Absolute Photon Energy Calibration of the BABAR Calorimeter Using 's

The e ect of residual 0 mass shift after \ideal" single photon calibration is discussed. For the case of the BABAR detector, operating in the (4S) energy region, the shift is estimated to be of the order of 2%. We discuss a new photon energy calibration algorithm using photons produced in 0 and decays. Based on 10 (4S) decays, we achieve a statistical error of better than 0.5% in the photon energy interval from 40MeV to 1GeV, reaching 0.1% around 300MeV. A demonstration version of the calibration procedure has been implemented in C++. Introduction. Experimental events in the (4S) energy region contain plenty of photons produced via 0 and decays. It is very desirable to calibrate the absolute photon energy using these photons in the energy range from about 40MeV up to 1GeV. The general idea is not new. For example, the Crystal Barrel experiment [1] used the nominal 0 mass for absolute energy calibration of every crystal in their calorimeter. The CLEO experiment [2] used a method similar to the one described here to obtain an energy-dependent correction factor. This paper describes an approach where individual crystals are rst calibrated with some other algorithm (say, using Bhabha scattering events), and it is necessary to derive an energyand polar angle-dependent correction factor to the reconstructed photon energy. More details can be found in BABAR Note #433 and a forthcoming SLAC-PUB document. 1) Work supported by Ministry of Science of the Russian Federation (Project BABAR) 2) Work supported by Department of Energy contract DE-AC03-76SF00515. Why is calibration with 0 desirable? If the task of identifying 's is considered, the absolute photon energy calibration with 's has an obvious advantage over the other types of absolute calibration: one calibrates photon energy using the target e ect. There are some additional arguments in favour of 0 calibration: \Non-conservation" of peak or average values. For such a complicated convolution of several probability distributions as present in the two-photon invariant mass formula m = q 2E1E2(1 cos ) ; (1) no peakor average-type of absolute single-photon energy calibration can put the average or peak value of the invariant mass distribution to the nominal value of the 0 mass. (Here the peak/average-type of absolute single-photon energy calibration refers to shifting the peak/average value of the energy of monochromatic photons to their true value of energy.) In order to estimate the residual 0 mass shift for the BABAR calorimeter, let us perform the absolute single-photon energy calibration in the low-energy region, where most of the 0 decay photons reside. That means, we should nd the correction function (lnEclus) of the energy deposit in a cluster, Eclus, such that the estimate of the photon energy E = Eclus exp [ (Eclus)] (2) puts the peak position at the true photon energy, E0. For this purpose, Monte Carlo samples of single-photon events with E0 = 0:02, 0:05, 0:07, 0:1, 0:2, 0:5, 1, 2GeV were simulated. Here and further on, standard BABAR software for simulation and reconstruction of events was used. In order to check the residual 0 mass shift after such an \ideal" single-photon energy calibration, a Monte Carlo sample of 100MeV/c single0 events was used. Fig.1 shows the distribution of these events vs. the normalized invariant mass of photon pairs before and after single-photon calibration. Fitting the distributions yields the following parameters: peak position xp FWHM hp Before calibration 0:9582 0:0029 0:0672 0:0092 After calibration 0:9794 0:0018 0:066 0:010 One can see that the residual shift of the 0 mass peak is of the order of 2%, although it is substantially reduced from the initial value of 4%. Obviously, the real size of this e ect in the experiment can be a little di erent from this gure, but the order of the e ect should be correct. Independence from background. Unlike many other schemes of absolute energy calibration, this type of calibration does not demand high-level rejection of background events. The only requirement is that a statistically signi cant 0 peak is 0 20 40 60 80 100 120 140 160 0.8 0.85 0.9 0.95 1 1.05 1.1 Mgg/Mpi N um be r of g am m aga m m a pa ir s FIGURE 1. Distribution of 100MeV/c 's over normalized invariant mass of the photon pairs before (dashed histogram) and after (solid histogram) single-photon calibration. 0 20 40 60 80 100 0.8 0.85 0.9 0.95 1 1.05 1.1 Mgg/Mpi N um be r of g am m aga m m a pa ir s FIGURE 2. Normalized invariant mass distribution of the photon pairs in 5k 100MeV/c single0 events before (open histogram) and after (shaded histogram) 0 calibration. present, and that the background distribution in the region of the 0 peak is smooth (which can be expected). Another commonly-used single-photon energy calibration process is radiative Bhabha scattering, but for low photon energies it has limited statistical accuracy and some systematic uncertainty due to the emission of additional soft photons. Calibration algorithm. For histogramming, let us use the logarithm of the normalized invariant mass of two photons with energies E1 and E2 and space angle between them: = 1 2 lnf2E1E2(1 cos )g lnm0 = 1 2 1 + 1 2 2 + ln q 2(1 cos ) m0 ; (3) where m0 is the nominal 0 mass, and = lnE. If these two photons are produced in a 0 decay and the energies and angle are exact, then = 0. Further, we denote the histograms over and corresponding variables with two indices, i and j, i j. Into the histogram [i; j] we collect the pairs of photons with i;j h=2 < lnE1;2 < i;j + h=2; i;j = 1 + ([i; j] 1)h : (4) The complete calibration procedure consists of the following steps: histogramming of two-photon invariant masses, peak search in every histogram (with error estimate), solving a system of equations to obtain the photon energy correction, and interpolation and smoothing of the correction coe cients. Determination of the peak position. Precise calibration can only be performed if the number of events in the 0 peak region, nk, is large enough. Then, we can use a simpli ed form of the likelihood function: L1 = X (f( k) nk)2 nk + 1 : (5) For tting the peak, we use the following function: