First measurement of the pi+pi- atom lifetime

Physics Letters B 619 (2005) 50–60 www.elsevier.com/locate/physletb First measurement of the π+π−atom lifetime B. Adevap,L.Afanasyevl,1, M. Benayoune, A. Benelliq,Z.Berkab, V. Brekhovskikho, G. Caragheorgheopolm, T. Cechakb, M. Chibak, S. Constantinescum, C. Detraza, D. Dreossig, D. Drijarda, A. Dudarevl,I.Evangeloud, M. Ferro-Luzzia, M.V. Gallasp,a, J. Gerndtb,R.Giacomichg, P. Gianottif,D.Goldinq,F.Gómezp,A.Gorino, O. Gorchakovl,C.Guaraldof, M. Hansroula,R.Hosekb, M. Iliescuf,m, V. Karpukhinl, J. Klusonb, M. Kobayashih, P. Kokkasd, V. Komarovl,V.Kruglovl, L. Krugloval, A. Kulikovl, A. Kuptsovl, I. Kurochkino, K.-I. Kurodal,A.Lambertog,A.Lanaroa,f, V. Lapshino,R.Lednickyc,P.Lerustee, P. Levi Sandrif, A. Lopez Aguerap, V. Lucherinif,T.Makij,N.Manthosd, I. Manuilovo, L. Montaneta, J.-L. Narjouxe, L. Nemenova,l, M. Nikitinl, T. Núñez Pardop,K.Okadai, V. Olchevskiil,A.Pazosp, M. Pentiam,A.Penzog, J.-M. Perreaua,C.Petrascuf,m,M.Plóp, T. Pontam,D.Popm, G.F. Rappazzog, A. Rodriguez Fernandezp,A.Romerop, A. Ryazantsevo,V.Rykalino, C. Santamarinap,q,a, J. Saboridop, J. Schacherr, Ch.P. Schuetzq,A.Sidorovo, J. Smolikc,F.Takeutchii, A. Tarasovl,L.Tauscherq, M.J. Tobarp,S.Trusovn, V. Utkin l, O. Vázquez Docep, P. Vázquezp,S.Vlachosq,V.Yazkovn, Y. Yoshimurah, M. Zhabitskyl,P.Zrelovl aCERN, Geneva, Switzerland bCzech Technical University, Prague, Czech Republic cInstitute of Physics ACSR, Prague, Czech Republic dIoannina University, Ioannina, Greece eLPNHE des Universites Paris VI/VII, IN2P3-CNRS, France fINFN, Laboratori Nazionali di Frascati, Frascati, Italy gINFN, Trieste and Trieste University, Trieste, Italy hKEK, Tsukuba, Japan iKyoto Sangyo University, Kyoto, Japan jUOEH-Kyushu, Japan kTokyo Metropolitan University, Japan lJINR, Dubna, Russia mIFIN-HH, National Institute for Physics and Nuclear Engineering, Bucharest, Romania nSkobeltsin Institute for Nuclear Physics of Moscow State University, Moscow, Russia oIHEP, Protvino, Russia pSantiago de Compostela University, Spain qBasel University, Switzerland rBern University, Switzerland 0370-2693 2005 Elsevier B.V. doi:10.1016/j.physletb.2005.05.045 Open access under CC BY license. B. Adeva et al. / Physics Letters B 619 (2005) 50–60 51 Received 22 April 2005; accepted 18 May 2005 Available online 31 May 2005 Editor: M. Doser Abstract The goal of the DIRAC experiment at CERN (PS212) is to measure the π+π−atom lifetime with 10% precision. Such a measurement would yield a precision of 5% on the value of the S-wave ππ scattering lengths combination |a0−a2|. Based on part of the collected data we present a first result on the lifetime, τ=[2.91+0.49 −0.62]×10−15 s, and discuss the major systematic errors. This lifetime corresponds to |a0−a2|=0.264+0.033 −0.020m−1 π. 2005 Elsevier B.V. PACS: 36.10.-k; 32.70.Cs; 25.80.E; 25.80.Gn; 29.30.Aj Keywords: DIRAC experiment; Elementary atom; Pionium atom; Pion scattering 1. Introduction The aim of the DIRAC experiment at CERN [1] is to measure the lifetime of pionium, an atom consisting of a π+and a π−meson (A2π). The lifetime is dominated by the charge-exchange scattering process (π+π−→π0π0)2and is thus related to the relevant scattering lengths [4]. The partial decay width of the atomic ground state (principal quantum number n=1, orbital quantum number l=0) is [2,5–9] (1)Γ1S=1 τ1S =2 9α3p|a0−a2|2(1+δ) with τ1Sthe lifetime of the atomic ground state, α the fine-structure constant, pthe π0momentum in the atomic rest frame, and a0and a2the S-wave ππ scattering lengths for isospin 0 and 2, respectively. The term δaccounts for QED and QCD corrections [6–9]. It is a known quantity (δ=(5.8±1.2)×10−2) ensuring a 1% accuracy for Eq. (1) [8]. A measurement of the lifetime therefore allows to obtain in a model-independent way the value of |a0−a2|.Theππ scattering lengths a0,a2have been calculated within the framework of standard chiral perturbation theory [10] with a precision better than 2.5% [11] (a0= E-mail addresses: leonid.afanase[email protected], afanase[email protected].ru (L. Afanasyev). 1PH Division, CERN, CH 1211 Geneva 23, Switzerland. 2Annihilation into two photons amounts to ≈0.3% [2,3] and is neglected here. 0.220 ±0.005, a2=−0.0444 ±0.0010, a0−a2= 0.265 ±0.004 in units of inverse pion mass) and lead to the prediction τ1S=(2.9±0.1)×10−15 s. The generalized chiral perturbation theory though allows for larger a-values [12]. Model independent measurements of a0have been done using Ke4decays [13,14]. Oppositely charged pions emerging from a high energy proton–nucleus collision may be either produced directly or stem from strong decays (“shortlived” sources) and electromagnetic or weak decays (“long-lived” sources) of intermediate hadrons. Pion pairs from “short-lived” sources undergo Coulomb final state interaction and may form atoms. The region of production being small as compared to the Bohr radius of the atom and neglecting strong final state interaction, the cross section σn Afor production of atoms with principal quantum number nis related to the inclusive production cross section for pion pairs from “short lived” sources without Coulomb correlation (σ0 s)[15] (2) dσn A dpA=(2π)3EA MA ΨC nr∗=0  2d2σ0 s dp+dp−    p+=p− with pA,EAand MAthe momentum, energy and mass of the atom in the lab frame, respectively, and p+, p−the momenta of the charged pions. The square of the Coulomb atomic wave function for zero distance r∗between them in the c.m. system is |ΨC n(0)|2= p3 B/πn3, where pB=mπα/2 is the Bohr momentum Open access under CC BY license. 52 B. Adeva et al. / Physics Letters B 619 (2005) 50–60 of the pions and mπthe pion mass. The production of atoms occurs only in S-states [15]. Final state interaction also transforms the “unphysical” cross section σ0 sinto a real one for Coulomb correlated pairs, σC[16,17]: (3) d2σC dp+dp− = ΨC − k∗r∗  2d2σ0 s dp+dp− , where ΨC − k∗(r∗)is the continuum wave function and 2 k∗≡qwith qbeing the relative momentum of the π+and π−in the c.m. system.3|ΨC − k∗(r∗)|2de- scribes the Coulomb correlation and at r∗=0 coincides with the Gamov–Sommerfeld factor AC(q) with q=|q|[17]: (4)AC(q) =2πmπα/q 1−exp(−2πmπα/q). For low q,0⩽q⩽q0,Eqs.(2)–(4) relate the number of produced A2πatoms, NA, to the number of Coulomb correlated pion pairs, NCC [18] NA NCC =σtot A σtot C|q⩽q0 =(2παmπ)3 π ∞ n=11 n3 q0 0AC(q) d3q (5)=kth(q0). Eq. (5) defines the theoretical k-factor. Throughout the Letter we will use (6)q0=2MeV/c and kth(q0)=0.615. In order to account for the finite size of the pion production region and of the two-pion final state strong interaction, the squares of the Coulomb wave functions in Eqs. (2) and (3) must be substituted by the square of the complete wave functions, averaged over the distance r∗and the additional contributions from π0π0→A2πas well as π0π0→π+π−[17].It should be noticed that these corrections essentially cancel in the k-factor (Eq. (5)) and lead to a correction of only a fraction of a percent. Thus finite size corrections can safely be neglected for kth. Once produced, the A2πatoms propagate with relativistic velocity (average Lorentz factor ¯γ≈17 in our case) and, before they decay, interact with target atoms, whereby they become excited/deexcited or 3For the sake of clarity we use the symbol Qfor the experimentally reconstructed and qfor the physical relative momentum. Fig. 1. Relative momentum distributions (q,qL) for atomic π+π− pairs at the point of break-up and at the exit of the target. Note that qLis almost not affected by multiple scattering in the target. break up. The π+π−pairs from break-up (atomic pairs) exhibit specific kinematical features which allow to identify them experimentally [15], namely very low relative momentum qand qL(the component of qparallel to the total momentum p++p−)asshown in Fig. 1. After break-up, the atomic pair traverses the target and to some extent loses these features by multiple scattering, essentially in the transverse direction, while qLis almost not affected. This is one reason for considering distributions in QLas well as in Qwhen analyzing the data. Excitation/deexcitation and break-up of the atom are competing with its decay. Solving the transport equations with the cross sections for excitation and break-up, [20–31] leads to a target-specific relation between break-up probability and lifetime which is estimated to be accurate at the 1% level [22,32,33]. Measuring the break-up probability thus allows to determine the lifetime of pionium [15]. The first observation of the A2πatom [34] has allowed to set a lower limit on its lifetime [18,19] of τ>1.8×10−15 s (90% CL). In this Letter we present a determination of the lifetime of the A2πatom, based on a large sample of data taken in 2001 with Ni targets. B. Adeva et al. / Physics Letters B 619 (2005) 50–60 53 Fig. 2. Schematic top view of the DIRAC spectrometer. Upstream of the magnet: target, microstrip gas chambers (MSGC), scintillating fiber detectors (SFD), ionization hodoscopes (IH) and iron shielding. Downstream of the magnet: drift chambers (DC), vertical and horizontal scintillation hodoscopes (VH, HH), gas Cherenkov counters (Ch), preshower detectors (PSh) and, behind the iron absorber, muon detectors (Mu). 2. The DIRAC experiment The DIRAC experiment uses a magnetic doublearm spectrometer at the CERN 24 GeV/c extracted proton beam T8. Details on the set-up may be found in [35]. Since its start-up, DIRAC has accumulated about 15000 atomic pairs. The data used for this work were taken with two Ni foils, one of 94 µm thickness (76% of the π+π−data), and one of 98 µm thickness (24% of the data). An extensive description of the DIRAC set-up, data selection, tracking, Monte Carlo procedures, signal extraction and a first high statistics demonstration of the feasibility of the lifetime measurement, based on the Ni data of 2001, have been published in [36]. The set-up and the definitions of detector acronyms are shown in Fig. 2. The main selection criteria and performance parameters [36] are recalled in the following. Pairs of oppositely charged pions are selected by means of Cherenkov, preshower and muon counters. Through the measurement of the time difference between the vertical hodoscope signals of the two arms, time correlated (prompt) events (σt =185 ps) can be distinguished from accidental events (see [36]). The resolution of the three components of the relative momentum Qof two tracks, transverse and parallel to the c.m. flight direction, Qx,Qyand QL, is about 0.5 MeV/c for Q⩽4MeV/c. Due to charge combinatorials and inefficiencies of the SFD, the distributions for the transverse components have substantial tails, which the longitudinal component does not exhibit[37]. This is yet anotherreason for analyzing both Qand QLdistributions. Data were analyzed with the help of the DIRAC analysis software package ARIANE [39]. The tracking procedures require the two tracks either to have a common vertex in the target plane (“V-tracking”) or to originate from the intersect of the beam with the target (“T-tracking”). In the following we limit ourselves to quoting results obtained with T-tracking. Results obtained with V-tracking do not show significant differences, as will be shown later. The following cuts and conditions are applied (see [36]): •at least one track candidate per arm with a confidence level better than 1% and a distance to the beam spot in the target smaller than 1.5 cm in xand y; •“prompt” events are defined by the time difference of the vertical hodoscopes in the two arms of the spectrometer of |t|⩽0.5ns; •“accidental” events are defined by time intervals −15 ⩽t ⩽−5 ns and 7 ⩽t ⩽17 ns, determined by the read-out features of the SFD detector (time dependent merging of adjacent hits) and exclusion of correlated π−ppairs. [36]; 54 B. Adeva et al. / Physics Letters B 619 (2005) 50–60 •protons in “prompt” events are rejected by time- of-flight in the vertical hodoscopes for momenta of the positive particle below 4 GeV/c. Positive particles with higher momenta are rejected; •e±and µ±are rejected by appropriate cuts on the Cherenkov, the preshower and the muon counter information; •cuts in the transverse and longitudinal components of Qare QT⩽4MeV/c and |QL|<15 MeV/c. The QTcut preserves 98% of the atomic signal. The QLcut preserves data outside the signal region for defining the background; •only events with at most two preselected hits per SFD plane are accepted. This provides the cleanest possible event pattern. 3. Analysis The spectrometer including the target is fully simulated by GEANT-DIRAC [38], a GEANT3-based simulation code. The detectors, including read-out, inefficiency, noise and digitalization are simulated and implemented in the DIRAC analysis code ARIANE [39]. The triggers are fully simulated as well. The simulated data sets for different event types can therefore be reconstructed with exactly the same procedures and cuts as used for experimental data. The different event types are generated according to the underlying physics. Atomic pairs. Atoms are generated according to Eq. (2) using measured total momentum distributions for short-lived pairs. The atomic π+π−pairs are generated according to the probabilities and kinematics described by the evolution of the atom while propagating through the target and by the break-up process (see [40]). These π+π−pairs, starting from their spatial production point, are then propagated through the remaining part of the target and the full spectrometer using GEANT-DIRAC. Reconstruction of the track pairs using the fully simulated detectors and triggers leads to the atomic pair distribution dnMC A/dQ. Coulomb correlated π+π−pairs (CC-back- ground). The events are generated according to Eqs. (3), (4) using measured total momentum distributions for short-lived pairs. The generated q-dis- tributions are assumed to follow phase space modified by the Coulomb correlation function (Eq. (4)), dNgen CC /dq ∝q2×AC(q). Processing them with GEANT-DIRAC and then analyzing them using the full detector and trigger simulation leads to the Coulomb correlated distribution dNMC CC /dQ. Non-correlated π+π−pairs (NC-background). π+π−pairs, where at least one pion originates from the decay of a “long-lived” source (e.g., electromagnetically or weakly decaying mesons or baryons) do not undergo any final state interactions. Thus they are generated according to dNgen NC /dq ∝q2, using slightly softer momentum distributions than for short-lived sources (difference obtained from FRITIOF-6). The Monte Carlo distribution dNMC NC /dQ is obtained as above. Accidental π+π−pairs (acc-background).π+π− pairs, where the two pions originate from two different proton–nucleus interactions, are generated according to dNgen acc /dq ∝q2, using measured momentum distributions. The Monte Carlo distribution dNMC acc /dQ is obtained as above. All the Monte Carlo distributions are normalized, Qmax 0(dNMC i/dQ)dQ =NMC i,i=CC,NC,acc, with statistics about 5 to 10 times higher than the experimental data; similarly for atomic pairs (nMC A). The measured prompt distributions are approximated by appropriate shape functions. The functions for atomic pairs, FA(Q), and for the backgrounds, FB(Q), (analogously for QL) are defined as FA(Q) =nrec A nMC A dnMC A dQ , (7) FB(Q) =Nrec CC NMC CC dNMC CC dQ +Nrec NC NMC NC dNMC NC dQ +ωaccNpr NMC acc dNMC acc dQ with nrec A,Nrec CC,Nrec NC the reconstructed number of atomic pairs, Coulomb- and non-correlated background, respectively, and ωacc the fraction of accidental background out of all prompt events Npr. Analyzing the time distribution measured with the vertical hodoscopes (see [36]) we find ωacc =7.1% (7.7%) for the 94 µm (98 µm) data sets [36,37] and keep it fixed when fitting. The χ2function for Q(analogously for B. Adeva et al. / Physics Letters B 619 (2005) 50–60 55 Fig. 3. Top: experimental Qand QLdistributions after subtraction of the prompt accidental background, and fitted Monte Carlo backgrounds (dotted lines). The peak at Q=4 MeV/c is due to the cut QT⩽4 MeV/c. Bottom: residuals after background subtraction. The dotted lines represent the expected atomic signal shape. The bin-width is 0.25 MeV/c. QL) to minimize is (8) χ2= νmax  νmin dNpr dQ Qν−([FA(Q) +FB(Q)]Q)ν2 dNpr dQ Qν+(σA)2 ν+(σB)2 ν with Q the bin width and σA,σBthe statistical errors of the Monte Carlo shape functions, which are much smaller than that of the measurement. The fit parameters are nrec A,Nrec CC,Nrec NC (see Eq. (7)). As a constraint the total number of measured prompt events is restricted by the condition Npr(1−ωacc)=Nrec CC + Nrec NC +nrec A. The measured distributions as well as the background are shown in Fig. 3 (top). The data taken with 94 and98 µm thick targets were analyzed separately. The total number of events in the prompt window is Npr =471290. First, we determine the background composition by minimizing Eq. (8) outside of the atomic pair signal region, i.e., for Q>4MeV/c and QL>2MeV/c. For this purpose we require nrec A=0. As a constraint, the background parameters Nrec CC and Nrec NC representing the total number of CC- and NC-events, have to be the same for Qand QL. Then, with the parameters found, the background is subtracted from the measured prompt distribution, resulting in the residual spectra. For the signal region, defined by the cuts Q=4MeV/c and QL=2MeV/c, we obtain the total number of atomic pairs, nresidual Aand of Coulomb correlated background events, Nsig CC. Results of fits for Qand QLtogether are shown in Table 1. CC-background and NC- or acc-backgrounds are distinguishable due to their different shapes, most pronounced in the QLdistributions (see Fig. 3, top). Accidental and NC-background shapes are almost identical for Qand fully identical for QL(uniform distributions). Thus, the errors in determining the accidental background ωacc are absorbed in fitting the NC background. The correlation coefficient between CC and NC background is −99%. This strong correlation leads to equal errors for Nrec CC and Nrec NC. The CC- background is determined with a precision better than 1%. Note that the difference between all prompt events and the background is Npr −Nrec CC −Nrec NC −ωaccNpr = 6590, hence very close to the number of residual atomic pairs (nresidual A) as expected. This relation is alsousedas a strictconstraintfor fits outside ofthesig- 56 B. Adeva et al. / Physics Letters B 619 (2005) 50–60 Table 1 Fit results (94 and 98 µm targets together, background shapes from Monte Carlo (MC)) for the parameters Nrec CC (total number of CC-events), Nrec NC (total number of NC-events) and nrec A(atomic pairs) and deduced results for the number of atomic pairs from the residuals (nresidual A)and the number of CC-background events in the signal region (Nsig CC). MC-a: background fit excluding the signal region. MC-b: fit of the entire momentum range including Monte Carlo shape for atomic pairs (“shape fit”). The cuts were at Qcut =4 MeV/c and QL,cut =2 MeV/c.Q and QL-distributions were fitted together. The normalized χ2were 0.9 for MC-a and MC-b Nrec CC Nrec NC nresidual Anrec ANsig CC MC-a Q374022 ±3969 56538 6518 ±373 106500 ±1130 QLsame same 6509 ±330 82289 ±873 MC-b Q374282 ±3561 56213 6530 ±294 106549 ±1014 QLsame same same 82345 ±783 nal region (>), N> pr −Nrec> CC −Nrec> NC −(ωaccNpr)>=0 and, hence, the fit requires only one free parameter, Nrec> CC . Second, the atomic pair signal may be directly obtained by minimizing Eq. (8) over the full range and including the Monte Carlo shape distribution FA (“shape fit”). The signal strength has to be the same for Qand QL. The result for the signal strength nrec A as well as the CC-background below the cuts, Nsig CC, are shown in Table 1. The errors are determined by MINOS [41]. The consistency between the analysis in Qwith the one in QLestablishes the correctness of the QTreconstruction. A 2D fit in the variables (QL,Q T) confirms the results of Table 1. 4. Break-up probability In order to deduce the break-up probability, Pbr = nA/NA, the total number of atomic pairs nAand the total number of produced A2πatoms, NA,havetobe known. None of the two numbers is directly measured. The procedure of obtaining the two quantities requires reconstruction efficiencies and is as follows. Number of atomic pairs. Using the generator for atomic pairs a large number of events, ngen A, is generated in a predefined large spatial acceptance window Ωgen, propagated through GEANT-DIRAC including the target and reconstructed along the standard procedures. The total number of reconstructed Monte Carlo atomic pairs below an arbitrary cut in Q,nMC-rec A(Q ⩽ Qcut)defines the reconstruction efficiency for atomic pairs cut A=nMC-rec A(Q ⩽Qcut)/ngen A. The total number of atomic pairs is obtained from the measured pairs by nA=nrec A(Q ⩽Qcut)/cut A. Number of produced A2πatoms.Hereweusethe known relation between produced atoms and Coulomb correlated π+π−pairs (CC-background) of Eq. (5). Using the generator for CC pairs, Ngen CC events, of which Ngen CC (q ⩽q0)(see Eq. (6))haveqbelow q0, are generated into the same acceptance window Ωgen as for atomic pairs and processed analogously to the paragraph above to provide the number of reconstructed CC-events below the same arbitrary cut in Qas for atomic pairs, NMC-rec CC (Q ⩽Qcut). These CC-events are related to the originally generated CC-events below q0through cut CC =NMC-rec CC (Q ⩽ Qcut)/Ngen CC (q ⩽q0). The number of produced atoms thus is NA=kth(q0)Nrec CC(Q ⩽Qcut)/cut CC (see Eq. (6)). The break-up probability Pbr thus becomes Pbr =nA NA=nrec A(Q ⩽Qcut) k(Qcut)Nrec CC(Q ⩽Qcut)with (9)k(Qcut)=kth(q0)cut A cut CC . In Table 2 the k-factors are listed for different cuts in Qand QLfor the two target thicknesses (94 and 98 µm) and the weighted average of the two, corresponding to their relative abundances in the Ni data of 2001. The accuracy is of the order of one part per thousand and is due to Monte Carlo statistics. With the k-factors of Table 2 and the measurements listed in Table 1, the break-up probabilities of Table 3 are obtained. The simultaneous fit of Qand QLwith the atomic shape results in a single value. B. Adeva et al. / Physics Letters B 619 (2005) 50–60 57 Table 2 k(Qcut)factors as a function of cuts in Qand QLfor the 94 and 98 µm thick Ni targets, and the weighted average of the two for a relative abundance of 76% (94 µm) and 24% (98 µm) k94 µm k98 µm kaverage Qcut =2 MeV/c 0.5535 ±0.0007 0.5478 ±0.0007 0.5521 ±0.0007 Qcut =3 MeV/c 0.2565 ±0.0003 0.2556 ±0.0003 0.2563 ±0.0003 Qcut =4 MeV/c 0.1384 ±0.0002 0.1383 ±0.0002 0.1384 ±0.0002 QL,cut =1 MeV/c 0.3054 ±0.0004 0.3044 ±0.0003 0.3050 ±0.0004 QL,cut =2 MeV/c 0.1774 ±0.0002 0.1776 ±0.0002 0.1774 ±0.0002 Table 3 Break-up probabilities for the combined Ni 2001 data, based on the results of Table 1 and the k-factors of Table 2 for the cuts Qcut = 4 MeV/c and QL,cut =2 MeV/c. Errors are statistical nresidual Anrec ANsig CC Pbr Q6518 ±373 106500 ±1130 0.442 ±0.026 QL6509 ±330 82289 ±873 0.445 ±0.023 Q&QL6530 ±294 106549 ±1004 0.447 ±0.023 The break-up probabilities from Qand QLagree within a fraction of a percent. The values from shape fit and from background fit are in perfect agreement (see Table 1). We adopt the atomic shape fit value of Pbr =0.447 ±0.023stat, because the fit covers the full Q,QLrange and includes correlations between nrec A and Nsig CC. Analyzing the data with three allowed hit candidates in the SFD search window instead of two, results in more atomic pairs (see Ref. [36], T-tracking). The break-up probabilities obtained are 0.440±0.024 and 0.430 ±0.021 for Qand QL, respectively. They are not in disagreement with the adopted value of 0.447. Despite the larger statistics, the accuracy is not improved, due to additional background. This background originates from additional real hits in the upstream detectors or from electronic noise and crosstalk. This has been simulated and leads essentially to a reduced reconstruction efficiency but not to a deterioration of the reconstruction quality. The additional sources of systematic uncertainties lead us not to consider this strategy of analysis further on. V-tracking provides a slightly different data sample, different k-factors and different signal strengths and CC-background. The break-up probability, however, does not change significantly and is PV-tracking br = 0.453±0.025stat, only 0.3σoff from the adopted value 0.447. The break-up probability has to be corrected for the impurities of the targets. Thus, the 94 µm thick target has a purity of only 98.4%, while the 98 µm thick target is 99.98% pure. The impurities (C, Mg, Si, S, Fe, Cu) being mostly of smaller atomic number than Ni lead (for the weighted average of both targets) to a reduction of the break-up probability of 1.1% as compared to pure Ni, assuming a lifetime of 3 fs. Therefore, the measured break-up probability has to be increased by 0.005 in order to correspond to pure Ni. The final result is (10)Pbr =0.452 ±0.023stat. 5. Systematic errors Systematic errors may occur through the analysis procedures and through physical processes which are not perfectly under control. We investigate first procedure-induced errors. The break-up probability will change, if the ratio Nrec CC/Nrec NC depends on the fit range. If so, the Monte Carlo distributions do not properly reproduce the measured distributions and the amount of CC-background may not be constant. In Fig. 4 the dependence is shown for the fits in Q,QLand both together. The ratio is reasonably constant within errors, with the smallest errors for a fit range of Q=QL=15 MeV/c. At this point the difference between Qand QLfits leads to a difference in break-up probability of P CC br =0.023. Consistency of the procedure requires that the break-up probability does not depend on Qcut.In Fig. 5 the dependence on the cut is shown for break-up probabilities deduced from nresidual A. There is a systematic effect which, however, levels off for large cut momenta. This dependence indicates that the shape of the atomic pair signal as obtained from Monte Carlo 58 B. Adeva et al. / Physics Letters B 619 (2005) 50–60 Fig. 4. Ratio of CC-background over NC-background as a function of fit range. (and used for the k-factor determination) is not in perfect agreement with the residual shape. This may be due to systematics in the atomic pair shape directly and/or in reconstructed CC-background for small relative momenta. The more the signal is contained in the cut, the more the Pbr values stabilize. As a consequence, we chose a cut that contains the full signal (see Eq. (10)). This argument is also true for sharper cuts in QTthan the one from the event selection. Cut momenta beyond the maximum cut of Fig. 5 would only test background, as the signal would not change anymore. To investigate whether the atomic pair signal shape is the cause of the above cut dependence, we studied two extreme models for atom break-up: break-up only from the 1S-state and break-up only from highly excited states. The two extremes result in a difference in break-up probability of P shape br =0.008. Sources of systematic errors may also arise from uncertainties in the genuine physical process. We have investigated possible uncertainties in multiple scattering as simulated by GEANT by changing the scattering angle in the GEANT simulation by ±5%. As a result, the break-up probability changes by 0.002 per one percent change of multiple scattering angle. Fig. 5. Pbr as a function of cut momentum for Qand QL. In fact we have measured the multiple scattering for all scatterers (upstream detectors, vacuum windows, target) and found narrower angular distributions than expected from the standard GEANT model [42].This, however, may be due also to errors in determining the thickness and material composition of the upstream detectors. Based on these studies we conservatively attribute a maximum error of +5% and −10% to multiple scattering. Another source of uncertainty may be due to the presence of unrecognized K+K−and ¯pp pairs that would fulfill all selection criteria [43]. Such pairs may be as abundant as 0.5% and 0.15%, respectively, of π+π−pairs as estimated for K+K−with FRITIOF- 64and for ¯pp from time-of-flight measurements in a narrow momentum interval with DIRAC data. Their mass renders the Coulomb correlation much more peaked at low Qthan for pions, which leads to a change in effective π+π−Coulomb background at small Q, thus to a smaller atomic pair signal and therefore to a decrease of break-up probability. The effect leads to a change of P ¯ KK, ¯pp br =−0.04. We do not 4FRITIOF-6 reproduces well production cross sections and momentum distributions for 24 GeV/c proton interactions.