Measurement of the cross section using
We report measurements of the exclusive cross section for as a function of center-of-mass energy from the threshold to 5.2 with initial-state radiation. No evidence is found for decays. The analysis is based on a data sample collected with the Belle detector at or near a center-of-mass energy of 10.58 with an integrated luminosity of at the KEKB asymmetric-energy collider.
The Belle Collaboration
Studies of exclusive open charm production near threshold in annihilation provide important information on the dynamics of charm quarks and on the properties of the states. During the past three years numerous measurements of exclusive cross sections for charmed hadron pairs have been reported. Most of these measurements were performed at -factories using initial-state radiation (ISR). Belle presented the first results on the cross sections to the , chcon (), , (including the first observation of decays) belle:dd (); belle:dst (); belle:4415 () and final states belle:x4630 (). BaBar measured cross sections to and recently to the , final states babar:dd (); babar:dd_new (). CLEO-c performed a scan over the energy range from 3.97 to 4.26 and measured exclusive cross sections for the , and final states at thirteen points with high accuracy cleo:cs (). The measured open charm final states nearly saturate the total cross section for charm hadron production in annihilation in the region up to . In the energy range above some room for contributions to the state from unmeasured channels still remains. The exclusive cross sections for charm strange meson pairs have been measured to be an order of magnitude smaller than charm meson production cleo:cs (). Charm baryon-antibaryon pair production occurs at energies above .
Another motivation for studying exclusive open charm production is the existence of a mysterious family of charmonium-like states with masses above open-charm threshold and quantum numbers . Although these have been known for over four years, the nature of these states, found in processes, remains unclear. Among them are the state observed by BaBar babar:y4260 (); babar:y4260_08 (), confirmed by CLEO cleo:y4260_isr (); cleo:y4260_scan () and Belle belle:y4260 (); the discovered by BaBar babar:y4350 () and confirmed by Belle belle:y4350 (); and two structures, the and the seen by Belle belle:y4260 (); belle:y4350 ().
No clear evidence for open charm production associated with any of these states has been observed. In fact the peak position appears to be close to a local minimum of both the total hadronic cross section bes:cs () and of the exclusive cross section for belle:dst (); babar:dd_new (). The , recently found in the cross section as a near-threshold enhancement belle:x4630 (), has a mass and width (assuming the to be a resonance) consistent within errors with those of the , supporting explanation that the is x4630:bugg () or bound state x4630:molecule (). However, this coincidence does not exclude other interpretations of the , for example, as a conventional charmonium state x4630:charm () or as baryon-antibaryon threshold effect x4630:thresh (), point-like baryons x4630:point (), or as a tetraquark state x4630:tetra ().
The absence of open charm decay channels for states, large partial widths for decay channels to charmonium plus light hadrons and the lack of available charmonium levels are inconsistent with the interpretation of the states as conventional charmonia. To explain the observed peaks, some models assign the , with shifted masses y:ding (), other explore coupled-channel effects and rescattering of charm mesons voloshin:rescattering (). More exotic suggestions include hadro-charmonium hadroch (); multiquark states, such as a tetraquark y4260:tetra () and or molecules y4260:molecule (). One of the most popular exotic options for the states are the hybrids expected by LQCD in the mass range from y4260:hybryds (). In this context, some authors expect the dominant decay channels of the Y(4260) to be .
In this paper we report a measurement of the exclusive cross section as a function of center-of-mass energy from the threshold to 5.2, as part of our studies of the exclusive open-charm production in this mass range. The analysis is based on a data sample collected with the Belle detector det () at the resonance and nearby continuum with an integrated luminosity of at the KEKB asymmetric-energy collider kekb ().
We employ the reconstruction method that was used for and exclusive cross section measurements belle:dd (); belle:4415 (). We select signal events by reconstructing the , and mesons. In general the is not required to be detected: instead, its presence in the event is inferred from a peak at zero in the spectrum of recoil mass squared against the system. The square of the recoil mass is defined as:
Here is the initial center-of-mass () energy, and are the energy and momentum of the combination, respectively. To suppress backgrounds two cases are considered: (1) the is outside of the detector acceptance and the polar angle for the combination in the c.m. frame is required to be ; (2) the fast is within the detector acceptance (), in which case it is required to be detected and the mass of the combination must be greater than (). To suppress background from processes we exclude events that contain additional charged tracks that are not used in , or reconstruction.
All charged tracks are required to originate from the vicinity of the interaction point (IP); we impose the requirements and , where and are the impact parameters perpendicular to and along the beam direction with respect to the IP. Charged kaons are required to have a ratio of particle identification likelihood, , larger than 0.6 nim (). Charged tracks not identified as kaons are assumed to be pions.
candidates are reconstructed from pairs with an invariant mass within of the mass. The distance between the two pion tracks at the vertex must be less than , the transverse flight distance from the IP is required to be greater than , and the angle between the momentum direction and the flight direction in the plane should be smaller than .
Photons are reconstructed from showers in the electromagnetic calorimeter with energies greater than that are not associated with charged tracks. ISR photon candidates are required to have energies greater than . Pairs of photons are combined to form candidates. If the mass of a pair lies within of the mass, the pair is fitted with a mass constraint and considered as a candidate.
candidates are reconstructed using five decay modes: , , , and . A mass window is used for all modes except for where a requirement is applied ( in each case). candidates are reconstructed using and decay modes bckg (); a mass window is used for both modes. To improve the momentum resolution of meson candidates, final tracks are fitted to a common vertex with a mass constraint on the or mass. candidates are selected via the and (for background study) decay modes with a mass-difference window (). A mass- and vertex-constrained fit is also applied to candidates.
To remove contributions from the process, we exclude combinations with invariant mass within of the nominal mass.
, , and mass sidebands are selected for the background study; these are four times as large as the signal region and are subdivided into windows of the same width as the signal. To avoid signal over-subtraction, the selected sidebands are shifted by ( for the mode) from the signal region. The candidates from these sidebands are refitted to the central mass value of each window. sidebands are shifted by to the higher mass side of the signal region.
The distribution of for the signal region in the data for is shown in Fig. 1 a). A clear peak corresponding to the process is evident around zero. The shoulder at positive values is due to events. We define the signal region for by a tight requirement around zero to suppress the tail from such events. The invariant-mass distribution of combinations in the data after the requirement on and the polar angle distribution of combinations shown in Fig. 1 b), c) are typical of ISR production and are in agreement with the MC simulation.
The spectrum obtained after all the requirements is shown in Fig. 2.
The contribution of multiple entries after all the requirements is found to be less than . In such case the single combination with the minimum value of is chosen, where and correspond to the mass fits for and candidates.
The following sources of background are considered:
combinatorial background under the () peak combined with a real () coming from the signal or other processes;
both and are combinatorial;
the reflection from the processes , where the is not reconstructed, including decays;
the reflection from the process , followed by , where the low-momentum is not reconstructed;
where the energetic is misidentified as a single .
The contribution of background (1) is extracted using the and sidebands. Background (2) is present in both the and sidebands and is, thus, subtracted twice. To take into account this over-subtraction we use a two-dimensional sideband region, when events are selected from both the and the sidebands. The total contribution from the combinatorial backgrounds (1–2) is shown in Figs. 1, 2 as a hatched histogram.
Most of the background (3–4) events are suppressed by the tight requirement on . The remainder of background (3) is estimated directly from the data by applying a similar reconstruction method to the isospin-conjugate process . Since there is a charge imbalance in the final state, only events with a missing extra can contribute to the signal window. To extract the level of background (3), the mass spectrum is rescaled according to the ratio of and reconstruction efficiencies and an isospin factor of 1/2. A negligibly small contribution of background (3) is found: only one event with . Uncertainties in this estimate are included in the systematic error. The remainder of background (4) is estimated from the data assuming isospin symmetry. We measure the process () by applying a similar reconstruction method. Only three events with are found in the data. Thus the contribution of background (4) is also found to be negligibly small; uncertainties in this estimate are included in the systematic error.
The contribution of background (5) is determined from the data using fully reconstructed events including the reconstruction of an energetic . Only one event with and is found in the data. Assuming a uniform polar angle distribution, this background contribution to the signal sub-sample (case 1) is 1 event/9 events in the entire mass range, where is the reconstruction efficiency. The probability of misidentification due to asymmetric decays is also estimated to be . Thus the contribution of background (5) is found to be negligibly small; uncertainties in this estimate are included in the systematic error.
The cross section is extracted from the background subtracted mass distribution
where , is the mass spectrum obtained without corrections for resolution and higher-order radiation, is the total efficiency, and the factor is the differential ISR luminosity cs (). The total efficiency determined by MC simulation grows quadratically with energy from 0.007% near threshold to 0.036% at 5.2 . The resulting exclusive cross section averaged over the bin width is shown in Fig. 3 with statistical uncertainties only. Since the bin width is much larger than the resolution, which varies from around threshold to at , no correction for resolution is applied.
The systematic errors for the measurement are summarized in Table 1.
|Cross section calculation|
The systematic errors associated with the background (1–2) subtraction are estimated to be 2% due to the uncertainty in the scaling factors for the sideband subtractions. This is estimated from fits to the and distributions in the data that use different signal and background parameterizations. Uncertainties in backgrounds (3–5) are estimated conservatively to be each smaller than 1% of the signal. The systematic error ascribed to the cross section calculation includes a 1.5% error on the differential luminosity and a 6% error in the total efficiency function. Another source of systematic errors is the uncertainties in track and photon reconstruction efficiencies (1% per track, 1.5% per photon and 5% per ). Other contributions come from the uncertainty in the identification efficiency and the absolute and branching fractions pdg (). The total systematic uncertainty is 10%.
We perform a likelihood fit to the distribution where we parameterize a possible signal contribution by an -wave relativistic Breit-Wigner (RBW) function with a free normalization. We use PDG values pdg () to fix its mass and total width. To take a non-resonant contribution into account we use a threshold function with a free normalization. Finally, the sum of the signal and non-resonant functions is multiplied by a mass-dependent second-order polynomial efficiency function and differential ISR luminosity.
The fit yields signal events for the state. The statistical significance for the signal is determined to be from the quantity , where is the maximum likelihood returned by the fit, and is the likelihood with the amplitude of the RBW function set to zero. The goodness of the fit is . The systematic errors of the fit yield are obtained by varying the mass and total width within their uncertainties, histogram bin size and the parameterization of the background function and efficiency.
We calculate the peak cross section for the process at from the amplitude of the RBW function in the fit to be nb at the 90% C.L. Using and PDG values of the mass, full width and electron width pdg () we found at the 90% C.L and at the 90% C.L. All presented upper limit values include systematic uncertainties. For illustration we include the corresponding fit function on the cross section distribution plot shown in Fig. 3.
To obtain limits on the decays , where denotes , , or states, we perform four likelihood fits to the spectrum each with one of the states, the state and a non-resonant contribution. For fit functions we use the sum of two -wave relativistic RBW functions with a free normalization and a threshold function with a free normalization. The sum of the signal and non-resonant functions is multiplied by the mass-dependent second-order polynomial efficiency function and differential ISR luminosity. For masses and total widths of the and states we use PDG values pdg (). The corresponding parameters of the , and states are fixed from Ref. bellebabar:y (); belle:x4630 (), respectively.
The significances for the , , and signal are found to be , , and , respectively. The calculated upper limits (at the 90% C.L.) on the peak cross sections for processes at are presented in Table 2. Using fixed values of masses and full widths we obtain upper limits on the at the 90% C.L. Finally, for the state we estimate the upper limit on at the 90% C.L. using pdg (). For the and states we calculate at the 90% C.L. taking into account bellebabar:y (). All upper limits presented in Table 2 are determined by choosing the maximum signal amplitudes that emerge from: varying masses and widths of the states within their uncertainties; varying the histogram bin size; and changing the parameterizations of the background & efficiency functions.
To estimate the effects of possible interference between final states we also performed a fit to the spectrum that includes complete interference between the RBW amplitude and a non-resonant contribution. We found two solutions both with ; the interference is constructive for one solution and destructive for the other. From the fit with destructive interference we find an upper limit on the peak cross section for process to be nb at the 90% C.L.
In addition we performed four likelihood fits to the spectrum with complete interference between the and states’ RBW amplitudes and a non-resonant contribution. We found four solutions for each fit with similar goodness-of-fit (=1.39, 1.23, 1.39 & 1.21) and obtained the upper limits on the peak cross sections for process to be less than 1.44, 1.92, 1.38 and 0.98 nb at the 90% C.L. for , , and , respectively.
In summary, we report the first measurement of the exclusive cross section over the center-of-mass energy range from 4.0 to 5.2. We calculate an upper limit on the peak cross section for the process at to be 0.76 nb at the 90% C.L. The values of the amplitude of the , , and signal function obtained in the fit to the spectrum are found to be consistent with zero within errors. We see no evidence for decays as predicted by hybrid models and obtain the upper limit at the 90% C.L.
We thank the KEKB group for excellent operation of the accelerator, the KEK cryogenics group for efficient solenoid operations, and the KEK computer group and the NII for valuable computing and SINET3 network support. We acknowledge support from MEXT, JSPS and Nagoya’s TLPRC (Japan); ARC and DIISR (Australia); NSFC (China); DST (India); MEST, KOSEF, KRF (Korea); MNiSW (Poland); MES and RFAAE (Russia); ARRS (Slovenia); SNSF (Switzerland); NSC and MOE (Taiwan); and DOE (USA).
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