Search for Strange-Pentaquark Production in e+e-Annihilation at sqrt{s}=10.58 GeV and in Upsilon(4S) Decays

We search for strange pentaquark states that have been previously reported by other experiments — the Θ(1540) + , Ξ 5 (1860) −− , and Ξ 5 (1860) 0 — in 123 fb − 1 of data recorded with the B A B AR detector at the PEP-II e + e − storage ring. We ﬁnd no evidence for these states and set 95% conﬁdence level upper limits on the number of Θ(1540) + and Ξ 5 (1860) −− pentaquarks produced per e + e − annihilation into qq and per Υ (4 S ) decay. For qq events these limits are about eight and four times lower, respectively, than the rates measured for ordinary baryons of similar mass.

79 University of Wisconsin,Madison,Wisconsin 53706,USA 80 Yale University, New Haven, Connecticut 06511, USA (Dated: February 2, 2005) We search for strange pentaquark states that have been previously reported by other experiments -the Θ(1540) + , Ξ5(1860) −− , and Ξ5(1860) 0 -in 123 fb −1 of data recorded with the BABAR detector at the PEP-II e + e − storage ring. We find no evidence for these states and set 95% confidence level upper limits on the number of Θ(1540) + and Ξ5(1860) −− pentaquarks produced per e + e − annihilation into qq and per Υ (4S) decay. For qq events these limits are about eight and four times lower, respectively, than the rates measured for ordinary baryons of similar mass.
We report the results of inclusive searches for Θ + → pK 0 s , Ξ −− 5 → Ξ − π − , and Ξ 0 5 → Ξ − π + in e + e − annihilation data, where we expect equal production of the charge conjugate states; their inclusion is implied throughout this Letter. The data were recorded with the BABAR detector [13] at the PEP-II asymmetric-energy e + e − storage ring located at the Stanford Linear Accelerator Center. The data sample represents an integrated luminosity of 123 fb −1 collected at an e + e − center-of-mass (CM) energy at or just below the mass of the Υ (4S) resonance.
The BABAR detector is described in detail in Ref. 13. We use charged tracks reconstructed in the five-layer silicon vertex tracker and the 40-layer drift chamber. The charged-particle momentum resolution is (σ(p T )/p T ) 2 = (0.0013p T ) 2 + 0.0045 2 , where p T is the momentum transverse to the beam axis measured in GeV/c. Particles are identified as pions, kaons, or protons with a combination of the energy-loss measured in the two tracking detectors and the Cherenkov angles measured in the detector of internally reflected Cherenkov radiation. We use all events accepted by our trigger, which is more than 99% efficient for both e + e − → qq and e + e − → Υ (4S) events.
To evaluate the efficiency and mass resolution for reconstructing pentaquarks, we simulate pentaquark signals with the JETSET [14] Monte Carlo generator by substituting a particle with the mass, width, and decay mode of a hypothetical pentaquark for an existing baryon already simulated by JETSET. We use large control samples of known particles identified in data to correct small inaccuracies in the performance predicted by the GEANT-based [15] detector simulation. The invariantmass resolution for the decay modes studied in this analysis ranges from less than 2 MeV/c 2 to approximately 8 MeV/c 2 , depending on the final state and the momentum of the pentaquark candidate.
We reconstruct Θ + candidates in the pK 0 S decay mode, where K 0 S → π + π − . A sample of K 0 S candidates is obtained from all pairs of oppositely charged tracks we identify loosely as pions (with more than 99% efficiency and [70-90]% rejection of K and p depending on momentum) that pass within 6 mm of each other. Each candidate is required to have a reconstructed trajectory passing within 6 mm of the interaction point (IP) in the plane transverse to the beam direction and within 32 mm of the IP along the beam direction, a positive flight distance, defined as the projection on its momentum direction of a vector from its point of closest approach to the beam axis to its decay point, and an invariant mass within 10 MeV/c 2 of the nominal K 0 S mass. We also require the helicity angle θ H of the candidate, defined as the angle between the π + and the π + π − flight directions in the π + π − rest frame, to satisfy | cos θ H | < 0.8, reducing background from Λ 0 decays and photon conversions.
We combine these K 0 S candidates with tracks we identify as p or p (with [55-99]% efficiency and [95-99]% rejection of π and K) that extrapolate within 15 mm (10 cm) of the IP in the plane transverse to (along) the beam direction. The invariant-mass distribution of pK 0 S pairs in data is shown in Fig. 1. No enhancement is seen near the mass of the reported Θ(1540) + (inset in Fig. 1). There is a clear peak containing 98,000 entries at 2285 MeV/c 2 from Λ + c → pK 0 S , with a mass resolution below 6 MeV/c 2 . We consider several additional criteria that might reduce background to a pentaquark signal. Increasing the required flight distance of the K 0 S candidates increases the Λ + c signal-to-background ratio, but does not reveal any additional structure. We also tried requiring at least one K − and/orp candidate in the event. The Λ + c signal is still visible and there is no sign of a pentaquark peak. To enhance our sensitivity to any production mechanism that gives a pK 0 S momentum spectrum in the CM frame (p * ) different from that of the background, we split the data into ten subsamples according to the value of p * for the pK 0 S candidate. The ten p * ranges are 500 MeV/c wide and cover values from 0 to 5 GeV/c, the kinematic limit for a particle of mass 1700 MeV/c 2 . The background is lower at high p * , so we are more sensitive to mechanisms that produce harder spectra. There is no evidence of a pentaquark signal in any p * range.
We quantify these null results for a Θ + mass of 1540 MeV/c 2 . We fit a signal-plus-background function to the pK 0 S invariant-mass distribution for candidates in each p * range. We use a p-wave Breit-Wigner lineshape convolved with a resolution function derived from the Λ + c data and simulation. The latter is a sum of two Gaussian distributions with a common center and an overall rootmean-squared-deviation (RMS) ranging from 2.5 MeV/c 2 at low p * to 1.8 MeV/c 2 at high p * ; this is narrower than the Λ + c resolution due to the proximity of 1540 MeV/c 2 to pK 0 S threshold. The best upper limit of 8 MeV/c 2 [5] on the natural width Γ of the Θ + is larger than our pK 0 S mass resolution, and Γ could be very small. Therefore, we use Γ = 1 MeV/c 2 and Γ = 8 MeV/c 2 in the fit and quote results for each assumed width. We account for broad structures (known and unknown resonances, reflections) in the pK 0 S mass distribution by using a wide mass range, from threshold to 1800 MeV/c 2 , and a seventhorder polynomial times a threshold function for the background shape; seventh is the lowest order giving an acceptable χ 2 .
For the nominal selection criteria, we find that in each p * range the fit quality is good and the signal is consistent with zero. We consider systematic effects in the fitting procedure by varying the signal and background functions and fit range; changes in the signal yield are negligible compared with the statistical uncertainties. Varying the mass assumed for the Θ + has effects consistent with expected statistical variations. The other selection criteria give similar results. Since the nominal selection results in the smallest absolute uncertainties after efficiency corrections, we use it to set upper limits on the production cross section.
We convert the signal yield in each range of p * into a cross section by dividing by the reconstruction and selection efficiency, the K 0 S → π + π − branching fraction, the integrated luminosity, and the p * range. If the Θ + decays strongly, we expect only two possible decay modes, nK + and pK 0 , with very similar Q values, so we assume B(Θ + → pK 0 S ) = 1/4. The efficiency for the simulated pentaquark signal varies from 13% at low p * to 22% at high p * . The efficiency calculation is verified by measuring the differential cross section for Λ + c production in the combination of qq (q = d, u, s, c) and Υ (4S) events represented in our data.
The resulting differential cross sections are shown for Γ = 1 MeV/c 2 and for Γ = 8 MeV/c 2 in Fig. 2. The error bars include the relative systematic uncertainties on the luminosity (1%) and efficiency (4.9% dominated by the uncertainties on track and displaced-vertex reconstruction efficiencies). We derive an upper limit on the Θ + production cross section for each p * range under the assumption that it cannot be negative: a Gaussian function centered at the measured value with RMS equal to the total uncertainty is integrated from zero to infinity, and the point at which the integral reaches 95% of this total is taken as the limit. These 95% confidence level (CL) upper limits are also shown in Fig. 2. We derive model-independent upper limits on the total number of pentaquarks produced per qq event and per Υ (4S) decay by summing the differential cross section over the kinematically allowed p * range for qq events (entire p * range) and for B meson decays (p * < 2.5 GeV/c), respectively, taking into account the correlation in the systematic uncertainty. The central value and the 95% CL upper limit on the total Θ + (plus Θ − ) production cross section for the p * range from 0 to 5 GeV/c are shown in Table I. Dividing this limit and the corresponding limit for the p * range from 0 to 2.5 GeV/c by the cross section for e + e − → qq and for e + e − → Υ (4S), respectively, we calculate limits on the number of pentaquarks per event, given in Table I. For the maximum width (Γ = 8 MeV/c 2 ), we obtain a 95% CL upper limit roughly a factor of eight below the typical values measured for ordinary octet and decuplet baryons of the same mass [16]. We search, as well, for the reported Ξ 5 (1860) −− and Ξ 5 (1860) 0 states decaying into a Ξ − and a charged pion, where Ξ − → Λ 0 π − and Λ 0 → pπ − . We reconstruct Λ 0 → pπ − candidates from all pairs of charged tracks that satisfy loose proton and pion indentification requirements and pass within 6 mm of each other. The Λ 0 candidate must have a positive flight distance from the IP and an invariant mass within 10 MeV/c 2 of the nominal Λ 0 mass. These Λ 0 candidates are combined with an additional negatively charged track passing loose pion identification requirements to form Ξ − candidates, which are required to form a good vertex, to have a positive flight distance from the IP, and to have an invariant mass within 20 MeV/c 2 of the nominal Ξ − mass. The flight distance of the Λ 0 candidate from the Λ 0 π − vertex is required to be positive. This selection yields 290,000 Ξ − candidates with a peak signal-to-background ratio of 23 in the Λ 0 π − mass distribution. Finally, we combine the Ξ − candidates with an additional charged track consistent with coming from the IP and passing loose pion identification requirements. The cosine of the angle between the reconstructed Ξ − trajectory, extrapolated back to the IP, and the additional track is required to be less than 0.998. This last requirement is especially important, since the Ξ − is charged and has a long lifetime; if it has a long flight distance, it can produce a reconstructed track that, if combined with itself, forms a false peak in the invariant-mass distribution. The reconstruction efficiency for the simulated pentaquark signal varies from 6.5% at low p * to 12% at high p * .
The invariant-mass distributions for Ξ − π − and for Ξ − π + combinations are shown in Fig. 3. In the Ξ − π + mass spectrum, we see clear peaks for the Ξ(1530) 0 and Ξ c (2470) 0 baryons, but no other structure is visible. There are no visible narrow structures in the Ξ − π − mass spectrum.
As in the Θ + search, we divide the Ξ − π − candidates into ten subsamples according to the p * value of the can- didate. We find no sign of a pentaquark signal for any range of p * . We fit a signal-plus-background function to the Ξ − π − invariant mass distribution, for each p * range. Here no broad resonances or reflections are evident, and we perform simpler fits over a Ξ − π − mass range from 1760 to 1960 MeV/c 2 using a linear background function. The resolution function is derived from the Ξ(1530) 0 and Ξ c (2470) 0 signals in data and simulation, and is described by a Gaussian function with an RMS of 8 MeV/c 2 . For the Breit-Wigner width we consider two possibilities, 1 and 18 MeV/c 2 , corresponding to a very narrow state and the experimental upper limit on the Ξ −− 5 width [11], respectively. We fix the Ξ −− 5 mass to 1862 MeV/c 2 . In all ranges of p * , the signal is consistent with zero. Systematic uncertainties on the fitting procedure are again found to be negligible compared with the statistical uncertainties, and variations of the Ξ −− 5 mass and selection criteria give consistent results.
We convert the measured yields for the Ξ −− 5 → Ξ − π − decays into cross sections as described above for the Θ + . The efficiency determined from simulation is verified by measuring the differential cross section for the observed Ξ(1530) 0 signal. The average relative systematic uncertainty on the efficiency is 6.2% with a slight p * dependence, and is larger than that for the pK 0 S mode because there are two displaced vertices and more particles in the final state. We have used a Ξ − π − branching fraction of one-half for purposes of calculating cross sections and limits, under the assumption that the two-body modes Ξ − π − and Σ − K − dominate and have similar branching fractions.
The measured cross section and 95% CL upper limits for Ξ −− 5 (plus Ξ ++ 5 ) production are shown in Fig. 2 and Table I. For Γ = 18 MeV/c 2 , the limit on the total production rate per qq event is roughly a factor of four below the typical values measured for ordinary octet and decuplet baryons of the same mass [16]. We perform a similar search for Ξ 0 5 →Ξ − π + , finding no signal in any p * bin. Since many decay modes are kinematically accessible to such a state with a mass of ∼1862 MeV/c 2 and the branching fraction is unknown a priori, we omit this state from Table I and express our upper limit on the total production of Ξ 0 5 and Ξ