Calibration and monitoring of the MEG experiment by a proton beam from a Cockcroft–Walton accelerator

Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima Calibration and monitoring of the MEG experiment by a proton beam from a Cockcroft–Walton accelerator J. Adam n,o, X. Bai k, A. Baldini a, E. Baracchini l, C. Bemporad a,b, G. Boca e,f, P.W. Cattaneo e, G. Cavoto g, F. Cei a,b, C. Cerri a, M. Corbo a,b, N. Curalli a,b, A. de Bari e,f, M. De Gerone c,d, T. Doke p, S. Dussoni c,d, J. Egger n,1, K. Fratini c,d, Y. Fujii k, L. Galli a,b, G. Gallucci a,b, F. Gatti c,d, B. Golden l, M. Grassi a, D.N. Grigoriev q, T. Haruyama m, M. Hildebrandt n, F. Ignatov q, T. Iwamoto k, P.-R. Kettle n, B.I. Khazin q, O. Kiselev n, A. Korenchenko r, N. Kravchuk r, A. Maki m, S. Mihara m, W. Molzon l, T. Mori k, D. Mzavia r,2, H. Natori k, D. Nicolo a,b, H. Nishiguchi m, Y. Nishimura k, W. Ootani k, M. Panareo i,j, A. Papa a,b, R. Pazzi a,b,2, G. Piredda g, A. Popov q, F. Renga g,h, S. Ritt n, M. Rossella e, R. Sawada k, F. Sergiampietri a, G. Signorelli a,, F. Tenchini a,b, C. Topchyan l, Y. Uchiyama k, R. Valle c,d,3, C. Voena g, F. Xiao l, A. Yamamoto m, Yu.V. Yudin q, D. Zanello g,1 a INFN Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy Dipartimento di Fisica dell’Universita , Largo B. Pontecorvo 3, 56127 Pisa, Italy INFN Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy d Dipartimento di Fisica dell’Universita , Via Dodecaneso 33, 16146 Genova, Italy e INFN Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy f Dipartimento di Fisica dell’Universita , Via Bassi 6, 27100 Pavia, Italy g INFN Sezione di Roma, Piazzale A. Moro 2, 00185 Roma, Italy h Dipartimento di Fisica dell’Universita ‘‘Sapienza’’, Piazzale A. Moro 2, 00185 Roma, Italy i INFN Sezione di Lecce, Via per Arnesano, 73100 Lecce, Italy j  Via per Arnesano, 73100 Lecce, Italy Dipartimento di Fisica dell’Universita, k ICEPP, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan l University of California, Irvine, CA 92697, USA m KEK, High Energy Accelerator Research Organization 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan n Paul Scherrer Institute PSI, CH-5232 Villigen, Switzerland o Swiss Federal Institute of Technology ETH, CH-8093 Zürich, Switzerland p Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan q Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia r Joint Institute for Nuclear Research, 141980, Dubna, Russia b c The MEG Collaboration a r t i c l e i n f o abstract Article history: Received 5 January 2011 Received in revised form 22 March 2011 Accepted 23 March 2011 Available online 13 April 2011 The MEG experiment at PSI searches for the decay m-eg at a level of  1013 on the branching ratio BRðm-eg=m-tot), well beyond the present experimental limit (BR r 1:2  1011 ) and is sensitive to the predictions of SUSY-GUT theories. To reach this goal the experiment uses one of the most intense continuous surface muon beams available (  108 m=s) and relies on advanced technology (LXe calorimetry, a gradient-field superconducting spectrometer as well as flexible and powerful trigger and acquisition systems). In order to maintain the highest possible energy, time and spatial resolutions for such detector, frequent calibration and monitoring, using a Cockcroft–Walton proton accelerator, are required. The proton beam is brought to the centre of MEG by a special bellows insertion system and travels in a direction opposite to the one of the normal m-beam. Protons interact with a lithium tetraborate (Li2B4O7) nuclear target and produce one g (17.6 MeV) from the reaction 73 Liðp, gÞ 84 Be or two 12  coincident gs (11.67 and 4.4 MeV) from the reaction 11 5 Bðp, g1 Þ 6 C . The 17.6 MeV g is used for Keywords: Calibration Cockcroft–Walton accelerator Beam monitoring g-rays  Corresponding author. Tel.: þ 39 050 2214 425; fax: þ39 050 2214 317. E-mail address: giovanni.signorelli@pi.infn.it (G. Signorelli). Retired. 2 Deceased. 3 Present address: Lames Holding S.r.l., 16043 Chiavari, Italy. 1 0168-9002/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2011.03.048 20 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 calibrating and monitoring the LXe calorimeter (sEg =Eg ¼ 3:85 7 0:15% at 17.6 MeV) while the coincident 11.67 and 4.4 MeV gs are used to measure the relative timing of the calorimeter and the spectrometer timing counters (sDt ¼ 0:450 7 0:015 ns). & 2011 Elsevier B.V. All rights reserved. 1. Introduction 3. Experimental set-up and performance Lepton flavour violation (LFV) in the neutral lepton sector and neutrino oscillations are now established facts. We are nevertheless very far from understanding the dynamics behind these phenomena. In the Standard Model (SM) with finite but tiny neutrino masses, flavour violating decays are predicted to be immeasurably small, hence any such observed flavour violating signal must be based on new physics beyond the SM. Supersymmetric (SUSY) and supersymmetric grand unified theories (SUSY-GUT) can naturally house finite neutrino masses and can also predict rather large branching ratios for lepton flavour violating decays [1]. In particular, in the charged lepton sector, the decay m þ -e þ g is predicted to be one of the most sensitive reactions for observing LFV-effects. The current upper limit on the branching ratio for this decay was obtained in 1999, by the MEGA experiment: BR r 1:2  1011 at 90% CL [2]. The MEG (Mu to E Gamma) Collaboration [3], made of Institutions from Italy, Japan, Russia, Switzerland, United States, aims at a sensitivity of  1013 on the m þ -e þ g branching ratio, a level within the prediction bands of many SUSY and SUSY-GUT theories. The experiment has been taking-data at Paul Scherrer Institute (PSI) since September 2008, using one of the most intense DC muon beam currently available in the world. The experiment has recently reached an upper limit BR r 2:8  1011 at 90% CL [4] on the m þ -e þ g branching ratio from its first three months of beam time. To explore branching ratios at the 10  13 level one primarily needs a high intensity muon beam that can stop in a target of minimal thickness. With a muon decay rate of  108 m=s, sensitivities to branching ratios t 1012 can be reached in some months of data-taking. Furthermore, the use of a direct current muon beam helps to minimize the rate of accidental coincidences, as in the case of the pE5 surface muon channel at PSI [5]. Here muons are created from pions decaying at rest on the surface of the production target, fed by the world’s most intense continuous proton cyclotron. In order to discriminate a m þ -e þ g signal from background, one requires the highest possible resolutions in energy, emission angle and timing for both the positron and the g-ray. Therefore a high sensitivity experiment demands the use of innovative detector technologies. In Table 1 the performances of previous m þ -e þ g experiments are compared with the expectations of MEG, for which the goal is to gain two orders of magnitude with respect to the present limit. This is clearly an experimental challenge and required a long R&D phase (see, for instance, Ref. [10]) in order to obtain adequate detector performances, as also listed in Table 1. A layout of the MEG detector is shown in Fig. 1. The pE5 surface muon beam is brought to rest in a thin (205 mm) polyethylene target, after passing through a degrader and a Wien filter which eliminates almost all of the contaminating beam positrons from the production target (at a separation level of 7:5s). The muon momentum is set to  28 MeV=c, where the surface muon production rate reaches its maximum. The stopping rate Rm is tuned to 3  107 stopping muons/s to achieve the best sensitivity and signal-to-noise ratio. The muon stopping target is slanted by 20.51 with respect to the beam direction in order to minimize the positron path in the material and reduce the multiple scattering in the target. The positron momentum is measured by a superconducting iron-free magnetic spectrometer, with an axial gradient field housing a system of sixteen ultra-thin radial drift chambers. The gradient field of the COBRA spectrometer (COnstant Bending RAdius) has the advantage of sweeping away low momentum particles, which would contribute to a high drift chamber occupancy and dead time, more efficiently than a pure solenoidal field. Moreover, monochromatic positrons describe trajectories with an almost constant projected bending radius, independent of their emission angle at the target. 2. Signal and backgrounds in the MEG experiment The signal for the m þ -e þ g decay at rest is given by a positron and a g-ray, emitted simultaneously and back-to-back, with the muon mass equally shared between the two particles each with 52.8 MeV kinetic energy. The background originates from two different contributions: (1) the correlated background, given by the muon radiative decay (inner bremsstrahlung) process m þ -e þ ne n m g. The expected number of background events of this type is directly proportional to the muon decay rate Rm ; (2) the uncorrelated background, given by the accidental coincidence of a positron from the normal Michel decay m þ -e þ ne n m and a g-ray from radiative decay or positron annihilation in flight in the materials of the experiment. This background is dominant for positron and g-energies energies in the signal window and its rate depends quadratically on Rm . Table 1 The performances of previous m þ -e þ g experiments compared with the expectation of MEG. All the quoted resolutions are FWHM. Place Year DEe =Ee ð%Þ DEg =Eg ð%Þ Dteg (ns) Dyeg Upper limit References SIN 1977 8.7 9.3 1.4 – o 1:0  109 [6] TRIUMF 1977 10 8.7 6.7 – o 3:6  109 [7] LANL 1979 8.8 8 1.9 37 mrad o 1:7  1010 [8] LANL 1986 8 8 1.8 87 mrad o 4:9  1011 [9] LANL 1999 1.2a 4.5a 1.6 17 mrad o 1:2  1011 [2] PSI  2012 0.8 4.0 0.15 12 mrad a Shows an average of the numbers given in Ref. [2]. 13 o 1  10 MEG [3] J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 21 Fig. 1. Layout of the MEG experiment. The current obtained energy and angular resolutions of the spectrometer are sE =E  0:7% and sy  11 mrad, sf  7 mrad.4 The positron timing is measured by two double-layer arrays of plastic scintillators, placed on either sides of the spectrometer (Timing Counters: TC). The external layer of each is equipped with 15 scintillating bars (one bar: 4  4  79.6 cm), while the internal layer is composed of scintillating fibres (one fiber: 0.6  0.6  156 cm). A measured timing resolution of st  70 ps was achieved almost uniformly along the bars and for a large range of impact angles. The g-rays, after crossing the very thin magnet superconducting coils with a  80% transmission probability, are detected by a  900 l volume liquid xenon LXe detector, where their energy, direction and timing are measured. This detector material was chosen because of its large light yield (comparable with that of NaI), its homogeneity and its fast scintillation light decay time (  45 ns for g-rays and  22 ns for a-particles). The LXe calorimeter is viewed by 846 Hamamatsu 2 in. PMTs [11], specially manufactured to operate at cryogenic liquid temperatures. The LXe purity is one of the crucial parameters for obtaining the desired performance. A liquid phase purification system was developed which employs a pump with a flow of 70 l/h, molecular filters and an O2-getter. Further purification is performed in the gaseous phase, taking advantage the thermodynamic equilibrium of gaseous and LXe at the top of the calorimeter vessel. A FPGA-FADC based digital trigger system was specifically developed for the MEG experiment. The trigger is organized in a tree-structure of different types of digital boards, which process the fast signals coming from the LXe calorimeter and the TC system to perform a fast estimate of the r-energy, timing and direction and of the positron timing and direction; all of this information is then combined to select events with a candidate m þ -e þ g decay signature. Starting from a stopping muon beam intensity of 3  107 m=s we obtain a data acquisition trigger rate of R  5 Hz. The signals coming from all detectors are sampled by a switched capacitor array ASIC named ‘‘Domino Ring Sampler’’ version 4 (DRS4) which has been designed specifically for this experiment [12]. The drift chamber signals are sampled with 800 MHz, while all PMTs are sampled at 1.6 GHz, with a signal-tonoise ratio of 11.4 bits. The waveform recording is of crucial importance, enabling rejection of accidental superimposition of 4 Taking the z-axis as the beam-axis, y is defined as the polar angle, while f is the azimuthal angle. low energy events within the acquisition timing window (‘‘pileup’’), which can mimic signal events. The experimental sensitivity is evaluated by computing the expected background in the signal region on the basis of experimental or predicted resolutions and of the muon stopping rate. Assuming Rm ¼ 3  107 m=s, one obtains an accidental background of 6  10  14 events per muon decay; the corresponding 90% CL upper limit on the m þ -e þ g branching ratio, in the case of no events observed in four years of data taking, is 1.7  10  13. 4. Calibration and monitoring considerations of MEG The calibration and monitoring (C&M) methods are the key to success for the difficult measurement MEG wants to perform. MEG is an ambitious experiment in terms of the sensitivity necessary in studying the process m-eg. This demands the highest precision in measuring the four-vectors of the m-decay products; moreover the precision must be coupled with a high running stability of all detectors, under high beam intensity and its possible time variations. These requirements suggested the integration of a 1000 keV C–W (Cockcroft–Walton) accelerator into the experiment. It was used to excite two nuclear reactions (discussed later): 73 Liðp, gÞ 84 Be and 115 Bðp, gÞ 126 C. The introduction of such an accelerator for an elementary particle experiment is rather unusual. It is of importance to stress that the use of the C–W allows the C&M of both of the LXe-detector and the magnetic spectrometer over long time periods, including accelerator shutdown periods or periods of beam-time dedicated to other experiments. This has the advantage that independent tuning of the detector can be undertaken, allowing for a more efficient usage of the allocated MEG beam-time. It is worth defining the meaning of ‘‘calibration and monitoring’’ in our case and to try to list the quantities one has to measure and monitor, mainly with respect to the ones of the LXe detector. By ‘‘calibration’’ one refers to the determination of the photomultipliers relative quantum efficiencies QE, of the PMT amplifications, of the degree of purity of the LXe, of the intensity and spectrum of the Xe light emission, as well as of the optical parameters of both the liquid and gaseous Xe (refractive index, Rayleigh scatteringlength, absorption-length [3,10,13]). It also refers to the determination of other important global quantities like the calorimeter energy calibration and resolution as a function of the g-ray energy and impact point, the time resolution, the resolution on the position of the impact point and the LXe-detector’s capacity for 22 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 separating two particles in time and in space. By ‘‘monitoring’’ one essentially means the check of the stability of all important quantities, as often and as completely as feasible, in conditions which are as close as possible, or similar to the normal running conditions of MEG (COBRA magnet at full field, high beam intensity, minimal modifications to the MEG set-up.). Another important calibration method, relevant to liquid scintillator calorimeters and in particular to liquid cryogenic noble gas detectors, is based on the use of multiple a-sources distributed in the detector sensitive volume. For the MEG experiment we developed 241Am point sources deposited on thin (100 mm diameter) gold-plated tungsten wires permanently suspended in the volume as well as sources fixed on the surfaces of the large vessel containing the LXe [14]. The method is valuable in measuring the relative QEs of all PMTs surrounding the sensitive LXe volume, for determining the LXe optical properties of the UV scintillation light and for checking the stability of the calorimeter properties during the experiment. Table 2 Characteristics of the MEG C–W. Proton beam properties MEG C–W Energy (keV) Energy spread (FWHM) (keV) Angular divergence (FWHM) (mrad  mrad) Spot size at 3 meter (FWHM) (cm  cm) Energy setting reproducibility (%) Energy stability (FWHM) (%) Range of the average current (mA) Current stability (%) Current reproducibility (%) Duty cycle (%) 300–1000 o 0:5 o3  3 o3  3 0.1 0.1 1–10 3 10 100 5. The Cockcroft–Walton accelerator project The Cockcroft–Walton (C–W) accelerator is in operation in the MEG experiment for calibrating, monitoring, and tuning the performance of the Liquid Xenon, the relative inter-bar timing of the TCs and the relative timing between the TC and LXe detector. These calibration measurements are necessary on a frequent basis and losses to the normal data-taking time should therefore be minimized. For ease of operation the following requirements were met: (i) a separate radiation-safety monitored area with controlled access; (ii) an automated, controlled beam-pipe insertion bellows system for the introduction of the LiF (or the Li2B4O7) target as well as the transportation of the proton beam to the centre of the COBRA spectrometer; (iii) a beam transport system, consisting of vacuum pipes, a set of two horizontal and two vertical steering magnets (parallel displacement), with axial injection. Fig. 2. A view of the Cockcroft–Walton accelerator. These measures minimize the effect of the COBRA stray magnetic field on the C&M accelerator and allow interventions on the accelerator to be performed, when necessary, in a separate area, without interfering with the MEG experiment. 5.1. The Cockcroft–Walton characteristics The accelerator which is coupled to MEG is a 1 MeV C–W of recent production [15]. Its performance is listed in Table 2. 5.2. The positioning of the C–W accelerator A picture of the C–W accelerator is shown in Fig. 2. The C–W accelerator is placed in a separate area, independently radiation surveyed, in which it can be opened, closed and tested. At the moment of performing a calibration, the C–W accelerator must be turned-on, conditioned and tuned. Since the accelerator is in a separate area, these operations can take place in parallel with the normal MEG running. Close to the accelerator, a system of two horizontal-deflecting and two vertical-deflecting magnets (parallel beam displacement) were installed allowing an axial injection into the solenoid to hit the centre of the target (see Fig. 4.) The problem of injecting a proton beam into COBRA to reach a target at the COBRA centre is very similar to the one of the normal m-beam. The particle momenta are similar and so are the optical Fig. 3. Layout of the MEG and C–W experimental areas. properties of the beam. The p-beam has to reach the target under vacuum. The p-beam is introduced into the spectrometer from downstream, in the opposite direction to the normal m-beam. The present layouts of the downstream-side of the MEG experiment and of the C–W area are shown in Fig. 3. J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 23 Fig. 4. A scheme of the proton beam optics, of the control elements and of the bellows system. The figure is not to scale and shows the logical sequence of all the elements. 5.3. The proton-beam line and remote target insertion system Both the accelerator and the beam line have optical elements for optimizing the beam at the target. The accelerator is placed some 5 m downstream of the COBRA magnet centre. The optics of the p-beam was studied by a Monte Carlo simulation and it did not present any problems. The COBRA magnet has a fringing field which reaches the accelerator, though, at a distance 4 3:5 m from COBRA centre, this is reduced to acceptable levels. A bellows system is required to introduce the nuclear target into COBRA at the magnet centre (see Fig. 4). Upstream of the bellows system, a rigid pipe section connects the bellows system to the accelerator, while downstream of the bellows system, another rigid pipe section, containing the target at its end, is used to enter the COBRA magnet. In order to enter the controlled He-atmosphere inside COBRA, a larger diameter synthetic-rubber bellows insertion system, which is part of the downstream COBRA end-cap, is utilized. This is coupled to the C–W bellows system and simultaneously driven to the centre of the detector. The speed of insertion, together with a pressure-control system, guarantees that the pressure differential on the thin cathode foils of the tracking chambers inside of COBRA, as well as the beam vacuum window in the upstream end-cap, does not exceed  10 Pa during insertion or extraction. When the calibration is performed, the bellows systems with the target pipe are fully extended into COBRA, placing the target at the COBRA centre. Once finished, the bellows systems are fully retracted, with the larger diameter bellows residing inside the end-cap, while the target pipe is fully retracted outside of the end-cap. The rigid pipe section entering COBRA has a length of 223 cm. It can be moved by 221 cm in total (the stroke). The bellows system which allows the stroke has a length of 360 cm. A general picture of the C–W bellows system is presented in Fig. 5. It was built by combining five bellows sections (stainless steel bellows by MEWASA AG [16]). The system is guaranteed for a lifetime of 500 kcycles. The operation of the system is computer controlled and allows fully remote insertion and extraction. There are several redundant safety systems built-in to ensure fault-free manipulation. Fig. 5. The C–W beam line and bellows system for introducing the nuclear target into COBRA; a detail view of the bellows. 6. Beam diagnostics and intensity measurements Luminescence based beam diagnostics, in various forms, is widely used at accelerators [17,18]. After the acquisition of the MEG C–W accelerator, this method was immediately applied for setting-up the proton beam-line from the accelerator to the COBRA magnet. The beam could be optimized by observing the beam spot at various positions with a TV camera. The radiator used was a quartz crystal, which emits a bluish fluorescence light. The method was simple and fast, consisting of introducing the crystal into the beam by means of a remotely controlled compressed-air actuator. The fluorescence light emitted from the crystal placed at an angle of 451 to the incoming proton beam, Fig. 6. TV camera and quartz crystal pneumatic actuator. 24 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 is recorded, through a plexiglass window placed at 901 to the beam, by a simple TV-camera (see Figs. 6 and 7). The properties of the MEG muon and proton beams are reported in Table 3. The quartz crystal is covered by a thin tungsten wire net, which is grounded to avoid the accumulation of beam charge and consequent sparking on the crystal. The light emitted by the crystal under proton bombardment (see example in Fig. 8) proved to be a linear function of the C–W current, as shown in Fig. 9. An example of the beam focusing procedure is presented in Fig. 10, where the varying dimensions of the proton beam-spot are shown as a function of the C–W extraction voltage; this parameter is related to the ion-source of the accelerator, and it is used to modify the beam focusing. The beam intensity distribution (in ADC units, 256 maximum) was obtained by a MATLAB based image processing procedure and the beam spot intensity contours are displayed for a full set of extraction voltages (7, 8, 9, 10, 11, 11.7, 12, 13, 14 kV) at a C–W energy of 500 kV. The different intensity contours in the pixel plane (0.2 real millimeters match into one pixel of 5.6 mm) correspond each to a difference of five ADC units. An optimum beam focus, with a s  8 mm, is reached at an extraction voltage of approximately 10 kV. This can be seen in Fig. 11, where the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2x þ s2y in milli- beam intensity distribution s (defined as s ¼ meters in the image plane) is plotted as a function of the C–W extraction voltage. One remaining problem was that of exactly positioning the proton beam on the nuclear target at the centre of the COBRA magnet. The presence of stray magnetic fields along the beamline, associated with the iron content of the experimental hall floor, requires a final check of the spot at the target. Here optical methods and TV cameras cannot be employed due to the high COBRA magnetic field. We therefore had to rely on a different approach: a rotating target support and a pixel centring device mounted at the end of the proton beam line. Normally the target is kept at an angle of 451 relative to the beam direction, but can be rotated into a parking position, out of the beam, when one uses the pixel centring device. This is achieved by circulating a current in a coil mounted at the back of the target support. The current generates a magnetic moment, producing a torque in the COBRA magnetic field which rotates the target (see Fig. 12). The pixel device has thin copper pixels deposited on vetronite. The beam position is reconstructed from the current readings of each independent pixel. The system is computer interfaced and an example of the current pattern is shown in Fig. 13. The proton beam intensity measurement can in principle be performed on any insulated beam intersecting device, such as the beam shutter or the quartz crystal holder, which can be inserted by a remotely controlled compressed air system. However these provide only a rough measurement, since they are affected by the COBRA fringing field and their structure cannot avoid a loss of electrons originating from the proton collisions. A precise measurement is provided by a suitably designed Faraday cup, containing a guardring to prevent the loss of electrons. The Faraday cup is also inserted by a remotely controlled compressed air system. Fig. 7. Detail of the quartz crystal actuator. The crystal has a diameter of 4 cm. light integral (a.u) 2.5 2 1.5 1 0.5 Table 3 Main properties of the MEG experiment particle beams. Beam Units Momentum MeV/c K.E. MeV Velocity Beta Intensity Particles/s Current mA C–W p MEG m þ 43.3 28.0 1 3.65 0.046 0.256 6.25  1012 3.0  107 1 4.8  10  6 0 0 0.5 1 1.5 2 proton current (µA) 2.5 3 Fig. 9. Fluorescence light emission from the quartz crystal, as a function of the proton beam current. Fig. 8. Light from quartz with beam defocussed (left) and focussed (right). 25 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 25 120 50 45 120 20 80 40 100 35 80 30 80 60 25 60 15 10 20 20 40 10 20 40 60 80 150 80 60 100 40 160 100 120 140 120 90 100 120 100 100 80 80 60 60 40 50 80 70 60 80 50 60 40 40 30 20 20 40 20 20 10 10 0 12 0 10 0 12 0 20 40 60 80 20 40 60 80 20 10 0 12 0 10 0 12 0 10 0 12 0 100 20 20 5 20 40 60 80 5 200 40 40 15 20 120 60 10 0 12 0 40 80 20 40 60 80 60 100 20 40 60 80 100 100 120 45 70 120 120 40 120 40 100 35 100 35 60 100 50 80 30 80 60 20 30 40 40 15 20 20 30 80 25 40 60 45 20 10 10 25 60 20 40 15 20 10 5 10 0 12 0 20 40 60 80 10 0 12 0 20 40 60 80 10 0 12 0 20 40 60 80 5 Fig. 10. Beam-spot contours as a function of the C–W extraction voltage (7, 8, 9, 10, 11, 11.7, 12, 13, 14 kV). The pixel number in the pixel-plane is indicated along the x,y-axes. The 0.2 real millimeters match into one pixel of 5:6 mm. The various current reading devices can be calibrated by means of the Faraday cup. 7. The nuclear calibration reactions used The main calibration method for defining the energy scale and for guaranteeing the stability of the LXe detector is the one based on the 17.6 MeV g-ray production by the reaction 73 Liðp, gÞ 84 Be [19]. Another important reaction is 115 Bðp, ggÞ 12 6 C [19], mainly used for the relative timing of the MEG detectors. Previous to its implementation in MEG, we did a preliminary test of the proposed method using the Van de Graaff accelerator of the Legnaro INFN National Laboratories. We measured the reaction rates at different energies and with various target thicknesses. The quality of the g-lines, in view of their use for energy calibration, was also studied by examining their widths, the signal to background ratios, the presence of unwanted tails in the energy distribution. 7.1. Protons on lithium The reaction 73 Liðp, gÞ 84 Be is resonant at Ep ¼ 440 keV, with a resonance-width G  15 keV. It produces a 17:6 MeVg-line, an energy factor three times smaller than that of the g-rays from the m-eg decay, but in an interesting region for C&M. This reaction, which is excitable by very low-energy protons, is highly exothermic and is almost unique in providing high-energy g-rays with a large peak cross-section (speak  5 mb), since, for this particular reaction, the normally preferred particle emission (i.e.: a-emission) is depressed [20,21]. The reaction also has a nonresonant component, but its cross-section, at energies larger or smaller than 440 keV, drops by a factor 4100. Since the 7 8 3 Liðp, gÞ 4 Be reaction has unique properties, it was used to C&M a previous version of the m-eg experiment [22]. It is worth pointing out that, for accelerators of energy higher than the 1000 keV of our C–W, other reaction channels open, with an unwanted increase in the background level of the experiment. At the resonance for 73 Liðp, gÞ 84 Be the expected reaction rate 26 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 depends on the cross-section integrated over the 440 keV resonance as well as on the total number of 73 Li nuclei reached by the protons. One operates in the so-called ‘‘thick target’’ mode corresponding to an effective target thickness of a fraction of a mm. The resulting 17.6 MeV g-rays are isotropic with a convenient rate of  1 MHz. The 73 Li reaction also produces a less intense and wider 14.6 MeV g-line. (Other lines at lower energies correspond to fluorine if a LiF target is used.) The NACRE information on the 73 Liðp, gÞ 84 Be reaction [19] is given in the form of the S-factor (MeV b), and in the form of crosssection, both as a function of the centre of mass total kinetic 30 25 σ (mm) 20 15 Fig. 14. 7Li cross-section for g-production as a function of Tp [19]. 10 5 0 0 2 4 6 8 10 12 14 RF extraction voltage (kV) 16 18 20 Fig. 11. Beam-spot dimensions as a function of the C–W extraction voltage. Fig. 12. Scheme of the movable target and of the pixel centring device. The pipe diameter is 10 cm. The drawing is not to scale. Fig. 15. Resonance in the 7Li cross-section for g-production as a function of Tp; Tp ¼ 440 keV at the resonance, GR  12:5 keV. Fig. 13. The pixel system mounted on a vacuum flange (left). Monitoring of the proton beam position by the pixel system (right). 27 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 energy TnIN and of the centre of mass proton kinetic energy Tnp. Some information on the angular distribution for the almost isotropic g-emission is also available. It is convenient to use the cross-section as a function of the proton laboratory kinetic energy Tp (see Fig. 14). The resonant part of the cross-section, as measured by us at the Legnaro INFN National Lab. is presented in Fig. 15. We give, as an example in Table 4, the computation of the energies of the g-rays, emitted at the LAB polar angle 01 (relative to the incident proton direction) and at 901, as a function of Tp for the reaction 73 Liðp, gÞ 84 Be. Kinematic variables in the LAB (unstarred) and CM (starred) systems and the total cross-section values are also reported. From the close examination of the table one obtains an estimate for the displacement of the g-lines when Tp is far from the resonance energy, due to the effect of Doppler shifts and, consequently, for the possible deformation of the g-line when protons are slowed-down in a thick target. Because of the cross-section behaviour as a function of Tp, the effects mentioned are more important for boron than for lithium. The isotopic composition of elements and in particular the one of Li can be found in Ref. [23]. Li has two main isotopes (6Li¼7.59%, 7Li¼ 92.41%). In the case of the use of a LiF target, with density rLiF ¼ 2:635 g=cm3 and NLiF ¼6.11  1022 cm  3, the g-ray spectrum generated by protons hitting such target, at resonance, is presented in Fig. 16 and complies with the ones available in literature [27]. The sharp line at Eg0 ¼ 17:6 MeV and the broad line at Eg1 ¼ 14:6 MeV are produced in a ratio g0 =ðg0 þ g1 Þ ¼ 0:72 70:07. One can also see some g-production from 19 F and some naturally occurring radioactivity lines. Table 4 Kinematic variables and 7Li cross-section (see text). Tp (keV) 250.0 350.0 450.0 550.0 650.0 750.0 850.0 950.0 Tp ðkeVÞ  TIN ðkeVÞ s (mbarn) Eg ð03 Þ MeV Eg ð903 Þ MeV 191.15 267.61 344.07 420.53 496.99 573.45 649.91 726.37 218.60 306.04 393.48 480.92 568.36 655.80 743.24 830.68 0.016 0.070 2.011 0.062 0.069 0.055 0.071 0.082 17.50 17.60 17.70 17.79 17.89 17.98 18.07 18.17 17.45 17.54 17.63 17.72 17.80 17.89 17.98 18.06 Fig. 16. The g-spectrum from the proton reaction on a LiF target. 7.2. Protons on fluorine Initially a lithium target in the form of lithium fluoride was used, therefore the g-lines emitted by fluorine from the reaction 19 Fðp, agÞ 16 O are always associated with those emitted by lithium under proton bombardment (see Fig. 16). It is worth noting that the 19 F g -line at about 6 MeV is actually a composite line corresponding to three g-energies: 6130, 6917, 7117 keV. The 6130 keV line is dominant; the three lines are somewhat differently populated as a function of the incident proton energy [28]. The 19F cross-section is presented in Fig. 17 [29]. When using a proton energy Tp ¼500 keV on a thick LiF target, protons are effectively captured by the 7Li 440 keV resonance but also by the main 19F resonances at Tp ¼340 and 225 keV, following the proton energy loss in the thick target. The 19F cross-section is roughly constant in the energy region around the 440 keV 7Li-resonance, therefore the 19F g-lines provide an effective proton-flux normalization when scanning the 440 keV 7Li-resonance. 7.3. Protons on boron The 11B cross-section is presented in Fig. 18 [19,30]. One can notice a large resonance at Tp ¼ 163 keV and a rising cross-section at larger Tp. One important observation is that if one excites the 11 12  5 Bðp, 1 Þ 6 C  12 reaction (followed by 12 6 C - 6 C þ g2 ) with protons far from the resonance energy, as with Tp  500 keV, hitting a thick boron target, then a large fraction of the (nominal) 16.11 (g0 ) and 11.67 MeV (g1 ) g-rays will be produced at proton energies higher than the resonant energy. When the (g1 ) is emitted it will always be accompanied by the carbon de-excitation line (g2 ) at 4.44 MeV. Energy conservation implies higher g-ray energies. This will spoil the (g0 )- and the (g1 )-lines by introducing a large high energy tail. The 4.44 MeV line is left unchanged since it corresponds to a precise 12C-level (and Doppler effects are small). The isotopic abundance of B can be found in Ref. [23]; there are two main isotopes (10B ¼19.9%, 11 B¼80.1%). The density is rB ¼ 2:46 g=cm3 and NB ¼1.37  1023 cm  3. The g-ray spectrum generated by protons hitting the B target is presented in Fig. 19. The sharp line at Eg0 ¼ 16:11 MeV and the much more abundant line at Eg1 ¼ 11:67 MeV are g Fig. 17. 19 F cross-section for g-production as a function of Tp [29]. 28 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 Fig. 18. 11 B cross-section for g0 - and g1 -production as a function of Tp [19,30]. targets had a limited lifetime and were slowly damaged by the proton beam, when proton intensities of the order of 1 or 2 mA were used. Since the target is positioned at the centre of our spectrometer, where water cooling is not advisable, we are limited to the use of a low proton beam current. The final choice for low-cost individual LiF and B targets were, in the case of LiF, optical UV-windows in thick crystal form from ALKOR [24]. These had dimensions of 40 mm diameter and 4 mm thickness. Even though these crystals showed optical signs of radiation damage, we were able to prove that there was no degradation in time of the Li g-ray lines. In the case of boron, durable targets of boron carbide (B4C, produced by FELDCO international [25]) were used, which had a negligible contribution from carbon g-rays. The use of separate targets was however superseded by the need for a combined Li and B target, as the advantage of the relative timing calibrations became apparent and hence the time required for the change of targets had to be reduced. The selection of a combined target material, having both suitable mechanical and thermal properties, led to the use of lithium tetraborate (Li2B4O7), crystal disks manufactured by Jinan Crystals [26]. We studied the relative yield of lithium and boron g-lines as a function of the proton beam energy. Since the calorimeter energy calibration depends on a sharp g-line at a fixed energy, we used the lithium reaction at its resonant energy. It was also verified that the quality of the lithium 17.6 MeV g-line from a lithium fluoride and from a lithium tetraborate target was identical. As the boron reaction is only used for timing and less dependent on the g-line quality, we used the boron reaction at relatively high proton energies (750–1000 keV) where the g-ray yield is much larger than the one at the boron 163 keV resonance. Lithium and boron calibrations were performed on alternate days, with a duration of about 20 min each (30 k-events for lithium, 10 k-events for boron). The preparation of the calibrations, such as the C–W tuning and the positioning of the targets at the centre of the experiment, was performed in parallel with other aspects of the experiment and did not require extra allotted time. 8. The study of the LXe calorimeter The MEG experiment has so far collected data during the last three months of 2008 and the last two months of 2009. Further runs started in the summer 2010 and are expected to last two years. During the periods the calorimeter properties were studied daily by calibration methods, in particular by the use of the C–W accelerator. As an example of the quality and reliability of MEG data during the run, we shall discuss the time evolution of the calorimeter behaviour as derived from calibration data. Fig. 19. The g-ray spectrum from the proton reaction on a B-target [30]. 8.1. The development of LXe calorimetry produced in a ratio g0 =ðg0 þ g1 Þ  ð3:5 70:07Þ  102 . The Eg ¼ 12  4:44 MeV, by the C de-excitation, is emitted in coincidence with the 11.67 MeV line. In the spectrum one can observe other weak lines and escape peaks. As already stated, the coincident Eg ¼ 4:44 and 11.67 MeV lines are used for timing. It is interesting to note that these lines also provide a method of testing our detector’s capability of distinguishing double g-rays entering the MEG calorimeter. 7.4. Choice of targets and calibration programme Targets for the MEG calibrations were optimized in a series of successive steps. Initially we produced LiF or B targets by depositing thick and thin layers of LiF and B on a copper support. Such The characteristics of the MEG calorimeter were briefly presented in Section 3. The design of the final calorimeter for the experiment was based on preliminary studies performed on calorimeter prototypes of smaller dimensions. The studies extended over several years and were important for obtaining a practical experience in the handling of such cryogenic detectors. The properties of LXe as a scintillator and a first determination of relevant quantities such as the LXe absorption length were discussed and presented in several publications [10,13,14]. We refer to those for all basic aspects of LXe calorimetry. It is advisable to recall briefly the relevant characteristics of xenon calorimetry by scintillation light. Pure liquid xenon emits light in the ultraviolet at l ¼ 178 nm. The scintillation light yield is similar to that of NaI. The average time constant for light emission is 20 ns for ions and 50 ns for electromagnetic radiation (electrons and gs), thus enabling particle discrimination. The light J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 propagation in liquid xenon follows the usual exponential law: x=latt IðxÞ ¼ I0 e ð1Þ 29 8.2. The determination of the calorimeter energy scale and energy resolution. where ldif is the diffusion length (photon elastic scattering, coinciding with Rayleigh scattering lR  45 cm) and labs is the absorption length (photon disappearance). Pure LXe is expected to be essentially transparent to its own radiation. The LXe refractive index is  1:6. The Rayleigh scattering length and the refractive index are related [10]. The parameters outlined for pure LXe are heavily affected by the presence of contaminants (mainly O2 and H2O), so it is important to reach the maximum LXe purity and to keep it stable during the experiment. Xenon is kept liquid in the cryostat at 165 K and 0.12 MPa during normal operations. The LXe active volume is 800 l (see Fig. 20), the total amount of LXe being approximately 900 l. A diagram of the liquid xenon cryogenic system is shown in Fig. 21. Xe can be stored either as a gas in eight tanks with a total volume of 2448 l, at a pressure of 70 bar or, as a liquid, in a 1000 l dewar using the cryogenic equipment in common with the cryostat. The inner and outer cryostat vessels form a C-shape, in which a similar photomultiplier support structure fits (see Fig. 22). Both the inner and the outer vessels have very thin steel windows (thickness about 3 mm) to minimize the interactions of g-rays from m-decay. A honeycomb structure is fixed to the inner thin window to prevent a shape distortion, from concave to convex, when vacuum is applied in the outer vessel and LXe is present in Fig. 20. The LXe cryostat and the LXe dewar. Fig. 22. The PMT support structure mounted inside the cryostat inner vessel. where latt is the light attenuation length. The attenuation is the result of light diffusion and of light absorption: 1 latt ¼ 1 labs þ 1 ð2Þ ldif Fig. 21. Diagram of the MEG LXe cryogenic system. 30 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 the inner one. The honeycomb is a thin carbon fiber structure characterized by a high mechanical rigidity. Xe is liquified by cooling the cryogenic vessel. Both the cryostat and the dewar are equipped with a pulse-tube cryocooler and liquid nitrogen (LN2 pipes). The pulse-tube cryocoolers and the LN2-pipes are placed at the top of both the cryostat and dewar. The cryostat is precooled to reduce the duration of the cooling phase, by LN2 circulating in pipes attached to the lateral walls of its inner volume. During the liquefaction process the pulse-tube cryocooler and the LN2 circulation system are switched on. At the end of the process the LN2 flow is switched off and the pulse-tube cryocooler alone maintains the Xe in the liquid state. As previously mentioned LXe is transparent to its own scintillation light, but possible contaminants, such as water or oxygen at the ppm level, could produce considerable absorption. Purification in the final calorimeter is achieved by using a molecular filter and a gas purifier operating in the liquid phase. The coupling of a cryogenic centrifugal pump to the filter and purifier achieved a purification corresponding to 40 ppb from an initial water impurity of 250 ppb, in only 5 h [31,32]. As an example of the importance of the Xe purity and of the usefulness of the calibration method based on the C–W to follow the evolution of the calorimeter response during the 2008 MEG data taking, we present in Fig. 23 the variation of the light emission yield corresponding to the Li 17.6 MeV g-line, as a function of time. The increase in the light yield and several steps present in the plot are associated with the period of operation of the purification methods. At the end of the data-taking period the LXe calorimeter reached a resolution of sEg =Eg ¼ 3:857 0:15% at the 17.6 MeV g-line, as can be seen in Fig. 24. XEC spectrum 300 250 200 150 100 50 0 0 2000 4000 6000 8000 qsum2 10000 12000 14000 Fig. 24. LXe calorimeter resolution at the 17.6 MeV g-line. The events in the 5000– 9000 region are due to the a-particles from the calibration wire sources. 9. The relative time tuning of the experiment The fine-tuning of the relative timing between the LXe calorimeter and the timing-counters is important in obtaining the best possible background rejection in the MEG experiment. To this purpose MEG exploits, for example, the radiative m-decay, in which a g-ray is emitted in addition to the electron and the neutrinos. The MEG Cockcroft–Walton provides both a complementary and simpler approach. The 115 Bðp, g1 g2 Þ 12 6 C is the only proton reaction on a natural element which is highly exothermic and which produces two usable coincident g-rays in the final state. One of these photons can be detected in the calorimeter, while the other might interact in front of or in the timingcounters, so also being detected. Coincidences can be obtained with a high rate, allowing a temporal connection between the calorimeter and the timing-counters to be made in a reproducible 22000 Gas Purification 20000 Fig. 25. The g-ray spectra (in MCA units) from a lithium tetraborate (Li2B4O7) target, as a function of Tp. way. The detected particles, their energies and their paths would however be different to those of the m-eg, or radiative m-decay channels, but nevertheless in a precise relation to them. Timewalk corrections due to the lower energies of the boron g-rays were determined and applied. Liquid Purification photoelectrons 18000 9.1. The boron experimental data 16000 14000 12000 10000 8000 6000 30/04/08 17/06/08 05/08/08 22/09/08 Date 10/11/08 28/12/08 Fig. 23. LXe light emission yield as a function of the calendar date. We measured the g-ray spectra emitted by the lithium tetraborate (Li2B4O7) target above the 163 keV boron resonance, for 400 rTp r 1000 keV. The spectra are shown in Fig. 25 and one can observe that the choice of proton energy ensures the dominance of selected g-lines: at 500 keV, just above the 7Li 440 keV resonance, the 7Li 17.6 MeV g-line is dominant and contributions of the 11B lines are visible at lower g-energies; at 1000 keV the 11B  11.7 MeV g-line is dominant, together with the 12 C 4.4 MeV deexcitation line. In contrast, below the Li-resonance at Tp ¼400 keV, the total rate is low and associated with only 11B. The quality of the 7Li 17.6 MeV line at Tp ¼500 keV, from LiF (red) J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 and from Li2B4O7 (black) is compared in Fig. 26. One can see how similar the two spectra are at around 17.6 MeV. A large fluorine contribution is present in the LiF data, while a small contribution from boron is visible around 11.7 and 4.4 MeV in the Li2B4O7 data. Oxygen does not contribute appreciably to the g-rate. A study of the boron g-coincidences in the LXe calorimeter and in the TC shows that while the g-energy energy is correctly determined in the LXe calorimeter, the 4.4 and 11.7 MeV g-rays interact mainly by Compton effect in the plastic scintillator TC bars. Thus the corresponding energy spectrum measured in the TC consists of two wide partially superimposed Compton electron energy distributions. A scattered plot of the TC energy (in arbitrary units) vs. the LXe calorimeter energy for coincident g-events is presented in Fig. 27. A simulation shows that g-rays reaching the LXe calorimeter are detected with good efficiency (  98%), while a much smaller fraction (  21%) of the g-rays, within the solid angle of the TC, corresponds to interactions. A g-ray is detectable if the 31 corresponding energy loss is 4 1 MeV. The overall efficiency for the detection of all the double boron g-events, generated over the full solid angle and surviving all analysis selections (to be discussed) is of the order of 1.6  10  3, corresponding to a possible acquisition rate of  20 Hz. The selected events provide a sufficiently precise determination of the relative timing of the calorimeter vs. the TC. 9.2. Measuring the time in the TC Prior to the description of the LXe-TC relative timing, let us briefly recall how the arrival time of the positron at the TC is determined. A schematic representation of a TC bar is shown in Fig. 28. The time t0 and t1 measured by the two photomultipliers at each end of a bar of length L, can be written as: c0 h þ b0 t0 ¼ TTC þ pffiffiffiffiffiffi þ A0 veff c1 Lh t1 ¼ TTC þ pffiffiffiffiffiffi þ þ b1 veff A1 ð3Þ ð4Þ where TTC is the arrival time of the positron at the the timing counter bar, pffiffiffiffiffimeasured with respect to an arbitrary reference. The terms ci = Ai , where Ai is the i-th PMT signal amplitude, represent the time walk corrections, h is the distance of the i-th impact point from the inner PMT, veff the effective light velocity in the bar and bi represent any electronic time offset in the same bar. The effective velocity is assumed to be constant along each bar (a good approximation). It is straightforward to extract the impact time of the positron at the TC from the above relations: !   t0 þ t1 1 c0 c1 L b0 þ b1 p ffiffiffiffiffi ffi p ffiffiffiffiffi ffi TTC ¼ þ  ð5Þ  þ 2 2veff 2 2 A0 A1 Note that the term L=ð2veff Þ þðb0 þ b1 Þ=2 is a constant kj characteristic of each TC bar and is thus an inter-bar time offset that needs to be determined and monitored. 9.3. Tuning the LXe-TC relative timing Fig. 26. The g-spectrum, at Tp ¼ 500 keV, from LiF (red) and Li2B4O7 (black); logarithmic scale. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 40 35 TC Energy (a.u.) 30 The study and the accurate monitoring of the LXe-TC timing is performed using boron C–W events yielding two photons in the final state, as previously mentioned. The energy of the g-rays in the LXe calorimeter is required to be less than 8 MeV; namely events are selected where the low energy g-ray enters the calorimeter and the high energy g-ray hits the TC. We define Tgg as the time difference of the two g-rays from the boron reaction, measured by the LXe calorimeter and the TC with reference to the target:     Lg,TC Lg,LXe Tgg ¼ Tg,LXe   Tg,TC  ð6Þ c c where Tg,LXe is the time measured by the LXe calorimeter, Lg,LXe =c is the g-ray time-of-flight from the target (assumed to be point-like and at the origin of the apparatus reference system) to the g-ray impact point on the calorimeter front face. Tg,TC is the TC time of 25 20 15 10 5 0 0 2 4 6 8 10 12 14 16 18 20 LXe Energy (MeV) Fig. 27. Scatter plot of energies measured in the LXe calorimeter and in the timing counter, for coincident 4.4 and 11.7 MeV g-events. Fig. 28. A schematic representation of a particle crossing a TC bar. 32 J. Adam et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 19–32 0.5 250 200 mean of ∆Tγγ (ns) Events/0.25ns Mean = (21.770 ± 0.012)ns Sigma = (0.449 ± 0.014)ns 150 100 0 -0.5 -1 -1.5 -2 50 -2.5 0 0 0 5 10 15 20 25 30 35 40 45 5 50 the first bar hit, using the algorithm previously described, and Lg,TC =c is the g-ray time-of-flight from the target to the TC. The impact point at the TC is derived from the known TC radial position and the z-coordinate measured by the bar PMT time difference. The time Tg,LXe is, at this stage, already corrected for the time offsets between different calorimeter PMTs. Thus, given that the two g-rays are emitted simultaneously, for g-rays impinging on the bar j of the TC we can write: Tgg,j ¼ b0,j þ b1,j L  þ TB ¼ kj þTB 2veff ,j 2 ð7Þ where TB is time offset between LXe and TC, given that the two sub-detectors times are measured by two independent clocks. Fig. 29 shows the Tgg,j distribution for a bar (bar 17). 9.4. Inter-bar offset determination using the Boron events We took advantage of the frequent (twice or three times per week) C–W data-taking planned for the LXe calorimeter calibrations. As already described in Section 7.3, the boron reaction yields two simultaneous g-rays, almost isotropically emitted, of energy 11.7 MeV (g1 , the high energy photon) and 4.4 MeV (g2 , the low energy photon). The distribution for each bar j is fitted by a Gaussian function, in the range of 1.2 ns around its maximum. The mean value of the Gaussian is, by definition, the offset kj þTB. If one arbitrarily chooses, say, bar 17 as the reference, the interbar offset of the j-th bar is the quantity (kj–k17). The tails of the distribution are due to cosmic ray contamination, as verified by data-taking with the C–W accelerator off and the same event selection. The systematic effects on the evaluation of the offsets due to cosmic rays are very small. Additional systematic effects related to the fitting procedure were found to be negligible. The inter-bar time offsets were rather stable during the three month duration of the MEG data-taking. This can be seen in Fig. 30 where the inter-bar offsets are shown as a function of the TC bar number and for various periods. 10. Conclusions Energy and timing calibrations using a proton beam from a Cockcroft–Walton proton accelerator were fully exploited during the 2008 and 2009 MEG data-taking. They were essential for satisfying the strict stability requirements of the experiment and 15 20 25 30 TC bar number Tγγ (ns) Fig. 29. Tgg,j distribution for a single bar (bar 17) with the Gaussian fit superimposed. 10 Fig. 30. The inter-bar offsets (relative to bar 17) vs. the TC bar number for different periods (corresponding to different colors). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) led to a better understanding of the complex processes associated with the use of such a detector. Acknowledgements Preliminary measurements on the nuclear reactions of interest for the MEG experiment were performed at the INFN Legnaro National Laboratories. We thank the laboratory personnel for the effective collaboration. We would also like to express our thanks to the PSI infrastructure groups involved with the construction and commissioning of the MEG C–W area. References [1] R. Barbieri, L.J. Hall, Phys. Lett. B 338 (1994) 212; R. Barbieri, L.J. Hall, A. Strumia, Nucl. Phys. B 445 (1995) 219. [2] M. Ahmed, et al., The MEGA Collaboration, Phys. Rev. D 65 (2002) 112002. [3] The MEG experiment: search for the m-eg decay at PSI (at /http://meg.psi. ch/docs/S). [4] J. Adam, et al., The MEG Collaboration, Nucl. Phys. 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