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J/psi,psi(2S) to mu+ mu- and B to J/psi,psi(2S) Cross Sections

This paper presents a measurement of J/psi,psi(2S) differential cross sections in p-pbar collisions at square root s = 1.8 TeV. The cross sections are measured above 4 GeV/c in the central region (|eta|<0.6) using the dimuon decay channel. The fraction of events from B decays is measured, and used to calculate b quark cross sections and direct J/psi,psi(2S) cross sections. The direct cross sections are found to be more than an order of magnitude above theoretical expectations.


Introduction
Charmonium production is currently the best way to study b quark production at CDF at the lowest possible transverse momentum of the b. While the signature and signal-to-noise for the J/ψ are excellent, the actual conclusions regarding b production are strongly dependent on the fraction of the data sample due to b decays. One obvious way of determining this fraction is to use the decay distance of the J/ψ state. In contrast, the fraction of ψ ′ 's from b decays is thought to be close to one [1]. Thus, in determining the P T spectrum of b quarks from a study of ψ ′ events, one does not have to worry about the fraction of ψ ′ production due to B decays. In the course of this analysis, however, a very large zero-lifetime component for the observed ψ ′ signal has been seen. Therefore, one still has to make use of the lifetime information.

Detector Description
The CDF detector has been described in detail elsewhere [2]. We describe here briefly the components relevant to this analysis. The CDF coordinate system defines the beam line to be the z direction. R is the radial distance from the beam line, and φ is the azimuthal angle. A solenoidal magnet generating a 1.4 T magnetic field surrounds the two tracking chambers used. The Central Tracking Chamber (CTC) is a cylindrical drift chamber surrounding the beam line.
The CTC contains 84 layers, which are grouped into nine superlayers, with 5 superlayers providing axial information and 4 providing stereo. It covers a pseudorapidity range of |η| < 1.1. The Silicon Vertex Detector (SVX) is a silicon microvertex detector. It consists of four layers 2.9 to 7.9 cm from the beam line and provides high resolution tracking information in the R − φ plane. When combined with a CTC track, it provides an impact parameter resolution of (13 + 40/P T )µm and a transverse momentum resolution of (0.0009P T ) 2 + (0.0066) 2 . Primary vertices have a Gaussian distribution with a width of about 27 cm, while the SVX only reaches to ±25cm, so only about 60% of the CTC tracks can be augmented with SVX information.
Outside the CTC are electromagnetic and hadronic calorimeters, which provide five absorption lengths of material before the Central Muon Chambers (CMU). The CMU consists of four layers of limited streamer chambers. It is divided into 72 segments which cover 85% of the φ region for |η| < 0.6. Muons with P T below ∼ 1.4 GeV/c range out in the calorimeters.
The CDF trigger consists of three levels. In the first level, both muons must be detected in the CMU. They must be seperated by at least 0.09 radians in φ and pass a slope cut in the R − φ plane. The slope cut is effectively a cut on the transverse momentum. To pass the second level, a fast hardware tracker must find at least one track that points to the correct muon chamber. For the third level, the full CTC track reconstruction is done. Both tracks must be found, and extrapolate to within 4σ of the muon chamber tracks in R − z and R − φ. σ is the expected multiple scattering error added in quadrature with the measurement error.

Event Selection
Further cuts are applied offline to produce a purer sample. The CTC track and the CMU segment are required to match better than 3σ in R − φ, and 3.5σ for the J/ψ and 3σ for the ψ ′ in R − z. Hadronic energy is required in the calorimetry tower that points to the muon chambers in the ψ ′ events. Both muons are required to have P µ T > 2.0 GeV/c and one muon must have P µ T > 2.8 GeV/c. The dimuon is required to have |η µµ | < 0.6 and P µµ T > 4 GeV/c. Runs with known hardware problems were excluded. Because there are much better statistics in the J/ψ, a tighter definition of bad runs was used there, resulting in a smaller integrated luminosity.
For the J/ψ, the CTC track is beam constrained. In the ψ ′ , the tracks are vertex constrained, using the SVX information if there are three or more hits. The χ 2 of this fit is required to be less than 10, with one degree of freedom. The resulting invariant mass is used to define a signal region of 3.0441 < m µµ < 3.1443 GeV/c 2 for the J/ψ and 3.636 < m µµ < 3.736 GeV/c 2 for the ψ ′ . Sideband regions of 2.9606 < m µµ < 3.0274 GeV/c 2 or 3.1610 < m µµ < 3.2278 GeV/c 2 for the J/ψ and of 3.52 < m µµ < 3.62 GeV/c 2 or 3.75 < m µµ < 3.85 GeV/c 2 for the ψ ′ are also defined. Figure 1 show the mass distribution of the events passing these cuts. There are a total of 26533 ± 175 J/ψ events and 896 ± 94 ψ ′ events.

B Fraction
For events where both muons have SVX tracks with at least three hits, we vertex constrain the tracks to measure l xy , the projection of the decay length onto the J/ψ,ψ ′ transverse momentum. This is converted into the proper lifetime of the parent by cτ = l xy /[(P T /m) · F corr ], where F corr is a Monte Carlo correction factor that relates the J/ψ,ψ ′ tranverse momentum to the transverse momentum of the parent.
The background cτ shape is measured from the sidebands. It contains non-Gaussian tails, so we parametrize it by where f + is the fraction in the positive exponential, λ + is the lifetime of the positive exponential, f − is the fraction in the negative exponential, λ − is the lifetime of the negative exponential, and σ is the width of the central Gaussian. The signal region is the fit to the function N · f sig (cτ ), where is the resolution function and σ is the width of the Gaussian, f r is the fraction of non-Gaussian tails in resolution function, and λ is the lifetime of non-Gaussian tails. R ⋆ E(cτ ) is the convolution of the resolution function with an exponential. We fix cτ 0 to 438 µm, as found by the CDF inclusive B lifetime measurement. [4]. f back is calculated by In the ψ ′ the data is fit using one unbinned log-likelihood fit. f back is not fixed, but a Poisson term is included for the likelihood that they fitted value fluctuates to the calculated value. σ is calculated on an event by event basis. Using the event-by-event error introduces non-Gaussian tails into the total resolution function, so f r is fixed at 1. The systematic error is estimated in part by allowing f r and λ to be fitted. In the J/ψ, the signal and sidebands are fit in seperate binned fits. f back is fixed and σ, f r and λ are fit. Figure 2 show the result of the fits.

P T dependence
It is expected that the B fraction in the J/ψ,ψ ′ samples rises with P T . To measure this, we divide the ψ ′ sample into three P T bins from 4 − 6 GeV, 6 − 9 GeV, and 9 − 20 GeV. The size of the last bin is neccesitated by the low statistics at high P T . We then repeat the above fitting procedure in each of the P T regions.
In the J/ψ sample, the "spectrum method" is used to calculate the P T dependence. This is done in three steps. First, the J/ψ P T spectrum is obtained. Then, the spectrum of events with cτ > 250µm is found. The two are normalized so that the ratio of the total area is the inclusive B fraction found above. The B fraction is then obtained by dividing the two distributions. The results are shown in Tables 1 and 2.

Acceptance and Efficiencies
The J/ψ,ψ ′ differential cross section is defined by where N is number of J/ψ,ψ ′ candidates in the bin, α is the detector and kinematic acceptance, ǫ is the trigger and cut efficiency, Ldt is the integrated lumonosity, and ∆P T is the size of the P T bin. The acceptance was determined from several Monte Carlo data sets. The ψ ′ acceptance used ψ ′ 's generated flat in P T and η. The J/ψ acceptance used several sets where b quarks were generated in different P T ranges, in order to provide sufficient statistics in all regions. The b quarks were generated using the next-to-leading order QCD calculation [3] and MRSD0 structure functions. The quarks were fragmented to B mesons using Peterson fragmentation [9] with ǫ b = 0.006 ± 0.002. A fast detector simulation was used on the events, and the kinematic cuts were then applied to the events. The J/ψ,ψ ′ acceptance is the ratio of events that survived this process to the number of generated events.
The b → J/ψ, ψ ′ acceptance used events where b quarks were generated and forced to decay to J/ψ,ψ ′ . The J/ψ,ψ ′ was forced to have the momentum spectrum measured by [5], [6]. The P T of the b quark is described by P min T . P min T is defined as the P T such that about 90% of the b quarks in our sample have P b T > P min T . The b quark acceptance is then calculated by The lack of a P T cut on the b in the numerator corrects for the fact that we are unable to remove those events with P b T < P min T . The efficiencies of the three triggers where studied with unbiased J/ψ events, as were the muon quality cuts. The efficiency of the CTC track reconstruction is 98.9 ± 1.0%. The efficiency of the muon reconstruction is 98 ± 1%.

Systematics
Systematic errors can arise in three distinct areas: measuring the J/ψ,ψ ′ cross sections, determining what portion of that cross section is from B decays, and extrapolating those results to a b quark cross section.

J/ψ,ψ ′ Cross Section Systematics
We calculate the uncertainty due to the trigger shape by varying the shape of the level 1 and level 2 trigger efficiency parametrizations. This is an 8% effect in the J/ψ and a 6.6% effect in the ψ ′ . We estimate the effect of the acceptance correction in the ψ ′ by varying the acceptance by the statistical error and by fitting the acceptance to a fifth degree polynomial, which is a 3.1% effect. In the J/ψ, fits to different order polynomials were used, giving a 1.5% error. A 5% error is assigned due to the J/ψ,ψ ′ polarization based on a ∼ 10% difference between the acceptance of maximallly polarized J/ψ's with extreme values of α = ±1. The 1% error measuring the cut efficiencies is neglibable compared to other errors. There is a 2% error associated with each of the level 3 trigger efficiency, the CTC tracking efficiency, and the muon reconstruction efficiency. We assign a 4% systematic to the uncertainty in the luminosity.

B Fraction Systematics
Potential sources of systematic errors arise from the B lifetime, the spread of the σ cτ distribution, and the fitting technique.
A single value for the cτ resolution is assumed in the J/ψ fit, while a wide range exists. The effect of this is estimated by applying a cut of σ cτ < 60µm, which removes the long tail in the distribution. σ cτ is related to the opening angle between the muons, which decreases at higher P T . Since the J/ψ from B decays have a harder P T spectrum, this may bias the B fraction, which is lower with this cut. The 7% difference is used as the systematic error. In the ψ ′ , the unbinned fit uses the event-by-event error, so this effect is missing. Varying the B lifetime by one sigma changes the B fraction by 0.002 or less. This is negligible compared to other contributions.
Changing the fitting technique and the form of the fitted function in the ψ ′ can change the B fraction by 7%, which is used as the systematic error.

B Cross Section Systematics
We assign a 1.3% systematic error due to the uncertainty in the rapidity spectrum in the range 0.6 < |y b | < 1.0. We take an uncertainty of 4.6% due to the uncertainty in the NDE spectrum with different values of µ and Λ. We assign 5% based on half the difference in the acceptance calculated with Peterson epsilon set to 0.004 and 0.008. A systematic of 5% is assigned based on the uncertainty in the CLEO J/ψ,ψ ′ momentum distribution. We assign a 1% error because of the statistics in the b to ψ ′ Monte Carlo.
In the ψ ′ , the effect of the large bin sizes for f B is estimated by fitting the B fraction to a straight line, and using a bin-by-bin correction factor. 7 Cross Section 7.1 J/ψ,ψ ′ Cross Section The cross sections are shown in Figure 3. The integrated cross sections are The cross section from B decays is extracted by multiplying the differential B fraction by the cross section. We can also obtain a prompt cross section by multiplying the cross section by one minus the B fraction. The results are shown in Figures 3 and 4. The prompt theory curves are from [11].