Study of the Glueball Candidate Fj(2220) at CLEO

PROCEEDINGS SUPPLEMENTS ELSEVIER Nuclear Physics B (Proc. Suppl.) 82 (2000) 33%343 www.dsevier.ni/locate/npe

Study of the glueball candidate fJ(2220) at CLEO

Hans P. Paar a aPhysics Department 0319, University of California San Diego, 9500 Gilman Drive, La Jolla CA 92093-0319. (e-mail address: [email protected])

The CLEO detector at the Cornell e+e - storage ring CESR was used to search for the two-photon production of the glueball candidate fJ(2220) in its decay to K~K~ and 7r+Tr-. I present restrictive upper limits on the product of the two-photon width and the respective branching fraction [F77BK~K~]fj(2220 ) < 1.3 eV, 95% CL and [FT~BTr+Tr-]fj(2220) < 2.beV, 95% CL. When these two limits are combined to calculate a lower limit on the Stickiness, a measure of the two-gluon coupling relative to the two-photon coupling, a lower limit SFJ(2220) > 102, 95% CL is found. A new measure of this ratio of couplings is the Gluiness; a combined lower limit of Gfj(2220) > 66, 95% CL is found. These limits on the Stickiness and the Gluiness indicate that the fJ(2220) is likely to have substantial neutral patton or glueball content.

1. INTRODUCTION while spin 0 is unlikely [7]. QCD predicts (using lattice calculations) that a tensor glueball exists The unequivocal demonstration that glueballs and that it should have a mass near 2.2 GeV [8]. exist would prove the existence of a new form A pure glueball will couple to photons only of matter. In this report I describe investiga- through its sea quarks. Therefore its two-photon tions [1-3] into the nature of the glueball candi- coupling is expected to be weak. The absence of date fj (2220). two-photon production of the fj (2220) would thus The fj (2220) was discovered in radiative J/¢ be a strong indication of a glueball nature of the decay [4] by the Mark III Collaboration at PEP fj (2220). A search for the two-photon production in the early 80's. Although the fJ(2220) has since of the fj (2220), decaying into K~K~ or 7r+Tr- was been observed in hadronic collisions[5], its pro- performed using the CLEO detector at the Cot- duction in radiative J/g, decay has only recently nell e+e - storage ring CESR. Below I describe been confirmed by the BES Collaboration who the detector and event simulation in Sec. 2, the have observed [6] the fJ(2220) in radiative J/¢ analysis procedures and results for the K~K~ and decay in four decay channels Qr+Tr-, p~, K+K -, 7r+Tr- final states in Sec. 3 and Sec. 4 respectively, and K~K~). The production in glue-rich radiative and the interpretation in Sec. 5. J/¢ decay, its narrow total width, and its flavor independent coupling (as evidenced by its similar branching fraction for final states that con- 2. DETECTOR AND tain non-strange or strange particles [6]) make the EVENT SIMULATION fj (2220) a promising candidate for a glueball. Be- cause the fj (2220) is not near a q~ meson and is The CLEO detector[9] is a general pur- narrow, it is not expected to mix with q~ states pose detector that provides charged particle and might therefore even be a candidate for a tracking, precision electromagnetic calorimetry, pure glueball (a hadron in which a/l valence par- charged particle identification, and muon detec- tons are gluons). The experiments favor a spin 2 tion. Charged particle detection over 95% of the assignment to the fj (2220) but spin 4 is possible solid angle is provided by three concentric wire chambers in a magnetic field of 1.5 T giving a mo-

mentum resolution ap/p = 0.5% at p = 1 GeV. and 2. There is a strong enhancement near the The driftchambers are surrounded by a time of ( m Kso,m Kso ) point. The m~r+7r_ mass resolution flight system and a CsI based electromagnetic near the K so mass is 3.3MeV. KsKo so events are calorimeter giving an energy resolution aE/E = selected by requiring both pion-pair masses to be 4% for 100 MeV electromagnetic showers. A su- within a circle of radius 10 MeV centered on the perconducting coil and muon detectors surround ( m~co"~s , mvo,,s) point and their K~K~ pair mass is the calorimeter. Three redundant triggers pro- formed. Fig. 2 shows the K~K~ pair mass distri- vide efficient registration of two- and four-prong bution. It has a significant f'2(1525) signal but no events. The CESR ring operates at a center-of- visible fj (2220) signal. mass energy of approximately 10.6 GeV. The re- The mass region near the fj (2220) is shown in sults in this paper are based upon 3.0 fb -1 of data detail in Fig. 3. In the absence of a signal, an up- for the K~K~ final state and 4.8fb -1 of data for per limit is set as follows. The background is fit- the 7r+Tr- final state. ted with a linear function from 2.05 to 2.35 GeV, The event simulation uses uses the BGMS [10] excluding a safely large +40 MeV region centered formalism for the event generation and GEANT on 2234 MeV. This gives an average background for the detector simulation down to the detec- of 1.8 ± 0.3 events per 10MeV. The signal re- tor component level. The trigger simulation and gion is determined by maximizing the ratio c 2/B the event reconstruction use this information to where ~ is the fraction of the signal and B the ex- determine the detector response. Photon form- pected number of background events within that factors based upon vector-meson dominance with region. This leads to a signal region of ±18 MeV a mass my = 768.5 MeV are used. The spin of the (centered on 2234 MeV) with c = 70%. fj (2220) is taken to be 2. Mass and width of the There are four events within the signal re- fj (2220) were obtained by averaging MarkIII [4] gion while the background is estimated to be 6.5 and BES [6] results: mfj (2220) = 2234 ± 6 MeV events. The standard PDG technique [7] for ex- and Ffj(2220) = 19 ± llMeV. A Breit-Wigner tracting an upper limit gives 4.9 events, 95% CL. line shape was used. The simulated data are pro- The curve in Fig. 3 is the sum of the background cessed through the same event reconstruction and and a signal of 4.9 events. From the simulation, analysis procedures as the real data. The trigger the detection efficiency is found to be 7.0% for simulation uses the raw data to determine which spin 2, helicity 0 and 15% for spin 2, helicity 2. triggers, if any, fired for a given event. With the ratio F~.r 2'2 : F.r.r 2'0 = 6 : 1 [11] an upper limit

3. THE KsKo os FINAL STATE [F~.r BK~K~]fj(2220 ) < 1.3eV, 95%CL (1)

The event selection required events to have ex- results. The upper limit can be specified without actly four tracks whose sum of charges is zero, to the assumption of a 6:1 ratio for helicity 2 and 0 have an event energy less than 6.0 GeV, to have as (0.52r~.r 2,° + 1.08F~.r2'2)BK~K~ < 1.3eV at the transverse component of the vector sum of 95% CL. the tracks to be less than 0.2 GeV, and to sat- When the mass and the width of the f3 (2220) isfy at least one of the three triggers. Events axe varied by 6 and llMeV respectively (one are required to have 7r+Tr- pairs whose vertices standard deviation), the upper limit ranges from have a separation in the plane perpendicular to 1.2 to 1.8 eV. The upper limit includes the effects the beam of at least 5 mm. The momenta of the of systematic uncertainties in the trigger (8%), four tracks at their respective vertices are used the tracking (7%), the event selection (7%), and to calculate two pion-pair masses [m~r+~r-]l and the background subtraction (16%). Other sources [m~r+~r- L. A legoplot of the pion-pair masses of systematic uncertainties, such as the photon is shown in Fig. 1. There are two entries per form-factor used in the simulation, are negligi- event corresponding to the exchange of labels 1 ble. Because of its similarity to the fJ(2220), the H.P Paar/Nuclear Physics B (Proc. Suppl,) 82 (2000) 337-343 339

3010'2sr/-00t .... J .... I .... ] .... E ....

40 > :i OT- 30 .... " ......

! ¢ :>O LU 20 ....

10- """ ...... " o 2.1o 2.15 2.20 2.25 2.30 2.35 O" InKs KS (GeV) o' 'tS-' llUm .... o.5o~'~ • 0.523 + - 0.493 m ('n'+Tr-)2 0"49~.4'03~ • 493 5 0.473 rn (~-+,~-), Figure 3. K~K~ pair mass distribution near the mass of the fJ(2220). The arrows indicate the signal region. The solid line is the sum of a fit to the background and a signal that corresponds to Figure 1. [mTr+~r-], versus [m +7i_]2. Each the 95% CL upper-limit of 4.9 events• event has two entries corresponding to exchange of the labels 1 and 2.

~(1525) decaying into K~K~ was analyzed as a check, using the same analysis procedures as for 50 '''1''''1 the fJ(2220). A value for [F~BK~K~]~(1525) was measured that is within one standard devia- 40 tion of the PDG [7] value of 22 eV. ~> (D 4. THE lr+~r - FINAL STATE O 30

© The event selection required events to have ex- CL actly two tracks whose sum of charges is zero, to 2O t have an event energy less than 6.0 GeV, and to © > © have the transverse component of the vector sum of the tracks to be less than 0.5 GeV. Events are vetoed if energy in the calorimeter not associated with either track is larger than 0.5 GeV or if ei-

1.0 1.5 2.0 2.5 3.0 ther track is identified as an electron or a muon. If E/p, the ratio of a track's energy deposition in the calorimeter and its momentum measured in the drift chambers, is in the range 0.85 - 1.10, the track is identified as an electron. Muons are Figure 2. K~K~ pair mass distribution. identified by the muon detectors. Two-photon produced final states of charged particle pairs are selected (and backgrounds from 340 H.P. Paar /Nuclear Physics B (Proc. Suppl.) 82 (2000) 337-343

16oo49e.OOl 2000 Bhabha scattering, muon pair production, and cosmic rays are suppressed) by requiring that the acolinearity of the two tracks is greater than 0.1. In addition, the acoplanarity is required to be less 1500 than 0.05. Acolinearity is the deviation from colinearity in three dimensions while acoplanarity is the deviation from colinearity in the plane trans- N 1000 verse to the beams 1. These last two requirements o are effective because the photon-photon center- w of-mass generally moves rapidly and at a small angle with respect to the beams. Events must 500 have satisfied at least one of the three triggers. The momenta of the two tracks are used to calculate a pion-pair mass m~r+zr_ assuming that 0 ,,,, I , , L I, ,, , I .... both particles are pions. A plot of mTr+~r_ in 2000 2100 2200 2300 2400 2500 Di-pion Mass (MeV) the mass region relevant for the fj (2220) is shown as the data points in Fig. 4. There is no evidence of an enhancement near the mass of the Figure 4. The 7r+Tr- invariant mass distribution fj(2220). A possible contribution from K+K - for the data in the region of the fj(2220). The is accounted for in the fit to the background hatched histogram is the expected signal shape described below. The contribution from pp is with arbitrary normalization. The solid curve is negligible due to the much larger photon-photon the sum of a fit to the background and a sig- center-of-mass energy W required for their pro- nal corresponding to the 95% CL upper limit on duction. There is no evidence of an enhance- F~B1r+zr- of 2.5 eV. In the insert the two curves ment near the mass of the fJ(2220). The mass are the background fit with and without this level distribution is fit with the sum of a signal and of signal added. a background assuming that there is no interfer- ence between the two. The signal shape is represented by a non-relativistic Breit-Wigner distribution with a mass m = 2231MeV [7] and a a standard deviation of 13% are observed in the width F = 23 MeV [7] convolved with the de- tracking trigger efficiency as function of the az- tector resolution of 12 MeV and is shown as the imuthal angle of the two tracks. These variations hatched histogram in Fig. 4. The background is are used to estimate a 13% systematic uncertainty represented by a third order polynomial that is due to the trigger. Data and simulation are com- fit to the mass region 2000 - 2500 MeV exclud- pared to determine smaller systematic uncertain- ing the region 2200 - 2268MeV. The fit gives ties of 2% per track from track reconstruction ef- a signal of -103 :t= 77 events with a X2 = 35.6 ficiency, 3% from the requirement on the energy for 36 degrees of freedom. From the simulation, deposition in the calorimeter, 3% from the trans- the detection efficiencies for helicity 0 and 2 are verse momentum requirement, 2% each from the found to be 13.1% and 26.9% respectively. For acolinearity and acoplanarity requirements, 5% a ratio [11] 6:1 for helicity 2 and helicity 0, the from the E/p requirement, and 4% from the muon efficiency is 24.9%. veto. The total systematic uncertainty is the sum Although simulations show no azimuthal de- in quadrature of the above sources and is 15%. pendence for the trigger efficiency, variations with An upper limit is obtained by only allowing for a positive number of signal events (N) in the standard PDG technique [7]. Uncertainties in the 1 acolinearity = arccos (-I#all#21) and acoplanarity = (_~~ mass and the width of the fj (2220) are taken into arccos \ iffTlllffT2l] account by forming likelihood functions for N for H.P. Paar/Nuclear Physics B (Proc. Suppl.) 82 (2000) 337-343 341 a range of the resonance mass and width, span- fJ(2220). The quantum number t is the rela- ning ±2.53 in each. These functions are then tive angular momentum between the two gluons weighted with Gaussian probabilities for the mass or photons. Ne is a normalization factor that and width to obtain a likelihood function LN. is chosen such that the Stickiness is normalized The product of the two photon partial width and to 1 for the f2(1270) which has g = 0 and for rr+rr - branching fraction F~.r B1r+r~- is given by the ~ which has g = 1. Thus glueball content the product of N and P. Here P is the partial of a particle is defined relative to these parti- width used in the simulation divided by the prod- cles. A value of (2.2 ± 0.6) x 10 -5 is obtained uct of luminosity, cross-section and efficiency; P for r[J/¢ ~ 7fj(2220)] B[fj(2220) --+ K~K~] by is assumed to be Gaussian distributed. The like- combining results from Mark III [4] and BES [6]. lihood function LrB is obtained by numerical in- Using the upper limit (1), the branching frac- tegration in the two-dimensional space of N and tion B[fj(2220) ~ K~K~] cancels, and a lower P. From LrB and with the assumption that the limit Sfj(2220) > 82, 95% CL is found. Statisti- ratio F~.~~'~ : F~ 2'° = 6 : 1 [11] the upper limit cal and systematic uncertainties are incorporated into this result. Similarly, using the upper limit [F77 BTr%r-]fj(2220 ) < 2.5eV, 95%CL (2) (2) a lower limit Sfj (2220) > 73, 95% CL is found results. The solid line in the main portion of from the zr+7~- final state. The two lower limits Fig. 4 is the sum of the fit to the background and on the Stickiness from the K~K~ and the 7r+n - fi- a signal that corresponds to this upper limit. The nal states can be combined to obtain a single more mass region 2150-2310 MeV is shown enlarged in stringent lower limit Sfj(2220) > 102, 95% CL. the inset in Fig. 4 with the two curves represent- Other particles with large Stickiness are ing the background fit with and without this level (from largest to smallest) the fJ(1710) (S > of signal added. The upper limit can be specified 25, 95% CL), the f~2(1525) (S = 14.5 + 3.7), and without the assumption of a 6:1 ratio for helic- the ~' (S = 2.9 ± 0.3). Their Stickinesses are ity 2 and 0 as (0.53F~.r ~'° + 1.08F.~2'~)BTr+7 r- < shown in Fig. 5 together with the lower limit 2.5 eV at 95% CL. for the fJ(2220) as measured by CLEO. The fj (1710) is generally considered a glueball candi- 5. INTERPRETATION date. Without glueball content, the largest value The small upper limits (1) and (2) indicate that of Stickiness is obtained by assuming that a par- the fj (2220) is likely to have a significant glueball ticle consists of down and strange valence quarks content. To make this statement more quantita- and anti-quarks because the two-photon width tive, it is customary to use the Stickiness S, intro- depends upon the fourth power of the quark duced by Chanowitz [12]. Stickiness is a measure charges. This gives a Stickiness of about 10-15 as of the ratio of the two-gluon and the two-photon in the case of the ~ (1525), whose valence quarks coupling of a particle. It is defined as [here and are thought to be predominantly s~. Only the below, fj stands for fj (2220)] Stickiness of the fJ(2220) is comfortably above that value. I(fJIgg)l 2 If the fj (2220) has J = 4, F~ would be reduced Sfa = 1(fji77)12 (3) by a factor 5/9 owing to the factor 2J+l from the relationship a-r~ ec (2J + 1)FT.r while the accep- = Ne( tufa )='+1F(J/¢--+Tfj ) tance would change little. The Stickiness would P(fj ~ 77) (4) \kg/¢_,rfj go up by this factor and by an additional factor The parameter kj/¢_~fj is the energy (in the (mfj/kj/e~Tf J)4 ~ 80 from (4). J/¢ rest frame) of the photon produced in the The relation between production of a q~ reso- radiative J/¢ decay. The factor with the 21 + 1 nance in photon-photon collisions and in radiative in the exponent is a phase space factor that re- J/¢ decay has been studied [13] using a model moves trivial dependence upon the mass of the motivated by perturbative QCD as applied to the 342 H.P Paar/Nuclear Physics B (Proc. Suppl.) 82 (2000) 337-343

non-relativistic quark model. Results in Ref. 15 can be cast in the form of a ratio G (for Glui- ness) of quantities that are measured in radiative J/¢ decay and photon-photon interactions with Stlck;ness calculable prefactors 120 J Gfj = C(e4o) a B(J/¢ ~ 7fJ) 100 \mf, / r(fj-+-rT) (5) 4 80 with C = 1.3 x 10 -3 for jPC = 2++ and as = 4 0.37+0.03 evaluated at a mass scale of m L/2 [13]. 60 C is slightly different for particles other than the fj (C varies by less than 10% for masses in the 40 range 1.0 - 2.3GeV). Here too, the branching L fractions of the fj (2220) cancel in the ratio. As 20 opposed to Stickiness which is a relative measure, Gluiness is normalized and is expected to be near 0 1 for a q~ resonance within the precision afforded by the approximations made in Ref. 13. The BES result [6] and the CLEO upper limits can be used again canceling the fj (2220) branching fractions. Taking into account the uncertainties as in the Figure 5. The Stickiness of selected particles case of the Stickiness, 95% CL lower limits for the and of the fj (2220) as measured in CLEO. Gluiness of the fJ(2220) of 48 for the 7r+~r- final state and 66 for the combined 7r+~r- and K~K~ final states are obtained. The factor (e~) was cal- Glu;ness culated assuming equal amplitudes for ug and dd 100 and zero amplitude for s$. Other tensor particles with large Gluiness are (from largest to smallest) the fj(1710) (G > 40), the f2(1270) (G = 3.0), 75 and the i~2(1525) (G = 0.6). The Gluiness of selected particles is shown in Fig. 6 together with the lower limit for the fj(2220) as measured by 50 CLEO. The Gluiness of the ~(1525) is not large even though its valence quarks are thought to be predominantly s$ (compare with Stickiness).

25 In general, particles with a small two-photon

r~ width have also small radiative J/¢ branching rN ,¢ 7. fractions. Examples include radial and angular excitations. The fj (2220) can not have spin 1 because its production in radiative J/¢ dec&y shows that it has C = +1 while 7r+Tr- in an L = 1 state have C = -1. It is possible to construct a particle consisting of a superposition of ug, dd, and s$ Figure 6. The Gluiness of selected particles quarks and anti-quarks with coefficients such that and of the fj(2220) as measured in CLEO. its two-photon coupling is arbitrarily small. As this requires relations between unrelated quantities such a fortuitous cancelation may be consid- H.P. Paar/Nuclear Physics B (Proc. Suppl.) 82 (2000) 337-343 343 ered 'unlikely'. Thus the large lower limits on the Phys. Rev. Lett. 79, 3829 (1997). Stickiness and the Gluiness of the fj (2220) are an 2. M.S. Alam et al. (CLEO Collaboration), indication of substantial neutral patton or glue- Phys. Rev. Lett. 81, 3328 (1998). ball content. 3. D.W. Bliss, PhD thesis (1997), UC San Diego, La Jolla CA, unpublished. 6. CONCLUSION 4. R. Baltrusaitis et al (Mark III Collaboration), Phys. Rev. Lett. 56, 107 (1986). I present in this report evidence for the likely 5. Alde et al (GAMS Collaboration), Phys. Lett. glueball nature of the fJ(2220). The arguments B 177, 120 (1986); D. Aston et al (LASS Col- rest upon the restrictive upper limits of the prod- laboration), Phys. Lett. B 215, 199 (1988); uct of its two-photon width and its branching B.V. Bolonkin et al (MSS Collaboration), fraction: [F~BK~K~]fj(2220 ) < 1.3eV, 95%CL Nucl. Phys. B 309, 426 (1988). J.E. Augustin and [F~BTr+~r-]fj(2220 ) < 2.5eV, 95%CL. Us- et al (DM2 Collaboration), Phys. Rev. Lett. ing the fj (2220) production rate in glue-rich ra- 60, 2238 (1988). diative J/~ decay these upper limits lead to a 6. J.Z. Bai et al (BES Collaboration), Phys. large lower limit on its Stickiness Sf3(2220) > Rev. Lett. 76, 3502 (1996). 7. C. Caso et al (Particle Data Group), Eur. 102, 95% CL. Similarly, a large lower limit is cal- Phys. Jour. 3, 1 (1998). culated for the Gluiness Gfj (2220) > 66, 95% CL. 8. C. Michael, hep-lat/9605243 (1966) and ref- These large values for the Stickiness and the Glui- erences therein; C. Morningstar, M. Peardon, ness of the fj (2220) are difficult to understand if Phys. Rev. D 56, 4043 (1997) and references the valence partons of the fj (2220) are quarks and therein. anti-quarks only. Therefore, the fj (2220) is likely 9. Y. Kubota et al (CLEO Collaboration), Nucl. to have a substantial neutral parton or glueball Instr. Meth. A 320, 66 (1992). content. 10. V.M. Budnev et al (BGMS), Phys. Rep. 15C, Additional supporting evidence comes from the 181 (1975). fact the the fj (2220) has a small total width and 11. M. Poppe, Int. Jour. Mod. Phys. A1, 545 has a flavor independent coupling (as evidenced (1986). by its similar branching fractions for final states 12. M. Chanowitz in Ith International Workshop that contain non-strange or strange particles). Its on Photon-Photon Collisions, ed. R. Lander mass is close to the mass obtained in lattice QCD (World Scientific, Singapore, 1984). calculations for a tensor glueball. 13. F.E. Close, G.R. Ferrar, Z. Li, Phys. Rev. D 55, 5749 (1997). ACKNOWLEDGMENTS I gratefully acknowledge the effort of the CESR staff in providing the luminosity and running con- ditions necessary to make this measurement possible and my CLEO colleagues upon whose effort this work is based. This work was supported by the Department of Energy, the National Science Foundation, and others. Finally, I would like to thank the organizers of Photon 99 for their hospi- tality and a well-organized and fruitful conference held in beautiful Freiburg.

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