arXiv:hep-ex/0505073v2 24 May 2005
Observation of the hc(1P1) State of Charmonium
J. L. Rosner,1N. E. Adam,2J. P. Alexander,2K. Berkelman,2D. G. Cassel,2V. Crede,2
J. E. Duboscq,2K. M. Ecklund,2R. Ehrlich,2L. Fields,2R. S. Galik,2L. Gibbons,2
B. Gittelman,2R. Gray,2S. W. Gray,2D. L. Hartill,2B. K. Heltsley,2D. Hertz,2
C. D. Jones,2J. Kandaswamy,2D. L. Kreinick,2V. E. Kuznetsov,2H. Mahlke-Kr¨ uger,2
T. O. Meyer,2P. U. E. Onyisi,2J. R. Patterson,2D. Peterson,2E. A. Phillips,2
J. Pivarski,2D. Riley,2A. Ryd,2A. J. Sadoff,2H. Schwarthoff,2X. Shi,2M. R. Shepherd,2
S. Stroiney,2W. M. Sun,2D. Urner,2T. Wilksen,2K. M. Weaver,2M. Weinberger,2
S. B. Athar,3P. Avery,3L. Breva-Newell,3R. Patel,3V. Potlia,3H. Stoeck,3
J. Yelton,3P. Rubin,4C. Cawlfield,5B. I. Eisenstein,5G. D. Gollin,5I. Karliner,5
D. Kim,5N. Lowrey,5P. Naik,5C. Sedlack,5M. Selen,5E. J. White,5J. Williams,5
J. Wiss,5K. W. Edwards,6D. Besson,7T. K. Pedlar,8D. Cronin-Hennessy,9K. Y. Gao,9
D. T. Gong,9J. Hietala,9Y. Kubota,9T. Klein,9B. W. Lang,9S. Z. Li,9R. Poling,9
A. W. Scott,9A. Smith,9S. Dobbs,10Z. Metreveli,10K. K. Seth,10A. Tomaradze,10
P. Zweber,10J. Ernst,11A. H. Mahmood,11H. Severini,12D. M. Asner,13S. A. Dytman,13
W. Love,13S. Mehrabyan,13J. A. Mueller,13V. Savinov,13Z. Li,14A. Lopez,14
H. Mendez,14J. Ramirez,14G. S. Huang,15D. H. Miller,15V. Pavlunin,15B. Sanghi,15
I. P. J. Shipsey,15G. S. Adams,16M. Cravey,16J. P. Cummings,16I. Danko,16
J. Napolitano,16Q. He,17H. Muramatsu,17C. S. Park,17W. Park,17E. H. Thorndike,17
T. E. Coan,18Y. S. Gao,18F. Liu,18M. Artuso,19C. Boulahouache,19S. Blusk,19
J. Butt,19O. Dorjkhaidav,19J. Li,19N. Menaa,19R. Mountain,19R. Nandakumar,19
K. Randrianarivony,19R. Redjimi,19R. Sia,19T. Skwarnicki,19S. Stone,19J. C. Wang,19
K. Zhang,19S. E. Csorna,20G. Bonvicini,21D. Cinabro,21M. Dubrovin,21R. A. Briere,22
G. P. Chen,22J. Chen,22T. Ferguson,22G. Tatishvili,22H. Vogel,22and M. E. Watkins22
1Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637
2Cornell University, Ithaca, New York 14853
3University of Florida, Gainesville, Florida 32611
4George Mason University, Fairfax, Virginia 22030
5University of Illinois, Urbana-Champaign, Illinois 61801
6Carleton University, Ottawa, Ontario, Canada K1S 5B6
and the Institute of Particle Physics, Canada
7University of Kansas, Lawrence, Kansas 66045
8Luther College, Decorah, Iowa 52101
9University of Minnesota, Minneapolis, Minnesota 55455
10Northwestern University, Evanston, Illinois 60208
11State University of New York at Albany, Albany, New York 12222
12University of Oklahoma, Norman, Oklahoma 73019
13University of Pittsburgh, Pittsburgh, Pennsylvania 15260
14University of Puerto Rico, Mayaguez, Puerto Rico 00681
15Purdue University, West Lafayette, Indiana 47907
16Rensselaer Polytechnic Institute, Troy, New York 12180
17University of Rochester, Rochester, New York 14627
18Southern Methodist University, Dallas, Texas 75275
19Syracuse University, Syracuse, New York 13244
20Vanderbilt University, Nashville, Tennessee 37235
21Wayne State University, Detroit, Michigan 48202
22Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
(Dated: May 23, 2005)
The hc(1P1) state of charmonium has been observed in the reaction ψ(2S) → π0hc→ (γγ)(γηc)
using 3.08 million ψ(2S) decays recorded in the CLEO detector. Data have been analyzed both
for the inclusive reaction, where the decay products of the ηcare not identified, and for exclusive
reactions, in which ηcdecays are reconstructed in seven hadronic decay channels. We find M(hc) =
3524.4 ± 0.6 ± 0.4 MeV which corresponds to a hyperfine splitting ∆Mhf(1P) ≡
M(1P1) = +1.0 ± 0.6 ± 0.4 MeV, and B(ψ(2S) → π0hc) × B(hc→ γηc) = (4.0 ± 0.8 ± 0.7) × 10−4.
Over the past thirty years charmonium spectroscopy has provided valuable insight into
the quark–antiquark interaction of quantum chromodynamics (QCD). QCD-based potential
models have been quite successful in predicting masses, widths, and dominant decays of
several charmonium states. The central potential in most of these calculations is assumed
to be composed of a vector Coulombic potential (∼1/r) and a scalar confining potential
(∼r). Under these assumptions, the spin-spin interaction in the lowest order is finite only for
L = 0 states. It leads to the hyperfine splittings ∆Mhf(nS) ≡ M(n3S1)−M(n1S0) between
spin-triplet and spin-singlet S-wave states of charmonium, which have been measured as
∆Mhf(1S) = M(J/ψ)−M(ηc) = 115±2 MeV , ∆Mhf(2S) = M(ψ(2S))−M(η′
43±3 MeV [1, 2]. It also leads to the prediction that the hyperfine splitting ∆Mhf(?M(3PJ)?−
M(1P1)) for P-wave states should be zero. Higher-order corrections are expected to provide
no more than a few MeV deviation from this result [3, 4, 5]. Lattice QCD calculations 
predict ∆Mhf(1P) = +1.5 to +3.7 MeV, but with uncertainties at the few-MeV level. Larger
values of ∆Mhf(1P) could result if the confinement potential had a vector component or if
coupled channel effects were important. In order to discriminate between these possibilities,
it is necessary to identify the hc(1P1) state and to measure its mass to O(1 MeV) as the
mass of the3PJcentroid is very well known, ?M(3PJ)? = 3525.36±0.06 MeV ,
In this Letter we report the successful identification of hcin the isospin-violating reaction
e+e−→ ψ(2S) → π0hc, hc→ γηc, π0→ γγ.(1)
Two methods are used: one in which the ηc decays are reconstructed (exclusive), which
has an advantage in signal purity, and the other in which the ηcis measured inclusively,
which has larger signal yield. Together these approaches provide a result of unambiguous
significance, and allow a precise determination of the mass of hcand the branching fraction
product BψBh, where Bψ≡ B(ψ(2S) → π0hc) and Bh≡ B(hc→ γηc). Theoretical estimates
of the product BψBhvary by nearly two orders of magnitude, (0.5 − 40) × 10−4[4, 5].
The Crystal Ball Collaboration at SLAC searched for hcusing the reaction of Eq. (1)
but were only able to set a 95% confidence upper limit BψBh < 16 × 10−4in the mass
range M(hc) = (3515 − 3535) MeV . The FNAL E760 Collaboration searched for hc
in the reaction p¯ p → hc → π0J/ψ, J/ψ → e+e−, and reported a statistically significant
enhancement with M(hc) = 3526.2±0.15±0.2 MeV, Γ(hc) ≤ 1.1 MeV . The measurement
was repeated twice by the successor experiment E835 with ∼2× and ∼3× larger luminosity,
but no confirming signal for hcwas observed in hc→ π0J/ψ decay .
A data sample consisting of 3.08 × 106ψ(2S) decays was obtained with the CLEO III
and CLEO-c detector configurations [10, 11, 12, 13] at the Cornell Electron Storage Ring.
The CLEO III detector features a solid angle coverage for charged and neutral particles of
93%. The charged particle tracking system achieves a momentum resolution of ∼0.6% at
1 GeV, and the calorimeter photon energy resolution is 2.2% for Eγ = 1 GeV and 5% at
100 MeV. Two particle identification systems, one based on energy-loss (dE/dx) in the drift
chamber and the other a ring imaging Cherenkov (RICH) detector, are used to distinguish
pions from kaons.
Half of the ψ(2S) data were accumulated with a newer detector configuration, CLEO-
c , in which the silicon strip vertex detector was replaced with an all-stereo six-layer
wire chamber. The two detector configurations also correspond to different accelerator
lattices. Studies of Monte Carlo simulations and the data reveal no significant differences
in the capabilities of the two detector configurations; therefore the CLEO III and CLEO-c
datasets are analyzed together.
FIG. 1: Exclusive analysis: (a) Scatter plot of the reconstructed ηccandidate mass vs. the recoil
mass against π0for data. The horizontal band in the vicinity of M(J/ψ) and the diagonal band
at larger ηc candidate mass correspond to ψ(2S) → π0π0J/ψ and ψ(2S) → γχc0, respectively.
The dashed lines denote the region M(ηc) = 2982 ± 50 MeV. Data events (open histograms)
and Monte Carlo background estimate (shaded histograms) of (b) reconstructed ηccandidate mass
projection for M(π0recoil) = 3524±8 MeV and (c) recoil hccandidate mass spectrum for M(ηc) =
2982±50 MeV. The peaks in b) near M=3.1 GeV and 3.25 GeV correspond to ψ(2S) → π0π0J/ψ
and ψ(2S) → γχc0, respectively. (d) Reconstructed ηccandidate mass for data in the direct decay
ψ(2S) → γηc. The peak near M = 3.4 GeV is from the direct decay ψ(2S) → γχc0.
The inclusive and exclusive analyses share a common initial sample of events and nu-
merous selection criteria. Details of the analyses are provided in a companion paper .
Event selection for both analyses require at least three electromagnetic showers and two
charged tracks, each selected with standard CLEO criteria. For showers, Eγ> 30 MeV is
required. Candidates for γγ decays of π0or η mesons satisfy the requirement that M(γγ) be
ψ(2S) and (b) data for 3 million ψ(2S). See text for details.
Inclusive analysis: Recoil mass against π0for (a) Monte Carlo sample for 39.1 million
within 3 standard deviations (σ) of the known π0or η mass, respectively. These candidates
are kinematically fit, constraining M(γγ) to the appropriate mass to improve π0/η energy
resolution. Charged tracks are required to have well-measured momenta and to satisfy cri-
teria based on the track fit quality. They must also be consistent with originating from the
interaction point in three dimensions.
Both techniques identify hcas an enhancement in the spectrum of neutral pions from the
reaction ψ(2S) → π0hc. For this purpose, it is useful to remove neutral pions originating
from any other reaction. It is easy to remove most of the π0arising from ψ(2S) → π+π−J/ψ,
with J/ψ → π0+ hadrons and π0π0J/ψ, with J/ψ → any. Since the recoil spectra against
M(π+π−) (both analyses) and M(π0π0) (inclusive only) show prominent peaks for J/ψ;
these events are removed by appropriate selection around M(J/ψ).
In the exclusive analysis, ηcare reconstructed in seven channels: K0
K+K−π+π−, π+π−π+π−, K+K−π0, π+π−η(→ γγ), and π+π−η(→ π+π−π0). The sum of
the branching fractions is (9.7 ± 2.7)% . The decay chain in Eq. (1) as well as these ηc
decays are identified from reconstructed charged particles, π0and η mesons. For η decays to
π+π−π0, the three-pion invariant mass is required to be within 20 MeV of the nominal η mass.
tracks with invariant mass within 10 MeV, roughly 4σ, of the K0
constrained 4C fit is performed for each event. A 1C fit is performed for the ηc→ K0
decay because the K0
explicit selection of the energy of the photon from hc→ γηcis required. The final selection
is on the ηccandidate mass; however, to improve resolution, the hcmass is calculated from
the 4-momentum of the ψ(2S) and the π0instead of the invariant mass of its decay products.
In addition to ψ(2S) → ππJ/ψ decays discussed above, a fraction of ψ(2S) decays proceed
through ψ(2S) → π0J/ψ and ψ(2S) → γχcJ→ π0X. To suppress the π0background, each
signal photon candidate is paired with all other photons in that event. If the invariant mass
of any pair is within the π0mass requirement, the event is removed.
Scandidates are selected from pairs of oppositely charged and vertex-constrained
Smass. A kinematically
Lis not detected. It is required that M(ηc) = 2980 ± 50 MeV. No
Fig. 1(a) shows the scatter plot of the ηccandidate mass versus π0recoil mass (sum of
all channels). Many events are seen in the vicinity of M(J/ψ). In the mass band M(ηc) =
2980±50 MeV an enhancement of events is observed at larger π0recoil mass. The projection
of the events in this band and the Monte Carlo background estimate is shown in Fig. 1(c).
A prominent peak is clearly visible over a very small background. The projection of the
events in the mass band M(π0recoil) = 3524 ± 8 MeV and the Monte Carlo background
estimate, shown in Fig. 1(b), indicate that most of these events arise from ηcdecay. The
π0recoil mass spectrum, in Fig. 1(b), is fit using a double Gaussian shape determined from
Monte Carlo simulation and an ARGUS function background . The maximum likelihood
fit yields 17.5 ± 4.5 counts in the peak and M(hc) = 3523.6 ± 0.9 MeV.
Several different methods have been utilized to estimate the statistical significance s
of the signal , including the fit to the recoil mass spectrum just described, Poisson
fluctuations of MC-predicted backgrounds inside the signal window, and a binomial statistics
calculation using the assumption that the events in the recoil mass distribution are uniformly
distributed. Using the difference between the likelihood values of the fit with and without
the signal contribution, we obtain s = 6.1σ; similar calculations with different ηcmass ranges
yield s = 5.5−6.6σ. The probability that Poisson fluctuations of the background, estimated
from the generic MC sample, completely account for the observed events in the signal region
is 1×10−9(s = 6.0σ). The binomial probability that the number of data events in Fig. 1(b)
and 1(c) fluctuate to be greater than the number of events in the signal region is 2.2×10−7,
corresponding to s ∼5.2σ.
To test our ability to reconstruct ηcdecays and provide normalization for the branching
fraction measurement, BψBh, the direct radiative decay ψ(2S) → γηcis studied. Events
are reconstructed in the same ηcdecay channels as for the hcsearch, but with much better
yields. Relative yields among the various channels are similar to previous results  and the
ηcpeak shape was verified for each channel. Figures 1(b) and 1(d) show the reconstructed
mass spectra for the ηccandidates from hcand direct ψ(2S) decay, respectively. The ηc
mass resolution in the photon recoil mass spectrum is identical for all seven channels. This
distribution summed over all channels (not shown) is fit using a peak shape which consists
of a Monte Carlo-derived double Gaussian convolved with a Breit-Wigner function (with
M(ηc) = 2979.7 MeV, Γ(ηc) = 27 MeV). It yields 220 ± 22 counts. The efficiency-corrected
ratio of hcdecays to direct decays, which corresponds to BψBh/BD, where BD≡ B(ψ(2S) →
γηc), is determined to be 0.178±0.049. The CLEO  and PDG  values are combined to
obtain BD= (0.296±0.046)%. Multiplying these two results yields BψBh= (5.3±1.5)×10−4
from the exclusive analysis.
In the inclusive analysis, we explore two methods to enhance the selection of neutral
pions which are part of the chain ψ(2S) → π0hc→ π0γηc. One way is to specify that there
be only one photon in the event with energy for the transition hc→ γηc, Eγ ≈ 503 MeV
(corresponding to M(hc) ≈ 3526 MeV). Another way is to specify that the mass recoiling
against the photon and π0for the event should be near the mass of ηc. Both approaches are
investigated, leading to consistent results, as detailed in Ref. .
A combined sample of generic ψ(2S) decay and signal Monte Carlo events is used to
optimize the criteria for the final event selection. The resulting selection criteria determined
were Eγ= 503±35 MeV for hard photon acceptance in one approach and M(ηc) = 2980±35
MeV in the other. As a result of the Monte Carlo studies, a number of selection criteria, in
which the two approaches occasionally differ, are made. These include requiring only one
π0in the signal region, removing hard photons that reconstruct η mesons with any other
FIG. 3: Inclusive analysis: Efficiency-corrected fit yields versus |cosθ| for data with Eγ= 503 ±
35 MeV, (a) for hcyield, the curve corresponds to the best fit ∝ (1+cos2θ) and (b) for the nearly
isotropic background yield.
TABLE I: Results for the inclusive and exclusive analyses for the reaction ψ(2S) → π0hc→ π0γηc.
First errors are statistical, and the second errors are systematic, as described in the text and
photon, accepting photons in the calorimeter endcaps, removing photons from the cascade
reaction ψ(2S) → γχJ→ γγJ/ψ, and the choice of the background shape.
The recoil spectrum for the total Monte Carlo sample of 39.1 million ψ(2S) (13 times the
size of the data sample), obtained in the Eγ-selection approach with its optimized selection
criteria, is shown in Fig. 2(a). A product branching fraction BψBh= 4×10−4was assumed.
The corresponding plot from the other approach is very similar. The hcsignal is evident.
The overall efficiencies determined from the Monte Carlo sample are 13.4% and 14.6% for
the two inclusive approaches. Input values of M(hc) and BψBhare well reproduced. Results
of Monte Carlo studies lead to the conclusion that the resonance fits to the data may be
expected to have significance levels of ∼4σ, statistical error on the mass of ∼±0.6 MeV, and
central values of the mass are reproduced within ∼±0.6 MeV of the generated M(hc).
Figure 2(b) shows the data and the fit using the Monte Carlo optimized criteria for
TABLE II: Summary of estimated systematic uncertainties and their sums in quadrature. N/A
means not applicable.
Number of ψ(2S)
B(ψ(2S) → γηc)
Binning, fitting range
Modeling of hcdecays
Sum in quadrature
the same inclusive approach as in Fig 2(a). Features in the Monte Carlo such as signal
width, signal to background ratio, and approximate background shape mirror the data
faithfully. The recoil spectrum and the fit for the other inclusive approach are very similar.
Fit significance is approximately 3.8σ. Results from the two inclusive approaches differ by
small amounts, with differences from the averages in M(hc) of ±0.5 MeV and in BψBhof
±0.05×10−4. The average results are listed in Table I.
The hc yield from the recoil mass against π0in the inclusive analysis is studied as a
function of the angular distribution of the hc→ γηcphoton. The hcyield, shown in Fig. 3(a),
is found to follow a 1+cos2θ distribution (χ2/d.o.f. = 1.7/2) as expected for an E1 transition
from a spin 1 state. The background yield, shown in Fig. 3(b), is uniform in cosθ. The
hc yield in the exclusive analysis is not sufficient to draw any conclusions regarding the
corresponding angular distribution.
Systematic uncertainties in the two analyses due to various possible sources have been
estimated. Many sources are common, such as choice of background parameterization, hc
resonance intrinsic width (Γ = 0.5−1.5 MeV), π0line shape, bin size, and fitting range. The
uncertainty in the branching ratio for ψ(2S) → γηcenters the systematic uncertainty for the
exclusive analysis only while the uncertainty on the number of ψ(2S) decays applies to the
inclusive analysis only. The estimated contributions are listed in Table II. For the inclusive
(exclusive) analysis they sum in quadrature to ±0.4 (0.5) MeV in M(hc) and ±0.7(1.0)×10−4
in BψBh. The largest systematic error for the exclusive analysis, B(ψ(2S) → γηc), cancels
in the ratio and we obtain BψBh/BD= 0.178 ± 0.049 ± 0.018.
To summarize, we have observed the hcstate, the1P1state of charmonium, in the reaction
ψ(2S) → π0hc, hc → γηc, in exclusive and inclusive analyses. The significance of our
observation is greater than 5σ under a variety of methods to evaluate this quantity. We
combine the results of the exclusive and inclusive analyses to obtain M(hc) = 3524.4±0.6±
0.4 MeV and B(ψ(2S) → π0hc) × B(hc→ γηc) = (4.0 ± 0.8 ± 0.7) × 10−4. The following
value is obtained for the hyperfine splitting:
−M(1P1)) = +1.0 ± 0.6 ± 0.4 MeV.
Thus, the combined result for M(hc) is consistent with the spin-weighted average of the χcJ
We gratefully acknowledge the effort of the CESR staff in providing us with excellent
luminosity and running conditions.This work was supported by the National Science
Foundation and the U.S. Department of Energy.
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