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Observation of the J P C = 0-+ (1800) and J = 2-+ 2 (1880) mesons in the - decay
PC

P. Eugenio,1 A. I. Ostrovidov,1 G. S. Adams,2 T. Adams,1 Z. Bar-Yam,3 J. M. Bishop,4 V. A. Bodyagin,5, D. S. Brown,6 , N. M. Cason,4 S. U. Chung,7 J. P. Cummings,2 K. Danyo,7 S. P. Denisov,8 V. Dorofeev,8 J. P. Dowd,3 X. L. Fan,6 A. M. Gribushin,5 R. W. Hackenburg,7 M. Hayek,3 , J. Hu,2 , § E. I. Ivanov,9 D. Joffe,6 W. Kern,3 E. King,3 O. L. Kodolova,5 V. L. Korotkikh,5 M. A. Kostin,5 J. Kuhn,2 , ¶ V. V. Lipaev,8 J. M. LoSecco,4 M. Lu,2 , J. J. Manak,4 J. Napolitano,2 M. Nozar,10 , § C. Olchanski,7 , § T. K. Pedlar,6, A. V. Popov,8 D. I. Ryabchikov,8 L. I. Sarycheva,5 K. K. Seth,6 N. Shenhav,3 , X. Shen,10 , W. D. Shephard,4 N. B. Sinev,5 D. L. Stienike,4 J. S. Suh,7 , §§ S. A. Taegar,4 A. Tomaradze,6 I. N. Vardanyan,5 D. P. Weygand,10 D. B. White,2 H. J. Willutzki,7 , M. Witkowski,2 and A. A. Yershov5 (E852 Collaboration)
3

Department of Physics, Florida State University, Tal lahassee, Florida 32306 Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180 Department of Physics, University of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747 4 Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 5 Nuclear Physics Institute, Moscow State University, Moscow, Russian Federation 119899 6 Department of Physics, Northwestern University, Evanston, Il linois 60208 7 Department of Physics, Brookhaven National Laboratory, Upton, New York 11973 8 Institute for High Energy Physics, Protvino, Russian Federation 142284 9 Department of Physics, Idaho State University, Pocatel lo, ID 83209 10 Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606 (Dated: February 14, 2007)
2

1

A partial-wave analysis of the reaction - p - p at 18 GeV/c has b een p erformed on a data sample of 4,400 events obtained by Brookhaven exp eriment E852. The J P C = 0-+ (1800) state with a mass of 1876 ± 18 ± 16 MeV/c2 and a width of 221 ± 26 ± 38 MeV/c2 is observed in the ao (980) and fo (1500) decay modes. The J P C = 2-+ 2 (1880) meson with a mass of 1929 ± 24 ± 18 MeV/c2 and a width of 323 ± 87 ± 43 MeV/c2 is seen decaying through a2 (1320) . Both states are p otential candidates for non-exotic hybrid mesons.
PACS numbers: 12.39.Mk, 11.80.Et, 13.25-k, 13.75.Gx

DRAFT 1.5
non-q q resonances are expected to have "exotic" quantum ¯ numbers J P C = 0-- , 0+- , 1-+ , 2+- , ... which are forbidden for ordinary mesons. Other non-q q states may have ¯ non-exotic J P C and, therefore, may mix with normal q q ¯ mesons. In this case, identification of the hybrid nature of a non-exotic state becomes difficult and requires, at a minimum, to study its branching ratios into various decay channels. In the framework of the flux-tube model, a J P C = -+ 0 hybrid meson is expected to have a mass of 1.92.0 GeV/c2 [1]. However, the same model also predicts that the second radial excitation of a pion should have approximately the same mass. Moreover, their total widths are expected to be similar and on the order of 230240 MeV/c2 [1]. Only branching ratios are predicted to be different. While no particular decay mode is expected to dominate the decay of the radial excitation (with partial width being the largest), the hybrid state should predominantly decay through the fo (1300) channel. The (1800) state was discovered in the 3 decay by SERPUKHOV-080 group in 1981[2]. Since then, its existence was confirmed by VES and E852 experiments. VES has seen the (1800) in the + - - , K + K - - , - , and - final states[3­5]. E852 experiment has observed this state in the + - - channel[6]. It is in-

This letter presents the results of a partial-wave analysis for the reaction - p - p at the beam momentum of 18 GeV/c. The data were obtained by the experiment E852 at Brookhaven National Laboratory. The primary goal of the E852 experiment was to search for non-q q mesons which are predicted to exist in QCD. ¯ In addition to multiquark states (q q q q , etc.) and quark¯¯ less glueballs (g g g ), hybrid mesons with excited gluonic degrees of freedom (q q g ) should also exist. Some of the ¯



Deceased Present address: Department of Physics, University of Maryland, College Park, MD 20742 Permanent address: Rafael, Haifa, Israel § Present address: TRIUMF, Vancouver, BC, V6T 2A3, Canada ¶ Present address: Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Present address: Department of Physics, University of Oregon, Eugene, Oregon 97403 Present address: Lab oratory for Nuclear Studies, Cornell University, Ithaca, NY 14853 Permanent address: Institute of High Energy Physics, Beijing, China §§ Present Address: Department of Physics, Kyungp o ok National University, Daegu, Korea


2 teresting to note that the measurements of the (1800) mass can be separated into two groups: one group with the mass around 1780 MeV/c2 (fo (980) , fo (1300) , Ko (1430)K ), and another group at 1860 MeV/c2 ( , - , - ). It is possible that two different states were actually observed. The history of the 2 (1880) resonance is much shorter. It was first observed in 2001 in the Crystal Barrel data[7] through its a2 (1320) decay, together with a higher mass 2 (2000) state in its a0 (980) decay[8]. These states were soon confirmed by E852 in the f1 [9] and [10] decay modes. A hint of the 2 (1880) presence was seen earlier by VES in their analysis[3], which is the most relevant to our case due to similarities in the production mechanisms.

(a)

(1800)

(b)

a o (980)

(c)

(d) f o (1500)

a 2 (1320)

Data sample

The data sample was collected by experiment E852 at the Multi-Particle Spectrometer facility at Brookhaven National Laboratory (BNL). 18.3 GeV/c2 - beam and a liquid hydrogen target were used. A description of the experimental apparatus can be found in Ref.[11]. More details about the analysis can be found on our website[12]. An online trigger requirement was to detect 3 forwardgoing charged tracks and 1 charged recoil track. 265 million events of this type were recorded during the 1995 run of the experiment. The following data selection cuts were applied after event reconstruction: (1) There should be a fully reconstructed beam track, two negative ( - ) and one positive ( + ) downstream tracks and one charged recoil track (p) originating at a common vertex (only the direction of the recoil track was measured). In addition, four photons should be detected. (2) The vertex should be within the target volume. (3) The square of the missing mass calculated from the beam and downstream tracks should be within 1 (GeV/c2 )2 from that of a proton. (4) The direction of the missing momentum vector is required to be within ±20 in azimuth from the direction of the recoil track. (5) The total energy deposit from large-angle photons should be 20 MeV to reject events with soft o 's from decays of recoil baryon isobars. (6) Fiducial volume cut at the edges of the detector. During the next stage of the event selection, a SQUAW kinematic fitter[13] was used to do a 3-C fit to select the + - o - p event sample. One pair of photons should be coming from a o decay, another pair of photons should originate from an decay, and the missing mass should be consistent with a proton. Events with a confidence level of greater than 5% were selected after the fit. At the same time, events were fitted to other hypotheses. The most important competing hypothesis is o + - o - p because the probability of 4 photons coming from a decay of 2 o is much greater than in the

(e)

(f)

FIG. 1: All plots except of (a) are for the final - event sample. a) Mass of + - o combination for a fraction of the + - o - events; b) Mass of - ; c) Mass of - ; d) Mass of ; e) cosine of the angle in the Gottfried-Jackson frame ( - as analyzer); f ) angle in the Gottfried-Jackson frame. Dashed lines show quality-of-the-fit comparison based on the final PWA results.

o case. Any event which had a competing hypothesis's confidence level better than 10% was rejected. Approximately 180,000 + - o - p events were selected at this stage. Fig. 1(a) shows the + - o mass distribution for a fraction of this sample. The meson is clearly seen in the 3 mass distribution, with a background level of less than 10%. Next, all events in which masses of both + - 0 combinations are above 650 MeV/c2 were rejected to reduce the background from + - o decay. At the last step, the final kinematic fit to the reaction - p - p was done with a 5% confidence level cut. This resulted in about 4,400 - events in the final data sample. Distributions for the final event sample are shown in Fig.1(b-f ). The 3-body invariant mass M ( ) peaks at 1.8 GeV/c2 . Among 2-body masses, M ( ) shows large contribution of the ao (980) channel and, to a much


3 smaller extent, the a2 (1320) decay. In turn, M ( ) has a structure at slightly below 1.5 GeV/c2 . As we found out from PWA, this structure corresponds to the J P C = 0++ isoscalar meson fo (1500). Some preliminary conclusions can be drawn from the angular distributions in the Gottfried-Jackson frames. The symmetric form of the cos(GJ ) distribution hints to the absence of any strong odd-even spin interference in the data likely caused by the dominance of either even-spin or odd-spin partial waves. The flat T Y distribution indicates that contribution from the pro jection waves with a non-zero pro jection M of the total spin J is likely to be small.
0-+ ao (980) S-wave
2000 1800 1600 1000 1400 1200

0 f o(1500) S-wave
-+

Events

1000 800 600 400

Events
2 2.1 2.2 2.3 2.4 2.5

1200

800

600

400

200 200 0 1.5 1.6 1.7 1.8 1.9 0 1.5 1.6 1.7 1.8 1.9

2

2.1 2.2 2.3 2.4 2.5

mass, GeV

mass, GeV 2 ao (980) D-wave
-+ 1800

Partial Wave analysis
1200

2 a2 (1320) S-wave
-+

Detailed description of the Partial Wave formalism used in this analysis can be found in Ref.[14]. Analysis was performed in the framework of an isobar model, with a sequential decay of a 3-body wave into an isobar and a final particle followed by a 2-body decay of the isobar into 2 other final particles. Each partial wave is characterized by the total spin, parity and C-parity J P C , by pro jection M of the total spin and reflectivity of the system, by the orbital momentum L between the isobar and the bachelor particle, and by the type of isobar. Notation M is omitted below because PWA studies indicated that only M = 0+ waves are present in this sample. Positive value of reflectivity indicates that production is dominated by natural parity exchange such as or Pomeron exchanges. All waves with J 3 and L 3 had been tried in the fits. Odd-spin waves 1++ and 3++ were found to be insignificant in contrast to even-spin waves 0-+ and 2-+ . Among isobars, the ao (980) , a2 (1320) , fo (1300) , f2 (1270) , and fo (1500) combinations had been considered. We didn't find any significant contribution from the fo (1300) and f2 (1270) modes which may be caused by small branching ratio of these isobars into . Simple Breit-Wigner parameterizations with PDG values were used to describe the ao (980) and a2 (1320) isobars. Parameters of the fo (1500) state are not well known. Use of 1507 MeV PDG mass did not result in a good fit which is not surprising considering the position of the peak in Fig.1(d). To determine best parameters for our case we did a systematic scan of the fo (1500) mass and width in 10 MeV steps. The best overall likelihood was achieved at M = 1480 ± 25 MeV and = 120+50 MeV -30 which is in very good agreement with conclusions from VES[3]. At the end, only 4 partial waves have remained in the final fit: 0-+ a0 (980) S -wave, 0-+ f0 (1500) S -wave, 2-+ a2 (1320) S -wave, and 2-+ a0 (980) D-wave. In addition, an isotropic non-interfering background wave was introduced in the fit to absorb the non- background. The background wave was at the level from 5% to 15% from the total intensity over the mass range of the fit. Quality of the fit was judged by comparing data dis-

1600
1000

1400 1200

600

Events
2 2.1 2.2 2.3 2.4 2.5

Events

800

1000 800 600 400

400

200

200
0 1.5 1.6 1.7 1.8 1.9

mass, GeV

0 1.5 1.6 1.7 1.8 1.9

2

2.1 2.2 2.3 2.4 2.5

mass, GeV

FIG. 2: Intensities for the following partial waves: a) 0-+ ao (980) S -wave; b) 0-+ fo (1500) S -wave; c) 2-+ a2 (1320) S -wave; a) 2-+ ao (980) D-wave. Smooth lines show results of the resonant Breit-Wigner fits.

tributions with the ones predicted by applying the fitted spin-density matrix and experimental Monte Carlo acceptance to the Monte Carlo phase space events. Predicted distributions for the final PWA fit are shown as dashed lines in Fig.1. Despite a very small number of partial waves, all data distributions are reasonably well described by the PWA fit as one can see from this figure. The final PWA fit was done in the mass range 1.52.5 GeV/c2 in 50 MeV/c2 steps for all values of the momentum transfer t. Its results are shown in Fig.2 for intensities of the partial waves, and in Fig.3 for some of the phase differences between them. Both 0-+ waves (Fig.2(a,b)) peak at 1.8 GeV/c2 indicating the presence of the (1800) meson in the data. Another peak is seen at 1.9 GeV/c2 in the 2-+ a2 (1320) S -wave (Fig.2(c)). It corresponds to the 2 (1880) state. Finally, the 2-+ a0 (980) D-wave (Fig.2(d)) is structureless but it accounts for the ma jority of events above 2 GeV/c2 . The phase of the 0-+ a0 (980) S -wave is rising in relation to the supposedly non-resonant phase of the 2-+ a0 (980) D-wave (Fig.3(a)). This indicates the resonant behavior of the former confirming the presence of the (1800) state. The phase difference of the same wave relative to the 2-+ a2 (1320) S -wave is more complex. It raises below 1.8 GeV/c2 and falls above this mass. Such


4
(0 S ao - 2 D ao)
-+ -+
3 3

(0 S ao - 2 S a2)
-+ -+

Phase difference, rad

1

Phase difference, rad

2

2

1

0

0

-1

-1

-2

-2

wave is isotropic in all angles, which makes it highly ambiguous with the isotropic background term over limited Dalitz plot. Without reliable and stable phase measurement, our claim about the fo (1500) decay mode of (1800) is based solely on the Breit-Wigner shape of the wave intensity. Assuming the same resonance in both 0-+ waves, a single-pole fit of their intensities was performed. It has 2 /dof = 1.2 with the following parameters for the (1800) state: M = 1876 ± 18 ± 16 MeV/c2 , = 221 ± 26 ± 38 MeV/c With these parameters fixed, the 2-+ a2 wave and its phase difference wave were fitted. This fit has 2 /dof = in Fig.2(c) and Fig.3(b). The 2 (1880) lowing parameters:
2

-3 1.5 1.6 1.7 1.8 1.9

2

2.1 2.2 2.3 2.4 2.5

-3 1.5 1.6 1.7 1.8 1.9

2

2.1 2.2 2.3 2.4 2.5

mass, GeV

mass, GeV

FIG. 3: Phase difference b etween the following partial waves: a) 0-+ ao (980) S -wave and 0-+ ao (980) D-wave. b) 0-+ ao (980) S -wave. and 2-+ a2 (1320) S -wave. Smooth lines show results of the resonant Breit-Wigner fits.

intensity of the with the 0-+ ao 1.1 and is shown state has the fol2

behavior is expected for 2 single-pole resonant waves with different pole positions. This speaks in favor of the presence of the 2 (1880) resonance. To confirm this conclusion, mass-dependent 2 fits were performed. Each of the resonant waves was parameterized with a single-pole relativistic Breit-Wigner form including Blatt-Weiskopf barrier factors. To accomodate for the subthreshold behavior of the a2 and fo waves at low mass, integration over the available width of decay isobars (a2 , ao , and fo ) was used in the parameterization. At first, only the intensities of two 0-+ waves were fitted to find the parameters of the (1800) state. When the poles in the ao and fo waves were treated independently, the fit resulted in a mass of M = 1882 ± 19 MeV/c2 and a width of = 236 ± 42 MeV/c2 for ao , and M = 1865 ± 25 MeV/c2 and = 191 ± 55 MeV/c2 for fo . This fit has 2 /dof = 0.83. The results are shown as smooth curves in Figs.2(a,b). As an illustration, the obtained phase of the 0-+ ao S -wave is plotted against a presumanbly constant phase of the non-resonant 2-+ ao D-wave in Fig.3(a) to confirm the resonant nature of the former. Unfortunately, the phase of the 0-+ fo (1500) wave cannot be measured reliably. Due to a limited phase space for near-threshold decays, the interference region of the 0-+ fo (1500) and 2-+ a2 (1320) waves is outside of Dalitz plot. At the same time, the other important interference term of the fo wave with the 0-+ ao (980)

M = 1929 ± 24 ± 18 MeV/c2 , = 323 ± 87 ± 43 MeV/c

The 2 (1880) parameters from Crystal Barrel are 1880 ± 20 MeV/c2 and 255 ± 45 MeV/c2 correspondingly[7]. The fitted Breit-Wigner shapes were integrated to determine the predicted number of events for each state. The following branching ratio was obtained: B R[ (1800) fo (1500) , fo ] = 0.48 ± 0.17 B R[ (1800) ao (980) , ao ] When the amplitudes of both (1800) waves were mixed together with an unknown branching ratio instead of being treated independently, and a maximum likelihood PWA fit was performed to determine it, a value of 0.40 was obtained. This branching ratio is significantly higher than the value of 0.08 ± 0.03 determined by VES[3] or the value of 0.030 ± 0.014 from Crystal Barrel[7]. Note that all values are given without correction for a fo (1500) branching ratio which is expected to be small. In summary, we conducted the partial-wave analysis of the reaction - p - p at 18 GeV/c2 on a sample of 4,400 events. We observe the 0-+ (1800) meson decaying through ao (980) and fo (1500) . We also observe the 2-+ 2 (1880) meson in its a2 (1320) decay. This research was supported in part by the U.S. Department of Energy, the U.S. National Science Foundation, and the Russian Ministry of Science and Education.

[1] T. Barnes, F. E. Close, P. R. Page, and E. S. Phys. Rev. D 55, 4157 (1997). [2] SERPUKHOV-080 Collab oration, G. Bellini et Rev. Lett. 48, 1697 (1981). [3] VES Collab oration. D. V. Amelin et al., Phys. 59, 976 (1996). [4] VES Collab oration. D. V. Amelin et al., Phy

Swanson, al.. Phys. At. Nucl. s. Lett. B

356, 595 (1995). [5] VES Collab oration. D 337, 219 (1994). [6] E852 Collab oration. S. 072001 (2002). [7] A. V. Anisovich et al., [8] A. V. Anisovich et al.,

. V. Amelin et al., Phys. Lett. B U. Chung et al., Phys. Rev. D 65, Phys. Lett. B 500, 222 (2001). Phys. Lett. B 517, 273 (2001).


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[9] E852 Collab oration. J. Kuhn et al., Phys. Lett. B 595, 109 (2004). [10] E852 Collab oration. M. Lu et al., Phys. Rev. Lett. 94, 032002 (2005). [11] E852 Collab oration. S. U. Chung et al., Phys. Rev. D 60, 092001 (1999), and references therein. [12] More details ab out this analysis are available at http://hadron.physics.fsu.edu/etaetapi/. [13] "SQUAW kinematic fitting program", Group A programming note P-126, Univ. of California, Berkley (1968), (unpublished). [14] S. U. Chung, "Formulas for Partial-Wave Analysis", Rep ort BNL-QGS-93-05, Brookhaven National Lab oratory (1993), (unpublished); J. P. Cummings and D. P. Weygand, "The New BNL Partial Wave Analysis Programs", Rep ort BNL-64637, Brookhaven National Lab oratory (1997), (unpublished).