ATMOSPHERIC MUONS IN HANOI

ATMOSPHERIC MUONS IN HANOI Pham Ngoc Diep, Pham Ngoc Dinh, Pham Thi Tuyet Nhung, Pierre Darriulat, Nguyen Thi Thao, Dang Quang Thieu and Vo Van Thuan Vietnam Auger Training Laboratory Institute for Nuclear Science and Technology 5T-160, Hoang Quoc Viet, Nghia Do, Cau Giay Hanoi, Vietnam Abstract Recent measurements of the atmospheric muon flux in Hanoi are reviewed. Being made in a region of maximal geomagnetic rigidity cutoff, they provide a sensitive test of air shower models used in the interpretation of neutrino oscillation experiments. In particular very good agreement is found between the data and the model of M.Honda. Introduction Recently, the study of atmospheric neutrinos, following the pioneering work of the Kamiokande collaboration [1], has reached unprecedented accuracy and unambiguously established the existence of oscillations between the heavier neutrino flavours [2]. The reduction and the interpretation of such data require a good knowledge of the atmospheric neutrino fluxes over the whole planet, as neutrinos reaching the detector may have been generated at any point in the earth atmosphere. This is done in practice with the help of Monte Carlo codes [3] simulating the generation of neutrinos as decay products of mesons, mostly pions and kaons, produced in the hadronic showers induced in the atmosphere by primary cosmic rays, mostly protons. Muons happen to be good tracers of muon neutrinos as both particles are produced in pairs. The fraction of muons originating from other sources (muon pairs coupled to a virtual photon, i.e. Drell-Yan or electromagnetic meson decays) is indeed negligible. However, while neutrinos are stable and reach the detector without interacting with the atmosphere, muons decay weakly into an electron and a pair of neutrinos (electronic and muonic) and loose energy by ionization (Bethe-Bloch). These effects introduce differences between the differential (w.r.t. momentum) neutrino and muon neutrino fluxes upon arrival on ground. They need to be corrected for, but such corrections are kept under easy control as the decay length is large with respect to atmosphere thickness and the energy loss small with respect to the average muon energy. The measurement of the atmospheric muon flux over various regions of the planet is therefore a valuable input for the elaboration of reliable and accurate Monte Carlo simulation codes. Of particular interest are measurements performed in regions that cover a broad range of geomagnetic rigidity cutoffs (a quantity that measures the shielding effect of the earth magnetic field on primary cosmic protons aiming at the earth). Hanoi happens to be located on the geomagnetic equator, in a place where the

rigidity cutoff is largest (Figure 1). It reaches the high value of 17 GV compared with 11 GV in Japan and typically 2 GV to 4 GV in most European and North American laboratories where the atmospheric muon flux has been accurately measured. Recent measurements of the atmospheric muon flux in Hanoi are reported hereafter and are compared with the predictions of a widely used simulation code [3]. The predicted spectrum of the muon kinetic energy, that is not accessible to the measurements reported here, is illustrated in Figure 2. It has a mean value of 4.8 GeV/c. The zenith angle (θ) dependence of the muon flux reflects mainly the differences in atmosphere thicknesses (~1/cosθ) traversed by the developing shower. In the present case of relatively low energy showers reaching sea level, the particle density has since long gone over its maximum and decreases rapidly when approaching ground. As a result the muon flux is nearly inversely proportional to the square of the atmosphere thickness traversed, (~cos 2 θ). A strong east-west asymmetry is expected from the fact that eastward- and westward-flying primary protons are affected differently by the rigidity cutoff. This asymmetry is essentially preserved in the hadronic shower development and its measurement is reported below. Figure1. Curves of constant rigidity cutoff. Figure2. The kinetic energy distribution of atmospheric muons in Hanoi as predicted by the Honda model [3]. Description of the apparatus The measurements have been performed using two different arrangements of scintillator plates. Each scintillator plate, 80 80 3 cm 3, was seen by a single 2" photomultiplier tube (PMT) through a 40 40 cm 2 light guide. Both the time of arrival and the area of each PMT signal were recorded for each event. In all cases the trigger was fully efficient and the accidental rate was negligible. In a first arrangement (Figure 3) 17 plates were used in a fixed geometry allowing for a measurement of the flux in a ~20 cone around the vertical [4]. The acceptance of the detector was 0.31 m 2 sr. The arrangement allowed for an effective segmentation of the detector that was used to help the separation of muons from electromagnetic showers (the main background in that case). Absorbers of different thicknesses were placed on top of the detector and used to correct for absorption in the roof of the laboratory. In a second geometry (Figure 4) six plates were used in an orientable telescope arrangement installed on the roof of the laboratory that provided full sky coverage up to

75 zenith angle. The acceptance of the detector was 0.022 m 2 sr, independent from the telescope orientation. The four plates in the rear of the detector were arranged in two sets of two, separated by an iron radiator (1.2 radiation lengths thick) used to monitor the electron contamination. Moreover data were taken at vertical incidence with a 10cm thick lead absorber in front of the four rear plates, sufficient to filter out any non-muon component with a very high efficiency. These data were used to normalise those collected at other incidence angles and to serve as a reference in the electron subtraction procedure. The same telescope was used to measure the zenith angle [5] and azimuthal [6] dependences of the muon flux. Roof a) b) Figure3. Fixed geometry hodoscope[4]. Bullets tell where light is collected from. Iron Figure4. Schematic telescope assembly [5,6] a) artist view of the orientable ensemble b) schematic scintillator arrangement. The effective momentum cutoffs of the two setups, fixed and orientable, were 190 and 120 MeV/c respectively. The latter is applied throughout the present work (including on model predictions) and the effect of the former has been corrected for accordingly. c arb. scale Figure5. Pulse area distribution [4] of a muon enriched sample (a) and of an electron enriched sample (b). Pulse area distributions [5] measured in front of the iron radiator (c): normal sequence telescope data at 75 zenith angle (up), normal sequence telescope data at 0 (middle), lead absorber telescope data at 0 (down).

Data analysis The methods of data analysis have been described in detail in References 4, 5 and 6. Here it is sufficient to recall the main points. The shape of the distribution of the PMT pulse area is a good revelator of the presence of background and is used to help muon identification. In the case of muons, it displays a characteristic Landau distribution while in the case of electrons it develops a tail at high values (Figure 5a). A cut on this quantity can be devised with both a high rejection power and a high efficiency. In the telescope arrangement a cut at 1.5 mip (minimum ionising particle equivalent) rejects also most of the genuine background (other than electrons) while retaining a 91% efficiency for muons( Figure 5b). At large zenith angles a time of flight cut between the front and rear telescope scintillators is used to reject a small fraction of backward flying particles that interact in the iron radiator and splash onto the front scintillators. The subtraction of the electron contamination is made using very different methods in the two arrangements. In the fixed geometry it uses the particle multiplicity as a rejection criterion while in the telescope geometry it uses the signal recorded beyond the iron radiator. Yet, both methods yield compatible results, 7.0±1.9% in the first case and 8.0±0.7% in the second. The second method is illustrated in Figure 6 where the pulse area distributions measured behind the iron radiator are displayed. Calling N 1 and N 2 the number of events recorded respectively below and above a 2mip cut one has N 1 =µ 1 +e 1 and N 2 =µ 2 +e 2 =αµ 1 +βe 1. The parameters α and β, assumed to be angleindependent, are obtained from the vertical incidence data recorded with and without the lead absorber (N lead and N lead + N respectively, N having been corrected for small differences in attenuation), namely α=[ N 2 / N 1 ] lead and β= N 2 / N 1. It is then possible to separate the electron and muon contributions at any angle according to: µ=(1+α)(β N 1 N 2 )/(β α) and e=(1+ β)(n 2 αn 1 )/(β α). Cut a b Pulse area behind iron Figure6. a) Pulse area distributions [5] measured behind the iron radiator: normal sequence telescope data at 0 zenith angle (up), normal sequence telescope data at 75 (middle), lead absorber telescope data at 0 (down). b) description of the electron subtraction procedure (see text).

Typical corrections are at the few percent level in each configuration. In the telescope data a global normalization uncertainty of 2.2% (having its origin in the lead absorber data) applies to all angles while additional point-to-point uncertainties apply to θ>0. They are listed below: Global uncertainties Point-to-point uncertainties Background (not muon) 1.2% Electron subtraction 0.7% Statistics 0.2% Backward electrons (60 ) 0.4% Acceptance 1.5% Hadron contamination 0.5% Hadron contamination 1.5% Statistics 0.5% Stopping muons 0.9% Angle setting accuracy 0.7% A 0.8% uncertainty has been used to account for effects that are not accounted for explicitly otherwise, such as the variation of atmospheric pressure with time. Indeed it was observed [7] that the muon flux decreases by 1.5 per mil when the ground atmospheric pressure increases by 1 mbar. Dependence on the ground temperature was found to be fully and trivially accounted for by the correlation that relates temperature and pressure at ground level. Results and conclusions The vertical muon flux was measured to be 71.3±2.8 m -2 sr -1 s -1 using the fixed geometry hodoscope in April 2001. Using the orientable telescope the values 70.9±0.6 m -2 sr -1 s -1-2 -1-1 and 70.3± 0.4 m sr s were measured in October-December 2002 and February-May 2003 with an additional common normalization uncertainty of ±2.2%. As mentioned earlier these numbers are for the total spectrum integrated above a common momentum cutoff of 120 MeV/c. The three experimental numbers are equal within errors with a weighted ave rage of 70.6±1.4 m -2 sr -1 s -1 in excellent agr eement with the prediction of the Honda model [3], 70.9 m -2 sr -1 s -1. At the level of sensitivity of the experiment, no significant variation of the muon flux has been observed over the two year period between spring 2001 and spring 2003. Indeed the solar activity stayed near maxim um during that period [8]. Zenith angle distributions were measured in 2002 with the telescope pointing to the north and in 2003 with the telescope pointing to the east and west. They are dominated by the ~cos 2 θ dependence mentioned earlier. For a presentation that can reveal small deviations between measurements and predictions it is convenient to remove most of the θ dependence by dividing the fluxes by an appropriate form. This is done in Figure 7a where the measured and predicted fluxes have been divided by cos 2 θ (1-0.108 sin 2 θ). The value of the parameter χ 2 describing the quality of the agreement between measurements and prediction is 43 for 20 degrees of freedom, reflecting a slight but significant steeper decrease of the experimental data with respect to model prediction. The model used here for the comparison is the three dimensional

version of the Honda model. The prediction of the earlier one dimensional version is slightly steeper and gives a better fit. The east-west asymmetry of the muon flux is displayed in Figure 7b. Data and prediction are in good agreement with a χ 2 of 11 for 10 degrees of freedom. Azimuthal distributions were measured at zenith angles of 50 and 65 where the east-west asymmetry is near maximum. The results are displayed in Figure 8. The χ 2 of the comparison between data and prediction is 53 for 35 degrees of freedom. It decreases to 26 when shifting the two curves with respect to each other by 4±3 and increasing the amplitude of the measured azimuthal oscillation by 16±4%. While there is no significant azimuthal phase shift between data and model prediction, the amplitude of the azimuthal oscillation is slightly smaller in the data than in the model. a Figure7. a) θ-dependence of the muon flux divided by cos 2 θ (1-0.108 sin 2 θ). East- west averaged (full circles, [6]) and north (open circles, [4]) data are compared with the predictions of the Honda model [3] (full and dashed lines respectively). b) θ-dependence of the east-west asymmetry. Data (full circles, [6]) are compared with the predictions of the Honda model (full line, [3]). b Figure8. Azimuthal dependence of the measured (full circles, [6]) and predicted (full lines, [3]) muon flux divided by cos 2 θ (1-0.108 sin 2 θ). a) at θ =50, b) at θ =65.

In summary, data and predictions show an excellent overall agreement within an experimental accuracy that is typically at the 2% level. These measurements, being performed on the geomagnetic equator, provide a useful check of the quality of the simulation codes used in the analysis of neutrino oscillation experiments. The small differences that have been occasionally noted are barely significant and at the limit of the experimental accuracy. In particular a better experimental sensitivity would be required to significantly discriminate between the predictions of the one-dimensional and threedimensional versions of the Honda model. Acknowledgements We thank Professor M. Honda for his keen interest in our work, for scientific advice and for having produced for us Monte Carlo files tailored to the conditions of the present experiment. We acknowledge the invaluable contribution of Mr. Nguyen Hai Duong to part of the data taking and analysis. We are deeply indebted to CERN, RIKEN, the French CNRS, the Rencontres du Vietnam, the Natural Science Council of Vietnam and the Pierre Auger Collaboration for support. References [1] KS Hirata et al., Phys. Rev. D38 (1998) 448. [2] SuperKamiokande Collaboration, Phys. Rev. Lett. 85(2000)3999 and references therein. [3] M Honda et al. in Proc. 2001 Int. Cosmic Ray Conf., ICRC 2001, Copernicus Gesellschaft, Hamburg, 3(2001)1162 and references therein; M Honda et al., in preparation. [4] PN Dinh et al., Nucl. Phys. B 627 (2002) 29. [5] PN Dinh et al., Nucl. Phys. B 661 (2003) 3. [6] PN Diep et al., Nucl. Phys. B 678 (2004) 3. [7] PN Diep et al., Com. Phys. Vietnam 14 (2003) 57. [8] JA Joselyn et al., Solar cycle 23 project, http://science.msfc.nasa.gov./ssl/pad/solar/predict.htm; EW Cliver and AG Ling, Astrophys. J. Lett. L 189 (2001) 551; U. of N. Hampshire/EOS and Chicago/LASR, cosm. phys. inst. in space, http://ulysses.sr.unh.edu/neutronmonitor/misc/neutron2.html;