Elastic Peak Monitoring for the CLAS

D.C.Vermette and G.P.Gilfoyle

Physics Department, University of Richmond, VA, USA, 23173

We have developed a system to monitor the performance of a large, particle detector, the Continuous Electron Beam Accelerator large acceptance spectrometer (CLAS), at the Thomas Jefferson National Accelerator Facility (TJNAF). TJNAF is centered on a race-track-shaped electron accelerator almost one mile in circumference. Electrons make up to five passes through the machine to gain energies as high as 5.5 billion electron volts (GeV). They are channeled into three experiment halls where a multitude of detectors study their interaction with nuclear targets. TJNAF uses a continuous beam of electrons to collect large amounts of data in short periods of time.

Electrons entering the center experiment hall, Hall B, are aimed at atomic nuclei. The particles scatter off the nuclei and are detected by the CLAS. The CLAS consists of layers of detectors surrounding the target nuclei at almost all angles. Closest to the target nuclei are drift chambers consisting of about 34,000 sense wires that detect the passage of a charged particle. The sense wires in these drift chambers are arranged in six sectors surrounding the target, and within each sector are three regions of wires at different distances from the target. A large toroidal magnet bends the charged particles going through the drift chambers. The signals from the drift chamber sense wires are used to measure the charged particles' trajectory through the CLAS and determine their momentum. Enclosing the drift chambers are scintillators that produce a fast electronic signal needed to start the data acquisition system and to make time-of-flight measurements. A layer of Cerenkov counters determine when a track through the CLAS is caused by an electron. To ensure the data is high quality, it is important to frequently determine the detector is working properly. We discuss here a system that will monitor the performance of the CLAS over time and record its time history.

The calibration of the CLAS is monitored using the W spectrum of the scattered electron defined by

$$W^2 = (P + q)^2 = M^2 + 2M\nu - Q^2$$

where P is the four-momentum of a target nucleon with mass M, $\nu$ is the lost energy of the electron, q is the four-momentum transferred to the target, and Q² = -q². This quantity W corresponds to the mass of the recoiling particle left behind by the electron after the collision. Figure 1 shows a portion of the Wspectrum for two detector runs.

 

Figure 1: W spectra for two energies in sector 2 of the CLAS.

The sharp peak at low W in each panel corresponds to the mass of the proton. It is this peak that we use as a tool to monitor the CLAS performance. Since we know that the mass of the proton is 938 MeV, the location of this elastic scattering peak is a good barometer of the CLAS's calibration. The natural width of the elastic peak is infinitely narrow because the proton is long lived. The finite resolution of the CLAS `smears' the measurement of W, so the width of the elastic peak is a measure of the resolution. While the detector is collecting data, the W spectrum is accumulated on an event-by-event basis.

With higher electron beam energies, more of the recoiling particles have higher masses. This effect is because the electron now has more energy to transfer to the target nucleus. The histogram in the lower panel of Figure 1 corresponds to an electron beam at 1.5 GeV. Here the number of elastic events is large compared with the number of higher W particles. The spectrum in the upper panel corresponds to an electron beam at 4.3 GeV. Here the proton peak is smaller compared with the number of higher W particles and it is wider. The greater width is due to a less accurate calibration for the higher energies. Spectra like these are extracted during data acquisition so the calibration of the CLAS has not yet been optimized.

Also shown on the two histograms is a Gaussian curve fit over the proton peak. Data are collected for 10,000 events in the CLAS and then the spectra for each sector are fitted with a Gaussian curve in the region of the elastic peak. The Gaussian curve has the form

$$N = N_0 e^{-(W - \overline W)^2/2\sigma^2}$$

where N is the number of counts, N₀ is the normalization, $\overline W$ is the peak position, and $\sigma$ is the width. The software package used to fit the data is called MINUIT [1]. The code starts from an initial guess of the centroid of the Gaussian curve, its width, and its height and then finds the best fit values. It makes an estimate of the uncertainties for each of the fit parameters. The values it measures for the centroid and width of the elastic peak are stored in a database and the results can be viewed over the internet after the data are recorded. After the fitting, the Wspectra are set to zero and data collection resumes for the next 10,000-event interval. This algorithm was incorporated into the on-line track reconstruction software for the CLAS and used during the spring of 1999.

The time histories of the elastic peak fit measured during the spring, 1999 experiments revealed several problems with the algorithm. Many of the fits had unnaturally large widths, high elastic peak locations, and anomalous uncertainties. Instead of elastic peak locations just under 1 GeV, the time histories showed some peak locations of 10 GeV or higher, with uncertainties just as large. Similar problems existed with the widths. Another problem was some fits had widths and associated uncertainties close to zero.

We hypothesized that one cause of the unsuccessful fits was not enough counts in the histogram for MINUIT to accurately fit the data. In order to resolve this problem, a threshold for the number of counts in the elastic peak region was found. Sample runs at different energies and with different currents in the toroidal magnet were fitted after varying numbers of counts were collected in the elastic peak region. Then, the uncertainties for both width ( $\sigma_{width}$) and peak location ( $\sigma_{peak}$) were plotted with respect to number of counts in the elastic region. Figure 2 shows results from a 2.6 GeV run.

 

Figure 2: Uncertainty in the elastic peak position and width as a function of the number of counts in the elastic peak region.

At low counts we see very large uncertainties in both the width and elastic peak location. At higher counts the uncertainties asymptotically approach 3-4 MeV. A threshold of 50 counts in the elastic peak region was a safe number for fitting the curve, regardless of the energy or torus current. The code was changed so that MINUIT would fit the data in each sector with a Gaussian curve only if the number of counts was above this threshold. For some running conditions (beam energy, etc.) the production of elastic events was low. If the spectra had fewer counts than required the data were not fitted, the histogram was not reset, and the data collection resumed for another 10,000-event interval until the number of counts in the elastic peak exceeded the threshold.

We also observed unnaturally small widths close to zero. We suspected MINUIT was finding a local minimum in the $\chi^2$ hypersurface and taking small steps around this minimum, unable to get out. By restarting MINUIT at the fit with the too-small widths, it will take large, initial steps and find its way out of this local minimum. We observed that while this local minimum produced very small uncertainties in the width and centroid, the uncertainty in the height of the peak was large; greater than the height. The code was changed so that when the uncertainty on the height was at least as big as half the height, MINUIT would be asked to fit the data a second time.

Figure 3 shows the results of the most recent version of the fitting algorithm for sector 3 in both a high and low electron beam energy run.

 

Figure 3: The centroid and width of the elastic peak in the W spectrum for two beam energies versus event number. For the 1.5-GeV run, only a portion of the results are shown to make the figure readable. These results are for sector 3.

In the upper panel is shown the centroids of the elastic peak taken from the fits for two energies as a function of the event number during the run. The widths extracted from the fits are displayed in the lower panel for the same data sets. The size of the uncertainties and the scatter of the data points are consistent. We no longer see the erratic behavior of the uncertainties in the centroid and width. The average position of the measured centroid is below the expected value of 938 MeV for the proton mass. This shift reflects inaccuracies in the on-line calibration that will be corrected in the off-line analysis. The higher energy run has a less accurate calibration causing the centroid of the elastic peak to deviate from the expected value more than the low energy run. The widths shown in the lower panel are consistent with this observation. The high-energy data with the less-accurate calibration has, on average, poorer resolution than the low-energy data.

After testing and modifying the fitting procedure, we now make precise fits to the W spectrum. We observe differences between the value of the centroid from the fit and the known mass of the proton, but this discrepancy is due to the un-optimized calibration which is the best one available at run time. These discrepancies disappear during the more careful (and much later) off-line analysis. The algorithm is stable; the centroid and widths no longer exhibit anomalous, unphysical values. In the future we will look at the behavior of the elastic peak's width and location over time and for different running conditions. Also, we can test the sensitivity of the monitoring algorithm to problems with the detector. The information provided by the procedure should be helpful in quickly uncovering problems with the CLAS detector. A final test of the algorithm will come in the fall of 1999 when the CLAS resumes collecting data with an electron beam.

We acknowledge support of the University of Richmond and the United States Department of Energy under contract DE-FG02-96ER40980.

References

[1] F.James and M.Roos, MINUIT, Function Minimization and Error Analysis, CERN D506, 1989.