed. The expected behaviour of LH, N T P and LP annihilation is confirmed, moreover, the contribution of P wave annihilation turn out to be not negligible also in LH. From table 1 the sealing with hydrogen density of ~$1 p.w. can be extracted and compared to the one obtained by ~p -÷ KsKL : some problems are still present in K+K%r v final state. Concerning resonance parameters, the main results are listed in the following: 1 - - mesons: ¢(1020) (m = 1019 + 5, r = 4.4 MeV), observed in K + K - decay mode (dm), is produced by aS1 and 1P1 p.w. 1P1 production is suppressed showing the effect af a dynamical selection rule. K*(892) (m = 893 -t- 3, F = 53 ± 5 MeV), observed in K ~ r °, K±%r ~ dm, is produced by two isospin eigenstates from all p.w. (m0 - m=~ = 12 ± 4 MeV). Concerning p, observed in 7r+Tr- , 7r%r °, K + K -, K ± K ° dm, and produced by all p.w., three poles are needed to fit the data. (m = 774±7, F = 142±15 MeV; m = 1414±20, F = 400=i=30 MeV; m = 1620+20, P = 300 4- 20 M e V ) The third pole, the only coupled to kaons, turn out to be necessary to reproduce the strong peak observed in the high K K invariant mass region: K* kinematic reflection alone is not sufficient. Concerning the spin, the alternative hypotheses s = 0, 2 are clearly rejected. 2 ++ mesons: a~(1320) (m -- 1317 =L 10, F = 150 MeV), observed in K+K - and K ± K ° dm, is produced by all/Sp initial states. Concerning f2, observed in ~r+r - and K + K - dm and produced by 1S0, aS1 and 3/92 p.w., three poles are needed to fit the d a t a (m = 1280 ± 5, F = 210 4- 20 MeV; m = 1511 4- 10 , F = 90 =t=10 MeV; m = 1505 + 10 , F = 110 ± 20 MeY). The first (f2(1270)) and the third (f2(1565)) pole
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N. Semprini Cesari /Nuclear Physics A655 (1999) 82c-88c
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Figure 2. Fit results corresponding to lr+zr-~r ° , K + K - T r ° and K ± K % r T final states (first, second and third row) and to LH, NTP and LP samples (first, second and third column). The represented invariant masses are lr+~r- , K + K - and K : e K ° respectively.
N. Semprini Cesari /Nuclear Physics A655 (1999) 82c-88c
Table 1 Final state branching ratios and partial waves percentages. FinalState P.W. LH NTP pp ~ 7r+~r-zr° ( B R * 10 -2) 05.36 + 0.27 5.16 4- 0.26 1S 0 14.3 4- 1.0 7.5 4, 0.8 3S~ 77.3 4- 1.0 40.4 4- 2.3 ~P~ < 0.3 18.4 4- 3.0 3P1 1.0 4- 0.5 21.9 + 2.0 3P2 7.4 4- 0.5 11, 8 + 1.0 pp~K+K-K°(BR*IO -4) 23.74-1.6 30.34-2.0 1So 37.6 + 1.0 9.5 4- 0.8 3S 1 49.7 4- 1.0 12.8 4- 2.0 1P1 < 0.5 25.1 4- 3.0 3P1 8.3 + 0.7 34.3 4- 2.0 3P2 3.9 4- 0.4 18.3 4- 1.0 ~p ~ K ± K % r t: ( B R * 10 -4) 46 4- 7 53 4- 8 1So 41.2 + 1.5 8.5 + 1.0 sS1 39.3 + 1.5 8.1 + 1.0 ~P~ < 0.6 15.5 4, 1.5 3p~ 15.1 4- 1.0 50.8 4- 1.8 3P2 4.4 + 1.5 17.1 4- 1.0
87c
LP 4.89 + 0.28 2.2 + 0.5 12.0 4- 1.5 30.4 4- 3.0 36.0 4- 3.0 19.4 4- 1.5 31.54-2.2 3.6 4- 0.3 4.8 4- 1.0 29.5 4- 3.0 40.5 4- 2.0 21.6 + 1.5 63 4- 9 3.1 4- 0.4 2.9 4- 0.2 17.4 4- 2.0 57.3 4- 2.0 19.3 J= 1.5
are mainly coupled to pions while the second (f~(1525)) is coupled to kaons. The enhanced production of tensor mesons from 3Pz p.w. is observed. • 0 ++ mesons: K~(1430) (m = 1446 ± 30, r = 100 ± 10 M e V ) , observed in K % r °, K~=°~rT dm, is produced by 1So, 1P1 and zP1 p.w. Resonance parameters are determined also by Kzr S-wave scattering d a t a [4]. Concerning ao, observed in K + K and K + K ° dm and produced by 1So, 3P1 and zP2 p.w., two poles are needed (m = 980 + 15, F -- 82 + 12 M e V ; m = 1300 + 15, I' = 100 + 10 M e V ) . The second pole is not consistent with the result of Crystal Barrel (CB) [8]. Concerning fo, observed in *c+~r- and K + K - dm and produced by 1So and 3P1 p.w. three poles are used (m = 9 6 6 + 10, P = 70=t= 15 M e V ; m = 1540+20, r -- 1 1 0 0 + 4 0 M e V ; m = 1460 + 20, r = 120 + 15 M e V ) . K [ ~ coupling of the first two poles turn out to be negligible. Usually resonance b.r. are calculated by counting the number of events over the d.p. generated by the best fit amplitude where only the production p a r a m e t e r fl of the considered resonance is selected. By means of this procedure we get B R (pp --+ four°, fo K + K - ) = (3.0 4- 0.3). 10 -4 and B R (i@ ~ f0 ~r°, f0 -~ ~r%r-) = (11.0 4- 1.0). 10 -4 by which we obtain r = 0.94 + 0.20 [1]. This value seems to exclude a gluonic component in f0(1500) [1] in contrast with the analogous CB result r = 0.24 + 0.09 [7], which can be interpreted as a mixed state of gluonium and quarkonium. In spite of this disagreement (our result could be affected by some systematics still present in the obtained fit solution) I ' m convinced that the problem is more radical and involves the whole procedure
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N. Semprini Cesari/Nuclear Physics A655 (1999) 82c-88c
Table 2 Scaling with density of 3St partial wave. Spin Parity LH pp ~ ~r%r-Tr° 1 pp ~ K + K - K ° 1 ~p -~ K+K%r m 1 Branching Ratios pp -~ K s K L 1 pp ~ ¢1r° 1
NTP 0.50 + 0.05 0.33 + 0.10 0.23 ± 0.10
LP 0.14 ± 0.02 0.13 ± 0.04 0.10 ± 0.03
0.45 ± 0.06 0.45 ± 0.03
0.1'3 ± 0.03 0.15 ± 0.03
employed to extract resonance b.r. In fact this procedure neglects expficitly interference effects, moreover, the production parameters /3 themselves are associated to K-matrix poles and these cannot be identified with physical states. The production parameters of the physical states should be evaluated by means of a diagonalization procedure which is usually employed only in the calculation of the masses. But, also in this case, we couldn't avoid the problem related to the interference among overlapping resonances, so I think it would be better to use the partial widths of the physical states (obtained by a diagonalization of K-matrix partial widths) to establish the flavour content of the resonance. The formal solution of this problem, raised also by Aitchinson [9], was discussed by Rosenfeld [10]. Following an equivalent solution recently proposed [11], we extract from spin parity analysis the 0 ++ isobar obtained by means of K-matrix and P-vector amplitude, then we fit this amplitude by means of Breit-Wigner (BW) poles by which we get the partial widths of physical states (in order to preserve unitarity, BW decomposition has to be performed directly on the isobar obtained by K-matrix amplitude). The result obtained in this way disagree, with respect to the one calculated in the usual way, also of a factor two. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
C. Amsler and F. Close, Phys. Rev. D 53, 295 (1996). G. Reifenrother and E. Klempt, Nucl. Phys. A 503, 885 (1989). G. Grayer et al., Nucl. Phys. B 75, 189 (1974). D. Aston et al., Nucl. Phys. B 296, 491 (1988). R.D. Amado, Nucl. Phys. B 56A, 22 (1997). A. Bertin et al., Phys. Left. B408, 476 (1997). A. Abele et al., Phys. Lett. B385, 425 (1996). C. Amsler et al., Phys. Left. B355, 425 (1995). I.J.R. Aitchinson, Nucl. Phys. A 189, 417 (1972). L. Rosenfeld, Acta Physica Polonica A38, 603(1970). T.S. Belozerova and V.K. Henner, Phys.Part.Nucl.29, 63(1998).
NUCLEAR PHYSICS A Nuclear PhysicsA655 (1999) 82c-88c www.elscvier.nl/locate/npe
Coupled-channel analysis of 7rTr~r and Kr~'Tr final states from /Sp annihilation at rest in hydrogen targets at three densities N. Semprini Cesari ~ * a Dip. di Fisica, Univ. di Bologna and INFN, Sez. di Bologna, Bologna, Italy The spin-parity analysis of the reactions pp ~ 7r+Tr-Tr°,K+K-Tr °, K * K % r ~ is performed in the context of an approach which solves the problems connected to the complexity of K + K - T r ° dynamics and to the number of partial waves involved in pp annihilation at rest. The preliminary results are presented. 1. I N T R O D U C T I O N Actually, the main interest of coupled channel analysis of lrTrTr and K/~Tr final states, is related to the problem of establishing the nature of f0(1500). Following [1], the quark or ghon content of this state can be determined by comparing the branching ratios (b.r.) in 7r+Tr- and K + K - final states. Up to now, the coherent realization of this program has been obstructed by the necessity of accounting the large number of partial waves (p.w.) of annihilating /~p system and by the complexity of K + K - ~ r ° dynamics. Our approach is conceived to solve both these problems, nevertheless, in our opinion, the uncertainty introduced by the currently used resonance b.r. definition turns out to be the most relevant. I think that, to give a solid foundation to the interpretation of exotic states, this problem must be solved. 2. T H E G E N E R A L A P P R O A C H One of the fundamental advantages given by/Sp annihilation at rest is represented by the fact that only S and P waves are involved. Nevertheless, due to the large number of produced resonaces, the five p.w. of protonium system (zP0 p.w. is forbidden by selection rules) bring in the problem too many parameters. To overcome the difficulty liquid hydrogen targets are used, with the additional hypothesis that only S-wave annihilation contributes. As known, in liquid hydrogen P-wave annihilation is suppressed [2], but its exclusion clearly contradicts the experimental data (as we shall see) and introduces a dangerous and incontrollable source of systematic errors. An alternative solution consists in collecting the same final state in different hydrogen densities, which means, different relative contribution of S and P waves [2]. This tecnique was developed and systematically employed, for the first time, by the Obelix experiment which collected data in liquid (LH) and low pressure hydrogen (LP, corresponding to 5 m b a r ) , dominated by S and P wave *For the Obelix Collaboration 0375-9474/99/$ see front matter © 1999 ElsevierScience B.V. All rights reserved. PII S0375-9474(99)00184-0
N. Semprini Cesari /Nuclear Physics A655 (1999) 82c-88c
83c
annihilation respectively and normal pressure hydrogen (NTP), where their contribution is comparable. A second fundamental aspect is related to the intrinsic complexity of K + K-Tr ° dynamics. From the point view of strong interactions, i@ system, in each p.w., is a mixing of I=0,1 isospin eigenstates with opposite G-parity, so, in general, G=+1,-1 and mixed resonances can be produced (all SU(3) nonet states). ~rTr~rdynamics remains simple because only G = - I ~p sources are involved and only G = + I resonances can be formed. On the contrary, K+K-Tr ° final state can be produced by G=+1,-1 and mixed intermediate states and all these can be excited by ~p system. Remarkable is the case of K* which is produced, in each p.w., by two isospin eigenstates. To get control over the dynamics we introduce in the game also K+K%r ~ final state: the involved physics is the same (no additional parameters are needed), moreover, only isovector resonances can be formed. In this way, by using K+K-Tr ° and K±K%r ~: channels, an isospin decomposition, at the level of experimental data, is performed. Summarizing, the data corresponding to i@ --+ lr+~r-lr°, K+K-lr°, K±K%r~: final states, each one collected at three different hydrogen densities, are analyzed in the same formalism frame (fig. 1). To constraint the difficult low energy behaviour of S-wave dimeson system, ~r~r [3] and ~rK [4] S-wave phase-shift data are included. To handle the large amount of experimental data and to perform the fits in a acceptable time, a parallel processes code was written (PVM package) and a HP multiprocessor (HP 9000/800/K250), equipped with 4 Risc-processor (64 bit PA-RISC 8000), is used. 3. T H E F O R M A L I S M
To take out the relevant physical information from experimental data (masses, partial and total widths of the produced resonances), it is necessary to give an acceptable description of the annihilation process, which involves QCD in the difficult low energy limit. As known, no explicit calculation are possible, nevertheless, it is widely believed that in this limit QCD looks like the so called Skyrme-Model, which sketchs annihilation as a fast process which produces a burst of mesons in a volume of about 1.5 fm [5]. The mutual interact!ions among mesons form the resonances observed in the experimental spectra. It is easy to recognize in this picture the physical basis of Final State Interaction hypothesis. If only binary interactions are considered (Isobar Model hypothesis), unitarity and analicity require real and smooth energy functions/3 to describe resonance production. Usually, isobar model approximations are avoided by taking these functions complex, but no theoretical motivations justify this choice. Mesonic interactions are described by means of resonances of mass m , coupled to dimeson systems in a universal fashion, independently of the production process (g). The explicit expression of the amplitude, written in the frame of K-matrix and P-vector formalism, which incorporate the dynamics so far discussed, can be found elsewhere [6]. Here we report only the expression of the probability density D(p) corresponding to a given point of the Dalitz plot (D.p.) and to a given target density p : D(p) =: ~
f2s+,L.,(p ) IA=,+,L,I ~
The coefficients
f2s+tLs(p),
(I)
which represent the weights of the five p.w. involved in i6p
84c
N. Semprini Ce~'arilNuclear Physics A655 (1999) 82c-88c
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iV.. Semprini Cesari /Nuclear Physics A655 (1999) 82c-88c
85c
annihilation at rest, are the only pressure depending terms. If l, j and p label the final state, the p.w. and the density respectively, their expression is:
f~t = NPt W~ i/3j[2
(2)
N pt is the number of collected/Sp events, W f the hyperfine level population and flj the arbitrary normalization of the production parameters. Let me now consider the following ratios: __
f]tlSo
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f[~a - N[~s~Wrs,
(3)
Due to the fact that Stark oscillations and dipolar transitions preserve the spin, the first ratio is density independent. Since NOl are known, the second ratio is fixed in each density. The third ratio can be directly compared to the ratio of two meson b.r., measured at the same densities, that proceed from the same initial states. Usually, these constraints are not imposed but we require they would be fulfilled by the found fit solution, obtaining in this way a strong consistency check. 4. F I T R E S U L T S The solution up to now obtained is preliminary and gives a normalized X2 of about two units (fig.2). In t a b l e l the b.r. and the p.w. percentages are listed. The expected behaviour of LH, N T P and LP annihilation is confirmed, moreover, the contribution of P wave annihilation turn out to be not negligible also in LH. From table 1 the sealing with hydrogen density of ~$1 p.w. can be extracted and compared to the one obtained by ~p -÷ KsKL : some problems are still present in K+K%r v final state. Concerning resonance parameters, the main results are listed in the following: 1 - - mesons: ¢(1020) (m = 1019 + 5, r = 4.4 MeV), observed in K + K - decay mode (dm), is produced by aS1 and 1P1 p.w. 1P1 production is suppressed showing the effect af a dynamical selection rule. K*(892) (m = 893 -t- 3, F = 53 ± 5 MeV), observed in K ~ r °, K±%r ~ dm, is produced by two isospin eigenstates from all p.w. (m0 - m=~ = 12 ± 4 MeV). Concerning p, observed in 7r+Tr- , 7r%r °, K + K -, K ± K ° dm, and produced by all p.w., three poles are needed to fit the data. (m = 774±7, F = 142±15 MeV; m = 1414±20, F = 400=i=30 MeV; m = 1620+20, P = 300 4- 20 M e V ) The third pole, the only coupled to kaons, turn out to be necessary to reproduce the strong peak observed in the high K K invariant mass region: K* kinematic reflection alone is not sufficient. Concerning the spin, the alternative hypotheses s = 0, 2 are clearly rejected. 2 ++ mesons: a~(1320) (m -- 1317 =L 10, F = 150 MeV), observed in K+K - and K ± K ° dm, is produced by all/Sp initial states. Concerning f2, observed in ~r+r - and K + K - dm and produced by 1S0, aS1 and 3/92 p.w., three poles are needed to fit the d a t a (m = 1280 ± 5, F = 210 4- 20 MeV; m = 1511 4- 10 , F = 90 =t=10 MeV; m = 1505 + 10 , F = 110 ± 20 MeY). The first (f2(1270)) and the third (f2(1565)) pole
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N. Semprini Cesari /Nuclear Physics A655 (1999) 82c-88c
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Figure 2. Fit results corresponding to lr+zr-~r ° , K + K - T r ° and K ± K % r T final states (first, second and third row) and to LH, NTP and LP samples (first, second and third column). The represented invariant masses are lr+~r- , K + K - and K : e K ° respectively.
N. Semprini Cesari /Nuclear Physics A655 (1999) 82c-88c
Table 1 Final state branching ratios and partial waves percentages. FinalState P.W. LH NTP pp ~ 7r+~r-zr° ( B R * 10 -2) 05.36 + 0.27 5.16 4- 0.26 1S 0 14.3 4- 1.0 7.5 4, 0.8 3S~ 77.3 4- 1.0 40.4 4- 2.3 ~P~ < 0.3 18.4 4- 3.0 3P1 1.0 4- 0.5 21.9 + 2.0 3P2 7.4 4- 0.5 11, 8 + 1.0 pp~K+K-K°(BR*IO -4) 23.74-1.6 30.34-2.0 1So 37.6 + 1.0 9.5 4- 0.8 3S 1 49.7 4- 1.0 12.8 4- 2.0 1P1 < 0.5 25.1 4- 3.0 3P1 8.3 + 0.7 34.3 4- 2.0 3P2 3.9 4- 0.4 18.3 4- 1.0 ~p ~ K ± K % r t: ( B R * 10 -4) 46 4- 7 53 4- 8 1So 41.2 + 1.5 8.5 + 1.0 sS1 39.3 + 1.5 8.1 + 1.0 ~P~ < 0.6 15.5 4, 1.5 3p~ 15.1 4- 1.0 50.8 4- 1.8 3P2 4.4 + 1.5 17.1 4- 1.0
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LP 4.89 + 0.28 2.2 + 0.5 12.0 4- 1.5 30.4 4- 3.0 36.0 4- 3.0 19.4 4- 1.5 31.54-2.2 3.6 4- 0.3 4.8 4- 1.0 29.5 4- 3.0 40.5 4- 2.0 21.6 + 1.5 63 4- 9 3.1 4- 0.4 2.9 4- 0.2 17.4 4- 2.0 57.3 4- 2.0 19.3 J= 1.5
are mainly coupled to pions while the second (f~(1525)) is coupled to kaons. The enhanced production of tensor mesons from 3Pz p.w. is observed. • 0 ++ mesons: K~(1430) (m = 1446 ± 30, r = 100 ± 10 M e V ) , observed in K % r °, K~=°~rT dm, is produced by 1So, 1P1 and zP1 p.w. Resonance parameters are determined also by Kzr S-wave scattering d a t a [4]. Concerning ao, observed in K + K and K + K ° dm and produced by 1So, 3P1 and zP2 p.w., two poles are needed (m = 980 + 15, F -- 82 + 12 M e V ; m = 1300 + 15, I' = 100 + 10 M e V ) . The second pole is not consistent with the result of Crystal Barrel (CB) [8]. Concerning fo, observed in *c+~r- and K + K - dm and produced by 1So and 3P1 p.w. three poles are used (m = 9 6 6 + 10, P = 70=t= 15 M e V ; m = 1540+20, r -- 1 1 0 0 + 4 0 M e V ; m = 1460 + 20, r = 120 + 15 M e V ) . K [ ~ coupling of the first two poles turn out to be negligible. Usually resonance b.r. are calculated by counting the number of events over the d.p. generated by the best fit amplitude where only the production p a r a m e t e r fl of the considered resonance is selected. By means of this procedure we get B R (pp --+ four°, fo K + K - ) = (3.0 4- 0.3). 10 -4 and B R (i@ ~ f0 ~r°, f0 -~ ~r%r-) = (11.0 4- 1.0). 10 -4 by which we obtain r = 0.94 + 0.20 [1]. This value seems to exclude a gluonic component in f0(1500) [1] in contrast with the analogous CB result r = 0.24 + 0.09 [7], which can be interpreted as a mixed state of gluonium and quarkonium. In spite of this disagreement (our result could be affected by some systematics still present in the obtained fit solution) I ' m convinced that the problem is more radical and involves the whole procedure
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N. Semprini Cesari/Nuclear Physics A655 (1999) 82c-88c
Table 2 Scaling with density of 3St partial wave. Spin Parity LH pp ~ ~r%r-Tr° 1 pp ~ K + K - K ° 1 ~p -~ K+K%r m 1 Branching Ratios pp -~ K s K L 1 pp ~ ¢1r° 1
NTP 0.50 + 0.05 0.33 + 0.10 0.23 ± 0.10
LP 0.14 ± 0.02 0.13 ± 0.04 0.10 ± 0.03
0.45 ± 0.06 0.45 ± 0.03
0.1'3 ± 0.03 0.15 ± 0.03
employed to extract resonance b.r. In fact this procedure neglects expficitly interference effects, moreover, the production parameters /3 themselves are associated to K-matrix poles and these cannot be identified with physical states. The production parameters of the physical states should be evaluated by means of a diagonalization procedure which is usually employed only in the calculation of the masses. But, also in this case, we couldn't avoid the problem related to the interference among overlapping resonances, so I think it would be better to use the partial widths of the physical states (obtained by a diagonalization of K-matrix partial widths) to establish the flavour content of the resonance. The formal solution of this problem, raised also by Aitchinson [9], was discussed by Rosenfeld [10]. Following an equivalent solution recently proposed [11], we extract from spin parity analysis the 0 ++ isobar obtained by means of K-matrix and P-vector amplitude, then we fit this amplitude by means of Breit-Wigner (BW) poles by which we get the partial widths of physical states (in order to preserve unitarity, BW decomposition has to be performed directly on the isobar obtained by K-matrix amplitude). The result obtained in this way disagree, with respect to the one calculated in the usual way, also of a factor two. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
C. Amsler and F. Close, Phys. Rev. D 53, 295 (1996). G. Reifenrother and E. Klempt, Nucl. Phys. A 503, 885 (1989). G. Grayer et al., Nucl. Phys. B 75, 189 (1974). D. Aston et al., Nucl. Phys. B 296, 491 (1988). R.D. Amado, Nucl. Phys. B 56A, 22 (1997). A. Bertin et al., Phys. Left. B408, 476 (1997). A. Abele et al., Phys. Lett. B385, 425 (1996). C. Amsler et al., Phys. Left. B355, 425 (1995). I.J.R. Aitchinson, Nucl. Phys. A 189, 417 (1972). L. Rosenfeld, Acta Physica Polonica A38, 603(1970). T.S. Belozerova and V.K. Henner, Phys.Part.Nucl.29, 63(1998).