A w 2 test used for particle identification with the Hall A RICH detector at JLab $ G.M. Urciuoli a,Ã , E. Cisbani b , F. Cusanno b , R. De Leo c , D. Di Bari c , S. Frullani b , F. Garibaldi b , M. Iodice d , L. Lagamba c , J.J. LeRose e , P. Markowitz f , S. Marrone c , B. Reitz e a INFN, Sezione di Roma, I-00185 Rome, Italy b INFN, Gruppo Collegato Sanit  a and Istituto Superiore di Sanit  a, I-00161 Rome, Italy c INFN, Sezione di Bari and University di Bari, I-70125 Bari, Italy d INFN, Sezione di Roma3, I-00146 Rome, Italy e Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA f Florida International University, Miami, FL 33199, USA article info Article history: Received 26 March 2009 Received in revised form 15 September 2009 Accepted 24 September 2009 Available online 4 October 2009 Keywords: RICH Particle identification Reconstruction algorithm Cochran’s theorem abstract An algorithm, based on the w 2 test, employed for particle identification by RICH detectors, is described. This algorithm is independent and complementary to the traditional algorithm based on the comparison between the average of the measured Cherenkov angles and the expected Cherenkov angles of the photons generated in the RICH by the particle to be identified. On the other hand it is much simpler and faster than a full likelihood analysis of the full event pattern. The particle rejection ratios achievable with the com- bined use of this algorithm and the algorithm based on the comparison between the average and the expected Cherenkov angles are very high. The algorithm also allows one to identify noise easily. The applica- tion of the algorithm is shown for the Hall A RICH detector in the E94-107 experiment at JLab. In this experi- ment an enormous background made up of pions and protons is 30 000 times bigger than the signal and had to be identified and rejected in order to extract the kaons from the electroproduction of hypernuclei. & 2009 Elsevier B.V. All rights reserved. 1. Introduction Most detectors measure variables which can assume con- tinuous values. In these cases, the average of single measurements surely provides the best estimate of the variable value to be measured. A ring imaging Cherenkov detector (RICH), however, is a quite peculiar detector: for charged particles of given momentum crossing it (and to be identified), the Cherenkov angle of the photons generated in it can assume, for a given value of the refractive index of the radiator (and neglecting dispersion smearing), only discrete mean values depending on the mass of the particle. In addition, for every particle crossing a RICH, single Cherenkov photon angle measurements are, with good approx- imation, normally distributed around these discrete values. One can try to take advantage of this and identify a particle that crosses a RICH by checking the whole distribution of the single photon Cherenkov angle measurements against the finite possi- bilities of Gaussian distributions that the RICH can provide. Gaussian distributions are defined by two parameters: their central value m and their variance s 2 . To check the central value of a Gaussian distribution the average of the measurements can be employed. The variance of the Gaussian distribution can be checked with a w 2 test (see Section 3.1), which can also be employed to identify no-photon signals miming the photons (‘‘noise’’ in the following, see Section 3.2). Such an algorithm was employed with the RICH detector first used in experiment E94- 107 at Thomas Jefferson National Accelerator Facility (JLab), in Hall A, in order to distinguish kaons from the enormous background of pions and protons. This paper will describe experiment E94-107 and the Hall A RICH detector briefly in Section 2. The mathematical approach will be demonstrated in Section 3. The detailed description of the algorithm and the obtained results will be discussed in Section 4. 2. E94-107 experiment at JLab and the RICH detector used in connection with it 2.1. E94-107 experiment Experiment E94-107, ‘‘High resolution 1p shell spectroscopy’’ of 9 L Li, 12 L B and 16 L N hypernuclei, took place in Hall A at JLab ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/nima Nuclear Instruments and Methods in Physics Research A 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.09.061 $ Notice: Authored and supported by The Italian Istituto Nazionale di Fisica Nucleare and The Southeastern Universities Research Association, Inc. under U.S. DOE Contract No. DE-AC05-84ER40150. The U.S. Government retains a non- exclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purposes. Ã Corresponding author. Tel.: +39 06 49914087; fax: +39 06 49914417. E-mail address: guido.maria.urciuoli@roma1.infn.it (G.M. Urciuoli). Nuclear Instruments and Methods in Physics Research A 612 (2009) 56–68