- Email: [email protected]
Three I=0 JPC=2−+ mesons
23 March 2000
Physics Letters B 477 Ž2000. 19–27
Three I s 0 J P C s 2yq mesons A.V. Anisovich c , C.A. Baker a , C.J. Batty a , D.V. Bugg b, A.R. Cooper b, C. Hodd b, V.A. Nikonov c , A.V. Sarantsev c , V.V. Sarantsev c , B.S. Zou b,1 a
c
Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK b Queen Mary and Westfield College, London E1 4NS, UK St. Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg district, 188350, Russia
Received 12 January 2000; received in revised form 11 February 2000; accepted 14 February 2000 Editor: L. Montanet
Abstract
™
High statistics data on pp hp 0p 0p 0 at nine beam momenta from 900 to 1940 MeVrc require the presence of three I s 0, J P C s 2yq mesons with masses and widths Ži. M s 1645 " 6Žstat. " 20Žsyst. MeV, G s 200 " 7 " 20 MeV, Žii. M s 1860 " 5 " 15 MeV, G s 250 " 25 " 25 MeV, Žiii. M s 2030 " 5 " 15 MeV, G s 205 " 10 " 15 MeV. The h 2 Ž1645. and h 2Ž2030., together with h 2 Ž2300. observed earlier, may be interpreted as a sequence of expected qq states. The h 2 at 1860 MeV appears to be an extra state, hence a candidate for a hybrid. Decay branching ratios of all three states to a 2 Ž1320.p , f 2 Ž1270.h and a0 Ž980.p are established. The h 2 at 1860 MeV decays dominantly to f 2h and a 2p , as predicted for a hybrid. The h 2 Ž2030. decays dominantly to a2p with orbital angular momentum L s 2 and slightly less strongly to a 2p with L s 0. q 2000 Elsevier Science B.V. All rights reserved.
An earlier publication described evidence for two J P C s 2yq mesons h 2 Ž1645. and h 2 Ž1870. w1x. These have since been confirmed in the WA102 experiment in decays to hpp w2x and KKp w3x. Here we present data taken by the Crystal Barrel collaboration at nine p momenta. Statistics are higher than in the earlier publication by a factor ; 7 per momentum. They confirm the presence of h 2 Ž1645. and h 2 Ž1870. and provide evidence for a third nearby h 2 at 2030 MeV. This makes too many states in a narrow mass range for all of them to be qq. First we describe briefly the experimental set-up and the selection of data. The p beam interacts in a
1 Now at the Institute for High Energy Physics, Beijing 100039, China.
liquid hydrogen target at the centre of the Crystal Barrel detector. Two veto counters 20 cm downstream of the target provide an interaction trigger. Charged particles are vetoed over 98% of the solid angle by multiwire chambers close to the target, hence providing an on-line trigger for neutral final states. Photons are detected over 98% of 4p solid angle in a barrel of 1380 CsI crystals; these crystals measure photons with high energy resolution and efficiency down to 20 MeV, and with an angular resolution of "20 mrad in azimuth and polar angle. The beam intensity was typically 2 = 10 5rs and the trigger rate typically 60rs. The off-line analysis follows the procedures of Ref. w1x; minor refinements in data selection have been made, based on a Monte Carlo simulation of background channels using GEANT. Events are se-
0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 0 0 . 0 0 2 3 6 - 7
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
20
Table 1 Numbers of events, reconstruction efficiency e , cross sections and background levels ŽBG., as a function of beam momentum. The second column shows the total available centre of mass energy Momentum CM Events e ŽMeVrc. Ž%. Energy ŽMeV.
s Žhp 0p 0p 0 . BG Ž m b. Ž%.
600 900 1050 1200 1350 1525 1642 1800 1940
35.9"2.2 36.1"2.2 33.7"1.0 36.1"1.1 34.4"1.0 40.0"1.2 38.6"1.2 31.9"1.0 27.5"0.8
1962 2050 2098 2149 2201 2263 2304 2360 2409
5062 24487 15709 35127 26379 21339 25394 28200 31388
0.132 0.128 0.130 0.127 0.124 0.119 0.116 0.113 0.111
7.7 7.7 7.7 7.7 8.0 8.4 8.9 9.6 9.3
lected containing exactly 8 photon showers, and 8C kinematic fits are made to 4p 0 , hp 0p 0p 0 and hhp 0p 0 . Events fitting h 3p 0 with confidence level
™
CL above 5% are used. A small number of events from hh , h 3p 0 Ždiscussed elsewhere w4x. are rejected within the mass range M Ž3p 0 . s 520 to 575 MeV; likewise, a few events due to p 0hX , hX hp 0p 0 w4x are rejected within the range M Žhp 0p 0 . s 928 to 988 MeV. Further cuts to reduce backgrounds are: Ži. CLŽ4p 0 . - 0.01%, Žii. CLŽh 3p 0 . ) CLŽhhp 0p 0 .. The Monte Carlo simulation reproduces the observed confidence level distribution down to the cut at 5%. Table 1 shows the numbers of events at each beam momentum, reconstruction efficiencies, overall cross sections and estimated backgrounds. The simulation estimates a surviving background of 7.7% at low beam momenta, increasing slightly at the higher momenta. The background comes largely from 4p 0 Žtypically 1.1%., from v 3p 0 , v p 0g after loss of one photon Ž3.0%., and from 5p 0 after the loss of 2 photons Ž2.5%..
™
™
Fig. 1. Mass distributions at a beam momentum of 1800 MeVrc for Ža. 3p , Žb. and Žd. pph , Žc. ph and Že. pp . Histograms show the maximum likelihood fit. In Žb., the h 2 Ž2030. is not included in the fit, in Žd. it is. Žf. shows the pph mass distribution for events where the ph mass lies in the range 1320 " 55 MeV; here, h 2 Ž2030. in included in the fit.
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
The physics of these competing channels has been studied; for example, results from 4p 0 are reported in w5x. Combinatorics are high in the background channels and events lie close to a phase space distribution. The Monte Carlo simulation shows that backgrounds surviving in the h 3p 0 channel, after cuts, are likewise close to phase space. This background is included in the amplitude analysis. Fig. 1 displays mass distributions, summed over all combinations, at a beam momentum of 1800 MeVrc. There are obvious enhancements due to a0 Ž980. and a2 Ž1320. in Fig. 1Žc., due to f 2 Ž1270. in Fig. 1Že. and f 1Ž1285. in Fig. 1Žd.. At this beam momentum, the signal from h Ž1440. is barely visible in the mass projection of Fig. 1Žd.. It is more clearly visible at lower beam momenta; a separate publication w6x discusses it and evidence for a related threshold enhancement in f 0 Ž980.h. The h 2 Ž1645. and h 2 Ž1870. are not distinguishable in Fig. 1Žb., because of the combinatorics. The histograms show the maximum likelihood fit described below. There is, however, a clear shoulder at 2030 MeV in Fig. 1Žb. which we find to be due to a third 2yq resonance. Fig. 1Žb. shows a fit without this component and Fig. 1Žd. a fit including it. Data at 1940 and 1642 MeVrc Žnot shown. provide similar evidence. Fig. 1Žf. shows the hpp mass projection after selection of events containing an hp combination within one half-width of h 2 Ž1320.; the shoulder at 2030 MeV is somewhat more prominent with this selection, though statistically weaker. The data are fitted by the maximum likelihood method to the following channels:
™ f Ž 1270. a Ž 980. , ™ a Ž 1320. s , ™ a Ž 980. s , ™ f Ž 1285. p , ™ h Ž 1440. p , ™ Xp , X ™ f Ž 980. h , ™ h Ž 1645. p , ™ h Ž 1870. p , ™ h Ž 2030. p , ™ f Ž 1920. p ,
pp
2
0
Ž 2.
0
Ž 3.
0
Ž 11 . Ž 12 .
2
2
Here s stands for the broad component of the pp S-wave amplitude, as parametrised by Zou and Bugg w7x; X stands for a 0yq threshold enhancement in f 0 Ž980.h w6x. The treatment of amplitudes is identical to that described in detail in Ref. w1x. In outline, the decay of each resonance is described fully in terms of helicity states. However, we average over the angular dependence of the production process, since there are too many partial waves to allow a complete description. Charge conjugation invariance requires that angular distributions are symmetric forwardbackward in the centre of mass system; the experimental data obey this constraint within the errors. An incoherent phase space background is included with magnitude adjusted to the background levels of Table 1. The method of calculation of integrated cross sections, the correction for observed rate dependence and the assessment of errors are described in Ref. w8x. Resulting integrated cross sections are shown in Fig. 2. Smooth curves are drawn through those for individual channels; errors for each channel at indi-
Ž 4. Ž 5. Ž 6.
2
Ž 7.
2
Ž 8.
2
Ž 9.
2
™ f Ž 2220. p , ™ p Ž 1670. h .
Ž 1.
2
1
21
Ž 10 .
™
Fig. 2. Points with errors show the integrated cross sections for present data, uncorrected for branching fractions of h gg and p 0 gg . Smooth curves are drawn through cross sections for individual channels.
™
22
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
surviving f 2 Ž1270. comes mostly from the strong high mass tail of h 2 Ž1870.. The fit also requires that the a2 Ž1320. contribution is strong for the mass region around 2030 MeV. At lower masses around 1645 MeV, Fig. 3Žc. shows that the a 2 Ž1320. signal grows in strength, due to h 2 Ž1645.. There is in addition a horizontal band close to a f 0 Ž980.. It is discussed at length in Ref. w6x. The detailed evidence for h 2 Ž1645. and h 2 Ž1870. has been discussed in Ref. w1x. Ultimately it depends on the amplitude analysis, which accommodates all combinations. Results obtained here confirm all features of this evidence very closely with an increase in statistics of a factor 7 at most momenta and with data at nine momenta rather than 2. We therefore concentrate attention on the masses and widths of these resonances and on additional decay channels which were not visible earlier. Fig. 4 shows the variation of log likelihood with the mass and width of each resonance. Curves are asymmetric about the optimum for the width; we find that 1rG is closer to a symmetric distribution. Full curves show results summed over all beam momenta and Table 2 collects
Fig. 3. Scatter plots of M Žpp . vs. M Žhp . for three ranges of M Žhpp .: Ža. 1945–2115 MeV, centred on h 2 Ž2030., Žb. 1775– 1945 MeV over h 2 Ž1870. and Žc. 1560-1750, centred on h 2 Ž1645..
vidual momenta are typically "Ž0.5–0.8. m b. There is an additional systematic error of "5% in all cross sections, arising from uncertainty in the target length; this has no effect on fitted physics, since it is common to all momenta and all channels. In order to display the essential characteristics of h 2 Ž1645., h 2 Ž1870. and h 2 Ž2030., Fig. 3 shows scatter plots of M Žpp . vs. M Žhp . for combinations within ranges of hpp mass centred on each resonance. The strongest f 2 Ž1270. signal appears as a horizontal band in Fig. 3Žb., and is due to decays of h 2 Ž1870.; this resonance has a decay mode appearing less strongly in a2 Ž1320. hp . Around 2030 MeV, Fig. 3Ža. shows that the f 2 Ž1270. becomes weaker, with constructive interference where the bands cross; the amplitude analysis requires that the
™
Fig. 4. Ssylog likelihood vs. Ža. the mass of h 2 Ž1645., Žb. the mass of h 2 Ž1870., Žc. the width of h 2 Ž1645., Žd. the width of h 2 Ž1870., Že. the mass of h 2 Ž2030., Žf. the width of h 2 Ž2030.. Curves are normalised to 0 at the minima. In Že., the dashed curve is for decays only to a 2 p with Ls 0 and the full curve for all decays. In Žb., broken curves shows data at individual momenta 900 MeVrc Ždashed., 1050 MeVrc Ždotted. and 1200 MeVrc Žchain curve.; the full curve is summed over all momenta.
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27 Table 2 Parameters of J P C s 2yq resonances Resonance
Mass ŽMeV.
Width ŽMeV.
h 2 Ž1645. h 2 Ž1870. h 2 Ž2030.
1645"6Žstat."20Žsyst. 1860"5Žstat."15Žsyst. 2030"5Žstat."15Žsyst.
200"7"25 250"25q50 y35 205"10"25
fitted resonance parameters. Our definition of log likelihood is such that it increases by 0.5 for a one standard deviation change in one parameter. In the table, systematic errors cover variations which are observed as ingredients in the amplitude analysis are varied. Our intention is that the systematic errors should be compounded linearly with statistical errors. As an example, for h 2 Ž1870., the width lies within the range 190–325 MeV. Fig. 4Žb. illustrates optima observed at individual beam momenta 900– 1200 MeVrc, where the h 2 Ž1870. signal is largest Ž; 30% of the integrated cross section in Fig. 2.. However, the width of h 2 Ž1870. is not particularly well determined, because this resonance overlaps significantly with both h 2 Ž1645. and h 2 Ž2030.. The h 2 Ž2030. decays to a 2 Ž1320.p with both orbital angular momenta L s 0 and 2, with the latter dominant. Fig. 4Že. shows mass scans for L s 0 Ždashed curve. and for the sum of all decay modes Žfull curve.. We attribute the slight difference between these two curves to the effect of the centrifugal barrier, which inhibits the dominant L s 2 decay at low masses. Data at all five beam momenta from 1350 to 1940 MeVrc show a distinct optimum within "15 MeV of 2030 MeV. We now present evidence for the quantum numbers of h 2 Ž2030.. Several qq states are expected near this mass with quantum numbers up to J P s 4q. States with J P s 1q or 3q cannot be formed with orbital angular momentum l s 0 in the production process, since this would require initial states with J P C s 1yq or 3yq, which are forbidden for qq. In testing these two possibilities, the amplitude analysis includes a Blatt-Weisskopf centrifugal barrier for production with l s 1. Fig. 5 shows the variation of log likelihood with mass for each J P, summed over data at five beam momenta from 1350 to 1940 MeVrc. For J P C s 2yq there is an optimum close to the shoulder observed in Figs. 1Žb. and Žd.. All other J P give fits which are worse by at least 20
23
standard deviations, taking account of the difference in the number of fitted parameters. The fit for J P C s 0yq shows a broad dip, but with poor log likelihood. This behaviour may be understood from a simulation of cross-talk between 0y and 2y. The hypothesis 0yq a 2 p and f 2 h requires decays with L s 2. These depend on three terms having the same angular dependence as the dominant L s 2 decay of h 2 Ž2030. to a2 p and f 2 h , but with different Clebsch-Gordan coefficients multiplying each term. If both 0y and 2y are included in the fit, ) 95% of the signal fits as 2y. For J P C s 4qq, there is no peak near the well known f 4Ž2050. w9x; the change in log likelihood with increasing mass is associated with the L s 3 centrifugal barrier for decays to a 2 p and f 2 h. Quantum numbers 1qq, 3qq, 1yq or 3yq Žthe latter two exotic. give poor fits with very small fitted contributions and no optimum as a function of mass. The 2qq possibility is absorbed into channels Ž10. and Ž11., which are discussed separately below. We now discuss decay modes. In Ref. w1x, the f 2 Ž1870. could be identified clearly only in decays to f 2 Ž1270.h , although there was tentative evidence for decays to a 2 Ž1320.p . With the much higher statistics now available, the latter decay mode is identified clearly, and also a decay mode to a 0 Ž980.p with L s 2. There is also evidence which will be discussed for decays to hs . Table 3 shows ratios of the magnitudes of coupling constants L fitted to all of these channels at individual beam momenta. The
™
Fig. 5. The variation of Ssylog likelihood with mass for alternative J P assignments to h 2 Ž2030..
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
24
Table 3 Ratios of coupling constants for decay modes of h 2 Ž1645., h 2 Ž1870. and h 2 Ž2030.. Errors are given in parentheses Momentum ŽMeVrc.
1645 < < L1645 a p rL a p
1870 < < L1870 a p rL f h
1870 < < L1870 a p rL f h
1870 < Lhs < rL1870 f h
2030 < L 2030 < a p , Ls0 rL a p , Ls2
2030 < L 2030 < a p rL a p , Ls2
900 1050 1200 1350 1525 1642 1800 1940
1.46Ž.40. 0.81Ž.22. 0.57Ž.19. 0.59Ž.15. 0.60Ž.19. 0.91Ž.14. 0.84Ž.09. 0.64Ž.08.
0.30Ž.06. 0.25Ž.04. 0.31Ž.03. 0.35Ž.04. 0.30Ž.16. 0.33Ž.11. 0.32Ž.07. 0.08Ž.12.
1.10Ž.09. 1.10Ž.06. 1.07Ž.04. 1.05Ž.05. 1.07Ž.08. 1.09Ž.09. 0.94Ž.10. 1.07Ž.16.
2.26Ž.35. 1.57Ž.29. 1.19Ž.24. 1.96Ž.26. 1.39Ž.52. 1.75Ž.48. 1.45Ž.45. 0.76Ž.57.
0.22Ž.06. 0.13Ž.08. 0.20Ž.06. 0.23Ž.05. 0.34Ž.06.
0.24Ž.07. 0.16Ž.05. 0.20Ž.04. 0.37Ž.08. 0.36Ž.07.
mean phaseŽrad.
0.77Ž.05. y0.60
0.30Ž.02. q3.92
1.07Ž.03. q4.92
1.53Ž.14. q0.70
0.24Ž.03. y1.11
0.23Ž.03. 1.36
0
2
2
2
0
2
™
amplitude for h 2 Ž1870. a0 Ž980.p , as an example, is expressed in the form: f s L BW Ž 1870 . FL Ž 980 . B2 Ž k . P2m Ž cos u , f . .
Ž 13 . Here BW Ž1870. is a relativistic Breit-Wigner amplitude of constant width, 1rŽ M 2 y s y iM G ., for the h 2 Ž1870. in hpp ; FLŽ980. is a Flatte´ form for the a0 Ž980. in hp w10x. The factor B2 Ž k . is a BlattWeisskopf centrifugal barrier factor for the decay h 2 Ž1870. a 0 Ž980.p in terms of the momentum k in the decay of each h 2 : B2 Ž k . s k 2rw k 2 Ž k 2 q Ry2 . q Ry4 x1r2 , with R s 0.8 fm. The Legendre polynomial P2m describes the dependence on decay angles u , f for helicity m of h 2 Ž1870.. Ratios of coupling constants in Table 3 show good consistency between momenta for decays to f 2 Ž1270.h , a2 Ž1320.p and a0 Ž980.p . There are some fluctuations for the less well identified decay to hs . The difficulty here is cross-talk with the strong a 2 Ž1320. s and a 0 Ž980. s channels, making this decay mode harder to identify. For h 2 Ž2030., there is again reasonable consistency for ratios of coupling constants between different momenta. The phases of different decays may be different, because of multiple scattering in the final state, generating strong interaction phases; these phases are likewise consistent within errors between momenta, and average values are shown in the last line of Table 3. For the principal decay modes of h 2 Ž1645. a 2 p and h 2 Ž1870. f 2 h , quantum numbers J P C s 2yq are definitely required, as shown in Ref. w1x. How-
™
™
™
2
2
2
0
2
ever, a question is whether one can be confident that all other decays are really to be attributed to h 2 Ž1870. and h 2 Ž1645.. Could they alternatively be due to nearby 1qq or 0yq resonances of similar mass and width? For h 2 Ž1870., the answer is firmly that decays to a 2 Ž1320.p and a0 Ž980.p require quantum numbers 2yq. Log likelihood values for the alternative 1qq or 0yq assignments are considerably worse, as shown in Table 4. This demonstrates that the decay angular distributions follow the expected forms for 2y; the amplitude analysis is sensitive to this, though we cannot readily display evidence graphically because of the combinatorics. Likewise, for h 2 Ž2030., log likelihood excludes alternative quantum numbers 3q, 1q and 0y for decays to a 2 p and a 0 p . A further check has been made, following procedures developed in Ref. w5x. In this check, different Žwrong. angles have been substituted for the correct ones; when this is done, the coupling Table 4 Changes in log likelihood, summed over beam momenta, when alternative quantum numbers are substituted for decays of the resonances Substitution
a2 p
a0 p
hs
1q Ž1870. 0y Ž1870. 1q Ž1645. 0y Ž1645. 3q Ž2030. 1q Ž2030. 0y Ž2030.
y285 y144 – – y99 y133 y174
y187 y326 y34 q4 y39 y52 y75
y58 q5 – – – – –
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
constants for the decay modes in question fall to low values, showing that the amplitude analysis can recognise the correct angular dependence. For h 2 Ž1645., quantum numbers 2y are significantly preferred over 1q for decays to a 0 p . However, there is no discrimination against the possibility of quantum numbers 0y for decays to a 0 Ž980.p . Likewise, for the resonance at 1860 MeV, it is not possible to distinguish clearly between the quantum numbers 2y and 0y for decays to hs . Despite this, there is circumstantial evidence that all decays of h 2 Ž1870. really correspond to the same resonance. Fig. 2 shows that its cross section varies strongly with beam momentum. The cross section for the hs decay follows this trend and suggests that h 2 Ž1870. decays at least partially to hs with L s 2. Branching ratios are as shown in Table 5, after integration over the whole phase space for each resonance and its decays. The third column shows the branching ratios observed in the present hp 0p 0p 0 data. The last column shows branching ratios corrected for all charges and also for all decay modes of f 2 , a 2 and a 0 . In this evaluation, we use values of the Particle Data Group w9x for decay branching ratios of f 2 Ž1270. and a 2 Ž1320.. For a 0 Ž980 . , we use the ratio BR w a 0 Ž980 . hp xrBRw a0 Ž980. all x s 0.76, obtained from the Flatte´ formula fitted to Crystal Barrel data on pp hp 0p 0 data at rest w10x. The WA102 group has just reported branching ratios for h 2 Ž1870. to a 2 p and a 0 Ž980. which are much larger than those found here, though with large errors w11x. The larger values and errors arise via strong destructive interference between h 2 Ž1645. and h 2 Ž1870. in their fit. We allow interferences between
™ ™
™
25
these two resonances, but find that they have only a small effect within our quoted errors. The Cello collaboration reported the first evidence for h 2 Ž1870. in gg hpp , with branching ratios of 53% to a 2 p and 47% to a 0 Ž980.p w12x. However, we warn that h 2 Ž1870. f 2 p produces a mass distribution which mimics a 0 Ž980.h rather closely. The f 2 Ž1270. is almost at rest in the h 2 Ž1870. decay frame, with the result that the hp mass combination peaks just above a0 Ž980.; it can be separated from the D-wave decay h 2 Ž1870. a 0 p only by angular momentum analysis. In earlier publications on pp p 0p 0h w13x we have reported independent evidence for an I s 0 J P C s 2yq resonance at 2040 " 40 MeV with G s 190 " 40 MeV. These parameters agree closely with the h 2 Ž2030. observed here. Nonetheless, there is one difference. In Ref. w13x, a strong decay to f 2 Ž1270.h was observed. Here, the f 2 h signal is weaker than that for a 2 p . Its branching ratio has a sizable error, because of uncertainties in separating it from the much stronger signal due to h 2 Ž1870.. It seems likely that the f 2 h channel observed in Ref. w13x arises largely from the high mass tail of h 2 Ž1870.. Since it appears in Ref. w13x at the bottom end of the available phase space, this is possible and requires further investigation. Ref. w13x also reports evidence for a further h 2 Ž2300.. In an extensive analysis of pp data w14x, we have reported a pattern of straight-line trajectories of resonances as a function of s s M 2 for many J P. The slopes of those trajectories do not allow four qq states in the mass range from 1645 to 2300 MeV. The simplest interpretation in terms of qq states is that h 2 Ž1645. is the ground-state partner of p 2 Ž1670.,
™
™
™
™
Table 5 Branching ratios; column 3 shows values for present data; column 4 shows values corrected for all charges and for all decay modes of f 2 , a 2 and a0 Resonance
Ratio
Present data
Corrected
h 2 Ž1645. h 2 Ž1870. h 2 Ž1870. h 2 Ž1870. h 2 Ž2030. h 2 Ž2030. h 2 Ž2030.
BRŽ a 0 p .rBRŽ a2 p . BRŽ a 2 p .rBRŽ f 2 h . BRŽ a 0 p .rBRŽ f 2 h . BRŽhs .rBRŽ f 2 h . BRw a 2 p x Ls0 rBRw a2 p x Ls2 BRŽ a 0 p .rBRw a 2 p x Ls2 BRŽ f 2 h .rBRw a2 p x Ls2
0.21 " 0.03 0.22 " 0.03 0.85 " 0.05 0.42 " 0.07 0.74 " 0.17 0.37 " 0.08 0.43 " 0.15
0.041 " 0.006 1.27 "0.17 0.95 "0.06 0.35 "0.06 0.74 "0.17 0.072 " 0.016 0.074 " 0.026
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
26
the h 2 Ž2030. is the first radial excitation close to f 4 Ž2050., and h 2 Ž2300. is the second radial excitation close to f 4Ž2300.. This leaves h 2 Ž1870. as an extra state. A hybrid with these quantum numbers is predicted in this mass range by Isgur et al. w15x in the flux-tube model. A feature of this model is that hybrids are expected to decay dominantly to a qq pair with L s 1. That is in accord with the strong decay modes observed here for h Ž1870. to f 2 Ž1270.h and a2 Ž1320.p . Barnes et al. w16x predicted a2 p and f 2 p widths of 160 and 20 MeV respectively for a hybrid at 1875 MeV. In a recent calculation, the decay branching ratio a 2 p : f 2 h s 3.9 is predicted for a hybrid at 2000 MeV by Page, Swanson and Szczepaniak w17x. Both these predictions are distinctly higher than observed here. What branching ratio BRw a2 prf 2 h x is to be expected for a qq state? For a2 p , there are three times the number of charge states as for f 2 h. If one integrates over h 2 Ž1870. and the available phase space for decays to f 2 h and a 2 p , then a 2 p is also favoured by a phase space factor of 3.4. For h 2 Ž2030., the corresponding factor is 2.5. However, one should expect a form factor expŽya q 2 . in the amplitude, where q is the momentum of the decay products in the rest frame of h 2 Ž1870. or h 2 Ž2030.. If a s R 2r6 and R 2 s 0.6 fm, a , 1.5 GeVy2 ; this form factor reduces the enhancement of the a 2 p decay to a factor 1.8 for h 2 Ž1870. and 2.1 for h 2 Ž2030.. If h 2 Ž1870. is a non-strange qq state Žas would be natural for strong production from pp ., it will couple only to the non-strange component of the h. Hence, for a qq state, one expects the branching ratio a 2 prf 2 h , 3 = 1.8r0.64 s 8.5, compared with the observed value 1.27 " 0.17. The strong decay of h 2 Ž1870. to f 2 h suggests a hybrid component which couples preferentially to the h via the f 2 h decay mode. The branching ratio w a 2 p x Ls0rf 2 h for h 2 Ž2030. is 10.0 " 1.8, compared with 9.7 predicted for a qq state. There is no evidence for decays of h 2 Ž2030. to f 2 h with L s 2; that is to be expected for the low momenta available to this decay, because of strong suppression by the centrifugal barrier. We now turn to the J P C s 2qq components in hpp , channels Ž10. and Ž11.. In Ref. w1x, a 2qq component was observed at a beam momentum of 1940 MeVrc and was attributed to a state with mass
'
2135 MeV, G s 250 MeV. However, the reservation was made that this interpretation depended on the assumption that a single 2q resonance is present. The present data make it clear that the situation is more complicated. At low beam momenta, 900–1200 MeVrc, there is a strong component which optimises at a mass of 1930 " 10 MeV with G s 250 MeV. These parameters are compatible with the f 2 Ž1920. which we have observed in an analysis of data on pp , hh and hhX w14x. We interpret it as the same state as observed by GAMS w18x and VES w19x, though with a width larger than they reported. Ref. w14x found three further 2q states f 2 Ž2020., f 2 Ž2230. and f 2 Ž2300.. In the present data, as the beam momentum rises, the average mass fitted to the 2q hpp component increases steadily and reaches 2150 " 20 MeV at a beam momentum of 1940 MeVrc, in agreement with Ref. w1x. The relative decays to a2 Ž1320.p and f 2 Ž1270.h also vary with momentum. It appears that the 2q component is a mixture of the f 2 ’s reported in Ref w14x. The data may be fitted well at all momenta with f 2 Ž1920. and f 2 Ž2230. and that is the fit given here. However, we do not regard that combination as unique; it is quite possible that all four f 2 contribute. Consequently, we withdraw the earlier claim to observe an f 2 Ž2135. w1x. In summary, we are able to demonstrate the presence of three I s 0 J P s 2yq mesons in the mass range 1645–2030 MeV, of which only two are likely to be qq states. This leaves the h 2 Ž1870. as an ‘extra’, i.e. non-qq state, hence a candidate for a hybrid. Several decay modes are established for these resonances. Acknowledgements We thank the Crystal Barrel collaboration for the use of these data. We wish to thank the technical staff of the LEAR machine group and of all the participating institutions for their invaluable contributions to the success of the experiment. We acknowledge financial support from the British Particle Physics and Astronomy Research Council ŽPPARC.. The St. Petersburg group wishes to acknowledge financial support from PPARC and INTAS grant RFBR 95-0267.
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x
J. Adomeit et al., Zeit. Phys. C 71 Ž1996. 227. D. Barberis et al., Phys. Lett. B 413 Ž1997. 217. D. Barberis et al., Phys. Lett. B 413 Ž1997. 225. X A.V. Anisovich et al., Data on pp p 0p 0 , hh and hh from 600 to 1940 MeVrc, Nucl. Phys. A, in press. C.A. Baker et al., Phys. Lett. B 449 Ž1999. 114. A.V. Anisovich et al., A J P C s 0yq Enhancement at the f 0 Ž980.h Threshold, submitted to Phys. Lett. B. B.S. Zou, D.V. Bugg, Phys. Rev. D 48 Ž1993. R3948. A.V. Anisovich et al., Phys. Lett. B 468 Ž1999. 304. Particle Data Group, Eur. Phys. J. C 3 Ž1998. 1. D.V. Bugg, V.V. Anisovich, A. Sarantsev, B.S. Zou, Phys. Rev. D 50 Ž1994. 4412.
™
27
w11x D.Barberis et al., submitted to Phys. Lett. B. w12x M. Karch et al., Zeit. Phys. C 54 Ž1992. 33. w13x A.V. Anisovich et al., Phys. Lett. B 452 Ž1999. 180; Nucl. Phys. A 651 Ž1999. 253. w14x A.V. Anisovich et al., Analysis of pp pypq, p 0p 0 , hh X and hh from Threshold to 2.5 GeVrc, Phys. Lett. B, to be published. w15x N. Isgur, R. Kokoski, J. Paton, Phys. Rev. Lett. 54 Ž1985. 869. w16x T. Barnes, F.E. Close, P.R. Page, E.S. Swanson, Phys. Rev. D 55 Ž1997. 4157. w17x P.R. Page, E.S. Swanson, A. P Szczepaniak, Phys. Rev. D 59 Ž1999. 034016. w18x D. Alde et al., Phys. Lett. B 241 Ž1990. 600. w19x S.I. Beladidze et al., Zeit. Phys. C 54 Ž1992. 367.
™
Physics Letters B 477 Ž2000. 19–27
Three I s 0 J P C s 2yq mesons A.V. Anisovich c , C.A. Baker a , C.J. Batty a , D.V. Bugg b, A.R. Cooper b, C. Hodd b, V.A. Nikonov c , A.V. Sarantsev c , V.V. Sarantsev c , B.S. Zou b,1 a
c
Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK b Queen Mary and Westfield College, London E1 4NS, UK St. Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg district, 188350, Russia
Received 12 January 2000; received in revised form 11 February 2000; accepted 14 February 2000 Editor: L. Montanet
Abstract
™
High statistics data on pp hp 0p 0p 0 at nine beam momenta from 900 to 1940 MeVrc require the presence of three I s 0, J P C s 2yq mesons with masses and widths Ži. M s 1645 " 6Žstat. " 20Žsyst. MeV, G s 200 " 7 " 20 MeV, Žii. M s 1860 " 5 " 15 MeV, G s 250 " 25 " 25 MeV, Žiii. M s 2030 " 5 " 15 MeV, G s 205 " 10 " 15 MeV. The h 2 Ž1645. and h 2Ž2030., together with h 2 Ž2300. observed earlier, may be interpreted as a sequence of expected qq states. The h 2 at 1860 MeV appears to be an extra state, hence a candidate for a hybrid. Decay branching ratios of all three states to a 2 Ž1320.p , f 2 Ž1270.h and a0 Ž980.p are established. The h 2 at 1860 MeV decays dominantly to f 2h and a 2p , as predicted for a hybrid. The h 2 Ž2030. decays dominantly to a2p with orbital angular momentum L s 2 and slightly less strongly to a 2p with L s 0. q 2000 Elsevier Science B.V. All rights reserved.
An earlier publication described evidence for two J P C s 2yq mesons h 2 Ž1645. and h 2 Ž1870. w1x. These have since been confirmed in the WA102 experiment in decays to hpp w2x and KKp w3x. Here we present data taken by the Crystal Barrel collaboration at nine p momenta. Statistics are higher than in the earlier publication by a factor ; 7 per momentum. They confirm the presence of h 2 Ž1645. and h 2 Ž1870. and provide evidence for a third nearby h 2 at 2030 MeV. This makes too many states in a narrow mass range for all of them to be qq. First we describe briefly the experimental set-up and the selection of data. The p beam interacts in a
1 Now at the Institute for High Energy Physics, Beijing 100039, China.
liquid hydrogen target at the centre of the Crystal Barrel detector. Two veto counters 20 cm downstream of the target provide an interaction trigger. Charged particles are vetoed over 98% of the solid angle by multiwire chambers close to the target, hence providing an on-line trigger for neutral final states. Photons are detected over 98% of 4p solid angle in a barrel of 1380 CsI crystals; these crystals measure photons with high energy resolution and efficiency down to 20 MeV, and with an angular resolution of "20 mrad in azimuth and polar angle. The beam intensity was typically 2 = 10 5rs and the trigger rate typically 60rs. The off-line analysis follows the procedures of Ref. w1x; minor refinements in data selection have been made, based on a Monte Carlo simulation of background channels using GEANT. Events are se-
0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 0 0 . 0 0 2 3 6 - 7
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
20
Table 1 Numbers of events, reconstruction efficiency e , cross sections and background levels ŽBG., as a function of beam momentum. The second column shows the total available centre of mass energy Momentum CM Events e ŽMeVrc. Ž%. Energy ŽMeV.
s Žhp 0p 0p 0 . BG Ž m b. Ž%.
600 900 1050 1200 1350 1525 1642 1800 1940
35.9"2.2 36.1"2.2 33.7"1.0 36.1"1.1 34.4"1.0 40.0"1.2 38.6"1.2 31.9"1.0 27.5"0.8
1962 2050 2098 2149 2201 2263 2304 2360 2409
5062 24487 15709 35127 26379 21339 25394 28200 31388
0.132 0.128 0.130 0.127 0.124 0.119 0.116 0.113 0.111
7.7 7.7 7.7 7.7 8.0 8.4 8.9 9.6 9.3
lected containing exactly 8 photon showers, and 8C kinematic fits are made to 4p 0 , hp 0p 0p 0 and hhp 0p 0 . Events fitting h 3p 0 with confidence level
™
CL above 5% are used. A small number of events from hh , h 3p 0 Ždiscussed elsewhere w4x. are rejected within the mass range M Ž3p 0 . s 520 to 575 MeV; likewise, a few events due to p 0hX , hX hp 0p 0 w4x are rejected within the range M Žhp 0p 0 . s 928 to 988 MeV. Further cuts to reduce backgrounds are: Ži. CLŽ4p 0 . - 0.01%, Žii. CLŽh 3p 0 . ) CLŽhhp 0p 0 .. The Monte Carlo simulation reproduces the observed confidence level distribution down to the cut at 5%. Table 1 shows the numbers of events at each beam momentum, reconstruction efficiencies, overall cross sections and estimated backgrounds. The simulation estimates a surviving background of 7.7% at low beam momenta, increasing slightly at the higher momenta. The background comes largely from 4p 0 Žtypically 1.1%., from v 3p 0 , v p 0g after loss of one photon Ž3.0%., and from 5p 0 after the loss of 2 photons Ž2.5%..
™
™
Fig. 1. Mass distributions at a beam momentum of 1800 MeVrc for Ža. 3p , Žb. and Žd. pph , Žc. ph and Že. pp . Histograms show the maximum likelihood fit. In Žb., the h 2 Ž2030. is not included in the fit, in Žd. it is. Žf. shows the pph mass distribution for events where the ph mass lies in the range 1320 " 55 MeV; here, h 2 Ž2030. in included in the fit.
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
The physics of these competing channels has been studied; for example, results from 4p 0 are reported in w5x. Combinatorics are high in the background channels and events lie close to a phase space distribution. The Monte Carlo simulation shows that backgrounds surviving in the h 3p 0 channel, after cuts, are likewise close to phase space. This background is included in the amplitude analysis. Fig. 1 displays mass distributions, summed over all combinations, at a beam momentum of 1800 MeVrc. There are obvious enhancements due to a0 Ž980. and a2 Ž1320. in Fig. 1Žc., due to f 2 Ž1270. in Fig. 1Že. and f 1Ž1285. in Fig. 1Žd.. At this beam momentum, the signal from h Ž1440. is barely visible in the mass projection of Fig. 1Žd.. It is more clearly visible at lower beam momenta; a separate publication w6x discusses it and evidence for a related threshold enhancement in f 0 Ž980.h. The h 2 Ž1645. and h 2 Ž1870. are not distinguishable in Fig. 1Žb., because of the combinatorics. The histograms show the maximum likelihood fit described below. There is, however, a clear shoulder at 2030 MeV in Fig. 1Žb. which we find to be due to a third 2yq resonance. Fig. 1Žb. shows a fit without this component and Fig. 1Žd. a fit including it. Data at 1940 and 1642 MeVrc Žnot shown. provide similar evidence. Fig. 1Žf. shows the hpp mass projection after selection of events containing an hp combination within one half-width of h 2 Ž1320.; the shoulder at 2030 MeV is somewhat more prominent with this selection, though statistically weaker. The data are fitted by the maximum likelihood method to the following channels:
™ f Ž 1270. a Ž 980. , ™ a Ž 1320. s , ™ a Ž 980. s , ™ f Ž 1285. p , ™ h Ž 1440. p , ™ Xp , X ™ f Ž 980. h , ™ h Ž 1645. p , ™ h Ž 1870. p , ™ h Ž 2030. p , ™ f Ž 1920. p ,
pp
2
0
Ž 2.
0
Ž 3.
0
Ž 11 . Ž 12 .
2
2
Here s stands for the broad component of the pp S-wave amplitude, as parametrised by Zou and Bugg w7x; X stands for a 0yq threshold enhancement in f 0 Ž980.h w6x. The treatment of amplitudes is identical to that described in detail in Ref. w1x. In outline, the decay of each resonance is described fully in terms of helicity states. However, we average over the angular dependence of the production process, since there are too many partial waves to allow a complete description. Charge conjugation invariance requires that angular distributions are symmetric forwardbackward in the centre of mass system; the experimental data obey this constraint within the errors. An incoherent phase space background is included with magnitude adjusted to the background levels of Table 1. The method of calculation of integrated cross sections, the correction for observed rate dependence and the assessment of errors are described in Ref. w8x. Resulting integrated cross sections are shown in Fig. 2. Smooth curves are drawn through those for individual channels; errors for each channel at indi-
Ž 4. Ž 5. Ž 6.
2
Ž 7.
2
Ž 8.
2
Ž 9.
2
™ f Ž 2220. p , ™ p Ž 1670. h .
Ž 1.
2
1
21
Ž 10 .
™
Fig. 2. Points with errors show the integrated cross sections for present data, uncorrected for branching fractions of h gg and p 0 gg . Smooth curves are drawn through cross sections for individual channels.
™
22
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
surviving f 2 Ž1270. comes mostly from the strong high mass tail of h 2 Ž1870.. The fit also requires that the a2 Ž1320. contribution is strong for the mass region around 2030 MeV. At lower masses around 1645 MeV, Fig. 3Žc. shows that the a 2 Ž1320. signal grows in strength, due to h 2 Ž1645.. There is in addition a horizontal band close to a f 0 Ž980.. It is discussed at length in Ref. w6x. The detailed evidence for h 2 Ž1645. and h 2 Ž1870. has been discussed in Ref. w1x. Ultimately it depends on the amplitude analysis, which accommodates all combinations. Results obtained here confirm all features of this evidence very closely with an increase in statistics of a factor 7 at most momenta and with data at nine momenta rather than 2. We therefore concentrate attention on the masses and widths of these resonances and on additional decay channels which were not visible earlier. Fig. 4 shows the variation of log likelihood with the mass and width of each resonance. Curves are asymmetric about the optimum for the width; we find that 1rG is closer to a symmetric distribution. Full curves show results summed over all beam momenta and Table 2 collects
Fig. 3. Scatter plots of M Žpp . vs. M Žhp . for three ranges of M Žhpp .: Ža. 1945–2115 MeV, centred on h 2 Ž2030., Žb. 1775– 1945 MeV over h 2 Ž1870. and Žc. 1560-1750, centred on h 2 Ž1645..
vidual momenta are typically "Ž0.5–0.8. m b. There is an additional systematic error of "5% in all cross sections, arising from uncertainty in the target length; this has no effect on fitted physics, since it is common to all momenta and all channels. In order to display the essential characteristics of h 2 Ž1645., h 2 Ž1870. and h 2 Ž2030., Fig. 3 shows scatter plots of M Žpp . vs. M Žhp . for combinations within ranges of hpp mass centred on each resonance. The strongest f 2 Ž1270. signal appears as a horizontal band in Fig. 3Žb., and is due to decays of h 2 Ž1870.; this resonance has a decay mode appearing less strongly in a2 Ž1320. hp . Around 2030 MeV, Fig. 3Ža. shows that the f 2 Ž1270. becomes weaker, with constructive interference where the bands cross; the amplitude analysis requires that the
™
Fig. 4. Ssylog likelihood vs. Ža. the mass of h 2 Ž1645., Žb. the mass of h 2 Ž1870., Žc. the width of h 2 Ž1645., Žd. the width of h 2 Ž1870., Že. the mass of h 2 Ž2030., Žf. the width of h 2 Ž2030.. Curves are normalised to 0 at the minima. In Že., the dashed curve is for decays only to a 2 p with Ls 0 and the full curve for all decays. In Žb., broken curves shows data at individual momenta 900 MeVrc Ždashed., 1050 MeVrc Ždotted. and 1200 MeVrc Žchain curve.; the full curve is summed over all momenta.
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27 Table 2 Parameters of J P C s 2yq resonances Resonance
Mass ŽMeV.
Width ŽMeV.
h 2 Ž1645. h 2 Ž1870. h 2 Ž2030.
1645"6Žstat."20Žsyst. 1860"5Žstat."15Žsyst. 2030"5Žstat."15Žsyst.
200"7"25 250"25q50 y35 205"10"25
fitted resonance parameters. Our definition of log likelihood is such that it increases by 0.5 for a one standard deviation change in one parameter. In the table, systematic errors cover variations which are observed as ingredients in the amplitude analysis are varied. Our intention is that the systematic errors should be compounded linearly with statistical errors. As an example, for h 2 Ž1870., the width lies within the range 190–325 MeV. Fig. 4Žb. illustrates optima observed at individual beam momenta 900– 1200 MeVrc, where the h 2 Ž1870. signal is largest Ž; 30% of the integrated cross section in Fig. 2.. However, the width of h 2 Ž1870. is not particularly well determined, because this resonance overlaps significantly with both h 2 Ž1645. and h 2 Ž2030.. The h 2 Ž2030. decays to a 2 Ž1320.p with both orbital angular momenta L s 0 and 2, with the latter dominant. Fig. 4Že. shows mass scans for L s 0 Ždashed curve. and for the sum of all decay modes Žfull curve.. We attribute the slight difference between these two curves to the effect of the centrifugal barrier, which inhibits the dominant L s 2 decay at low masses. Data at all five beam momenta from 1350 to 1940 MeVrc show a distinct optimum within "15 MeV of 2030 MeV. We now present evidence for the quantum numbers of h 2 Ž2030.. Several qq states are expected near this mass with quantum numbers up to J P s 4q. States with J P s 1q or 3q cannot be formed with orbital angular momentum l s 0 in the production process, since this would require initial states with J P C s 1yq or 3yq, which are forbidden for qq. In testing these two possibilities, the amplitude analysis includes a Blatt-Weisskopf centrifugal barrier for production with l s 1. Fig. 5 shows the variation of log likelihood with mass for each J P, summed over data at five beam momenta from 1350 to 1940 MeVrc. For J P C s 2yq there is an optimum close to the shoulder observed in Figs. 1Žb. and Žd.. All other J P give fits which are worse by at least 20
23
standard deviations, taking account of the difference in the number of fitted parameters. The fit for J P C s 0yq shows a broad dip, but with poor log likelihood. This behaviour may be understood from a simulation of cross-talk between 0y and 2y. The hypothesis 0yq a 2 p and f 2 h requires decays with L s 2. These depend on three terms having the same angular dependence as the dominant L s 2 decay of h 2 Ž2030. to a2 p and f 2 h , but with different Clebsch-Gordan coefficients multiplying each term. If both 0y and 2y are included in the fit, ) 95% of the signal fits as 2y. For J P C s 4qq, there is no peak near the well known f 4Ž2050. w9x; the change in log likelihood with increasing mass is associated with the L s 3 centrifugal barrier for decays to a 2 p and f 2 h. Quantum numbers 1qq, 3qq, 1yq or 3yq Žthe latter two exotic. give poor fits with very small fitted contributions and no optimum as a function of mass. The 2qq possibility is absorbed into channels Ž10. and Ž11., which are discussed separately below. We now discuss decay modes. In Ref. w1x, the f 2 Ž1870. could be identified clearly only in decays to f 2 Ž1270.h , although there was tentative evidence for decays to a 2 Ž1320.p . With the much higher statistics now available, the latter decay mode is identified clearly, and also a decay mode to a 0 Ž980.p with L s 2. There is also evidence which will be discussed for decays to hs . Table 3 shows ratios of the magnitudes of coupling constants L fitted to all of these channels at individual beam momenta. The
™
Fig. 5. The variation of Ssylog likelihood with mass for alternative J P assignments to h 2 Ž2030..
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
24
Table 3 Ratios of coupling constants for decay modes of h 2 Ž1645., h 2 Ž1870. and h 2 Ž2030.. Errors are given in parentheses Momentum ŽMeVrc.
1645 < < L1645 a p rL a p
1870 < < L1870 a p rL f h
1870 < < L1870 a p rL f h
1870 < Lhs < rL1870 f h
2030 < L 2030 < a p , Ls0 rL a p , Ls2
2030 < L 2030 < a p rL a p , Ls2
900 1050 1200 1350 1525 1642 1800 1940
1.46Ž.40. 0.81Ž.22. 0.57Ž.19. 0.59Ž.15. 0.60Ž.19. 0.91Ž.14. 0.84Ž.09. 0.64Ž.08.
0.30Ž.06. 0.25Ž.04. 0.31Ž.03. 0.35Ž.04. 0.30Ž.16. 0.33Ž.11. 0.32Ž.07. 0.08Ž.12.
1.10Ž.09. 1.10Ž.06. 1.07Ž.04. 1.05Ž.05. 1.07Ž.08. 1.09Ž.09. 0.94Ž.10. 1.07Ž.16.
2.26Ž.35. 1.57Ž.29. 1.19Ž.24. 1.96Ž.26. 1.39Ž.52. 1.75Ž.48. 1.45Ž.45. 0.76Ž.57.
0.22Ž.06. 0.13Ž.08. 0.20Ž.06. 0.23Ž.05. 0.34Ž.06.
0.24Ž.07. 0.16Ž.05. 0.20Ž.04. 0.37Ž.08. 0.36Ž.07.
mean phaseŽrad.
0.77Ž.05. y0.60
0.30Ž.02. q3.92
1.07Ž.03. q4.92
1.53Ž.14. q0.70
0.24Ž.03. y1.11
0.23Ž.03. 1.36
0
2
2
2
0
2
™
amplitude for h 2 Ž1870. a0 Ž980.p , as an example, is expressed in the form: f s L BW Ž 1870 . FL Ž 980 . B2 Ž k . P2m Ž cos u , f . .
Ž 13 . Here BW Ž1870. is a relativistic Breit-Wigner amplitude of constant width, 1rŽ M 2 y s y iM G ., for the h 2 Ž1870. in hpp ; FLŽ980. is a Flatte´ form for the a0 Ž980. in hp w10x. The factor B2 Ž k . is a BlattWeisskopf centrifugal barrier factor for the decay h 2 Ž1870. a 0 Ž980.p in terms of the momentum k in the decay of each h 2 : B2 Ž k . s k 2rw k 2 Ž k 2 q Ry2 . q Ry4 x1r2 , with R s 0.8 fm. The Legendre polynomial P2m describes the dependence on decay angles u , f for helicity m of h 2 Ž1870.. Ratios of coupling constants in Table 3 show good consistency between momenta for decays to f 2 Ž1270.h , a2 Ž1320.p and a0 Ž980.p . There are some fluctuations for the less well identified decay to hs . The difficulty here is cross-talk with the strong a 2 Ž1320. s and a 0 Ž980. s channels, making this decay mode harder to identify. For h 2 Ž2030., there is again reasonable consistency for ratios of coupling constants between different momenta. The phases of different decays may be different, because of multiple scattering in the final state, generating strong interaction phases; these phases are likewise consistent within errors between momenta, and average values are shown in the last line of Table 3. For the principal decay modes of h 2 Ž1645. a 2 p and h 2 Ž1870. f 2 h , quantum numbers J P C s 2yq are definitely required, as shown in Ref. w1x. How-
™
™
™
2
2
2
0
2
ever, a question is whether one can be confident that all other decays are really to be attributed to h 2 Ž1870. and h 2 Ž1645.. Could they alternatively be due to nearby 1qq or 0yq resonances of similar mass and width? For h 2 Ž1870., the answer is firmly that decays to a 2 Ž1320.p and a0 Ž980.p require quantum numbers 2yq. Log likelihood values for the alternative 1qq or 0yq assignments are considerably worse, as shown in Table 4. This demonstrates that the decay angular distributions follow the expected forms for 2y; the amplitude analysis is sensitive to this, though we cannot readily display evidence graphically because of the combinatorics. Likewise, for h 2 Ž2030., log likelihood excludes alternative quantum numbers 3q, 1q and 0y for decays to a 2 p and a 0 p . A further check has been made, following procedures developed in Ref. w5x. In this check, different Žwrong. angles have been substituted for the correct ones; when this is done, the coupling Table 4 Changes in log likelihood, summed over beam momenta, when alternative quantum numbers are substituted for decays of the resonances Substitution
a2 p
a0 p
hs
1q Ž1870. 0y Ž1870. 1q Ž1645. 0y Ž1645. 3q Ž2030. 1q Ž2030. 0y Ž2030.
y285 y144 – – y99 y133 y174
y187 y326 y34 q4 y39 y52 y75
y58 q5 – – – – –
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
constants for the decay modes in question fall to low values, showing that the amplitude analysis can recognise the correct angular dependence. For h 2 Ž1645., quantum numbers 2y are significantly preferred over 1q for decays to a 0 p . However, there is no discrimination against the possibility of quantum numbers 0y for decays to a 0 Ž980.p . Likewise, for the resonance at 1860 MeV, it is not possible to distinguish clearly between the quantum numbers 2y and 0y for decays to hs . Despite this, there is circumstantial evidence that all decays of h 2 Ž1870. really correspond to the same resonance. Fig. 2 shows that its cross section varies strongly with beam momentum. The cross section for the hs decay follows this trend and suggests that h 2 Ž1870. decays at least partially to hs with L s 2. Branching ratios are as shown in Table 5, after integration over the whole phase space for each resonance and its decays. The third column shows the branching ratios observed in the present hp 0p 0p 0 data. The last column shows branching ratios corrected for all charges and also for all decay modes of f 2 , a 2 and a 0 . In this evaluation, we use values of the Particle Data Group w9x for decay branching ratios of f 2 Ž1270. and a 2 Ž1320.. For a 0 Ž980 . , we use the ratio BR w a 0 Ž980 . hp xrBRw a0 Ž980. all x s 0.76, obtained from the Flatte´ formula fitted to Crystal Barrel data on pp hp 0p 0 data at rest w10x. The WA102 group has just reported branching ratios for h 2 Ž1870. to a 2 p and a 0 Ž980. which are much larger than those found here, though with large errors w11x. The larger values and errors arise via strong destructive interference between h 2 Ž1645. and h 2 Ž1870. in their fit. We allow interferences between
™ ™
™
25
these two resonances, but find that they have only a small effect within our quoted errors. The Cello collaboration reported the first evidence for h 2 Ž1870. in gg hpp , with branching ratios of 53% to a 2 p and 47% to a 0 Ž980.p w12x. However, we warn that h 2 Ž1870. f 2 p produces a mass distribution which mimics a 0 Ž980.h rather closely. The f 2 Ž1270. is almost at rest in the h 2 Ž1870. decay frame, with the result that the hp mass combination peaks just above a0 Ž980.; it can be separated from the D-wave decay h 2 Ž1870. a 0 p only by angular momentum analysis. In earlier publications on pp p 0p 0h w13x we have reported independent evidence for an I s 0 J P C s 2yq resonance at 2040 " 40 MeV with G s 190 " 40 MeV. These parameters agree closely with the h 2 Ž2030. observed here. Nonetheless, there is one difference. In Ref. w13x, a strong decay to f 2 Ž1270.h was observed. Here, the f 2 h signal is weaker than that for a 2 p . Its branching ratio has a sizable error, because of uncertainties in separating it from the much stronger signal due to h 2 Ž1870.. It seems likely that the f 2 h channel observed in Ref. w13x arises largely from the high mass tail of h 2 Ž1870.. Since it appears in Ref. w13x at the bottom end of the available phase space, this is possible and requires further investigation. Ref. w13x also reports evidence for a further h 2 Ž2300.. In an extensive analysis of pp data w14x, we have reported a pattern of straight-line trajectories of resonances as a function of s s M 2 for many J P. The slopes of those trajectories do not allow four qq states in the mass range from 1645 to 2300 MeV. The simplest interpretation in terms of qq states is that h 2 Ž1645. is the ground-state partner of p 2 Ž1670.,
™
™
™
™
Table 5 Branching ratios; column 3 shows values for present data; column 4 shows values corrected for all charges and for all decay modes of f 2 , a 2 and a0 Resonance
Ratio
Present data
Corrected
h 2 Ž1645. h 2 Ž1870. h 2 Ž1870. h 2 Ž1870. h 2 Ž2030. h 2 Ž2030. h 2 Ž2030.
BRŽ a 0 p .rBRŽ a2 p . BRŽ a 2 p .rBRŽ f 2 h . BRŽ a 0 p .rBRŽ f 2 h . BRŽhs .rBRŽ f 2 h . BRw a 2 p x Ls0 rBRw a2 p x Ls2 BRŽ a 0 p .rBRw a 2 p x Ls2 BRŽ f 2 h .rBRw a2 p x Ls2
0.21 " 0.03 0.22 " 0.03 0.85 " 0.05 0.42 " 0.07 0.74 " 0.17 0.37 " 0.08 0.43 " 0.15
0.041 " 0.006 1.27 "0.17 0.95 "0.06 0.35 "0.06 0.74 "0.17 0.072 " 0.016 0.074 " 0.026
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
26
the h 2 Ž2030. is the first radial excitation close to f 4 Ž2050., and h 2 Ž2300. is the second radial excitation close to f 4Ž2300.. This leaves h 2 Ž1870. as an extra state. A hybrid with these quantum numbers is predicted in this mass range by Isgur et al. w15x in the flux-tube model. A feature of this model is that hybrids are expected to decay dominantly to a qq pair with L s 1. That is in accord with the strong decay modes observed here for h Ž1870. to f 2 Ž1270.h and a2 Ž1320.p . Barnes et al. w16x predicted a2 p and f 2 p widths of 160 and 20 MeV respectively for a hybrid at 1875 MeV. In a recent calculation, the decay branching ratio a 2 p : f 2 h s 3.9 is predicted for a hybrid at 2000 MeV by Page, Swanson and Szczepaniak w17x. Both these predictions are distinctly higher than observed here. What branching ratio BRw a2 prf 2 h x is to be expected for a qq state? For a2 p , there are three times the number of charge states as for f 2 h. If one integrates over h 2 Ž1870. and the available phase space for decays to f 2 h and a 2 p , then a 2 p is also favoured by a phase space factor of 3.4. For h 2 Ž2030., the corresponding factor is 2.5. However, one should expect a form factor expŽya q 2 . in the amplitude, where q is the momentum of the decay products in the rest frame of h 2 Ž1870. or h 2 Ž2030.. If a s R 2r6 and R 2 s 0.6 fm, a , 1.5 GeVy2 ; this form factor reduces the enhancement of the a 2 p decay to a factor 1.8 for h 2 Ž1870. and 2.1 for h 2 Ž2030.. If h 2 Ž1870. is a non-strange qq state Žas would be natural for strong production from pp ., it will couple only to the non-strange component of the h. Hence, for a qq state, one expects the branching ratio a 2 prf 2 h , 3 = 1.8r0.64 s 8.5, compared with the observed value 1.27 " 0.17. The strong decay of h 2 Ž1870. to f 2 h suggests a hybrid component which couples preferentially to the h via the f 2 h decay mode. The branching ratio w a 2 p x Ls0rf 2 h for h 2 Ž2030. is 10.0 " 1.8, compared with 9.7 predicted for a qq state. There is no evidence for decays of h 2 Ž2030. to f 2 h with L s 2; that is to be expected for the low momenta available to this decay, because of strong suppression by the centrifugal barrier. We now turn to the J P C s 2qq components in hpp , channels Ž10. and Ž11.. In Ref. w1x, a 2qq component was observed at a beam momentum of 1940 MeVrc and was attributed to a state with mass
'
2135 MeV, G s 250 MeV. However, the reservation was made that this interpretation depended on the assumption that a single 2q resonance is present. The present data make it clear that the situation is more complicated. At low beam momenta, 900–1200 MeVrc, there is a strong component which optimises at a mass of 1930 " 10 MeV with G s 250 MeV. These parameters are compatible with the f 2 Ž1920. which we have observed in an analysis of data on pp , hh and hhX w14x. We interpret it as the same state as observed by GAMS w18x and VES w19x, though with a width larger than they reported. Ref. w14x found three further 2q states f 2 Ž2020., f 2 Ž2230. and f 2 Ž2300.. In the present data, as the beam momentum rises, the average mass fitted to the 2q hpp component increases steadily and reaches 2150 " 20 MeV at a beam momentum of 1940 MeVrc, in agreement with Ref. w1x. The relative decays to a2 Ž1320.p and f 2 Ž1270.h also vary with momentum. It appears that the 2q component is a mixture of the f 2 ’s reported in Ref w14x. The data may be fitted well at all momenta with f 2 Ž1920. and f 2 Ž2230. and that is the fit given here. However, we do not regard that combination as unique; it is quite possible that all four f 2 contribute. Consequently, we withdraw the earlier claim to observe an f 2 Ž2135. w1x. In summary, we are able to demonstrate the presence of three I s 0 J P s 2yq mesons in the mass range 1645–2030 MeV, of which only two are likely to be qq states. This leaves the h 2 Ž1870. as an ‘extra’, i.e. non-qq state, hence a candidate for a hybrid. Several decay modes are established for these resonances. Acknowledgements We thank the Crystal Barrel collaboration for the use of these data. We wish to thank the technical staff of the LEAR machine group and of all the participating institutions for their invaluable contributions to the success of the experiment. We acknowledge financial support from the British Particle Physics and Astronomy Research Council ŽPPARC.. The St. Petersburg group wishes to acknowledge financial support from PPARC and INTAS grant RFBR 95-0267.
A.V. AnisoÕich et al.r Physics Letters B 477 (2000) 19–27
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x
J. Adomeit et al., Zeit. Phys. C 71 Ž1996. 227. D. Barberis et al., Phys. Lett. B 413 Ž1997. 217. D. Barberis et al., Phys. Lett. B 413 Ž1997. 225. X A.V. Anisovich et al., Data on pp p 0p 0 , hh and hh from 600 to 1940 MeVrc, Nucl. Phys. A, in press. C.A. Baker et al., Phys. Lett. B 449 Ž1999. 114. A.V. Anisovich et al., A J P C s 0yq Enhancement at the f 0 Ž980.h Threshold, submitted to Phys. Lett. B. B.S. Zou, D.V. Bugg, Phys. Rev. D 48 Ž1993. R3948. A.V. Anisovich et al., Phys. Lett. B 468 Ž1999. 304. Particle Data Group, Eur. Phys. J. C 3 Ž1998. 1. D.V. Bugg, V.V. Anisovich, A. Sarantsev, B.S. Zou, Phys. Rev. D 50 Ž1994. 4412.
™
27
w11x D.Barberis et al., submitted to Phys. Lett. B. w12x M. Karch et al., Zeit. Phys. C 54 Ž1992. 33. w13x A.V. Anisovich et al., Phys. Lett. B 452 Ž1999. 180; Nucl. Phys. A 651 Ž1999. 253. w14x A.V. Anisovich et al., Analysis of pp pypq, p 0p 0 , hh X and hh from Threshold to 2.5 GeVrc, Phys. Lett. B, to be published. w15x N. Isgur, R. Kokoski, J. Paton, Phys. Rev. Lett. 54 Ž1985. 869. w16x T. Barnes, F.E. Close, P.R. Page, E.S. Swanson, Phys. Rev. D 55 Ž1997. 4157. w17x P.R. Page, E.S. Swanson, A. P Szczepaniak, Phys. Rev. D 59 Ž1999. 034016. w18x D. Alde et al., Phys. Lett. B 241 Ž1990. 600. w19x S.I. Beladidze et al., Zeit. Phys. C 54 Ž1992. 367.
™