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Hadron energy resolution as a function of iron plate thickness and hadron direction resolution in INO ICAL Lakshmi S Mohan, For the INO collaboration The Institute of Mathematical Sciences, Chennai 600 113, India E-mail: [email protected] Abstract. The India-based Neutrino Observatory (INO) is a proposed underground laboratory designed to study atmospheric neutrino properties using a magnetized iron calorimeter detector (ICAL). This helps in the identification and easy calibration of (anti)-muons produced in the interactions of (anti)-neutrinos with the iron nuclei in the detector. The hadrons produced in the neutrino interactions appear only as showers in the detector. The GEANT4based simulation studies of the dependence of hadron energy resolution on the thickness of the iron plate, and the methods to reconstruct hadron direction in ICAL are presented along with the preliminary results. 1. Introduction The proposed India-based Neutrino Observatory (INO) is an underground laboratory designed primarily to study atmospheric neutrino properties using a magnetised iron calorimeter (ICAL) detector. ICAL is mainly sensitive to muons produced in the charged-current (CC) interactions of (anti)-neutrinos with the target iron nuclei [1]. To reconstruct the energy and direction of the incident neutrino, the energy and direction of the hadrons in the final state have to be measured as well; in fact, the physics reach of ICAL can be improved by adding the information from these final state hadrons. Unlike muons, hadrons do not leave a long clean track in the ICAL detector. Instead of measuring the energies of individual hadrons in a shower, total number of hits due to hadrons are used to calibrate the energy deposited [2]. The hit pattern is used to reconstruct the net hadron direction too. In this article, the GEANT4-based simulation studies of resolutions of hadron energy as function of iron plate thickness and reconstruction of hadron direction in the detector are discussed. 2. INO ICAL detector The default design of INO ICAL detector has three modules of 151 layers of magnetised iron plates of thickness 5.6 cm. Each module is 16 m × 16 m in the X-Y plane, interspersed with Resistive Plate Chambers (RPC) as active detector elements (for more details, see Refs. [1] and [2]). Iron is the target material for (anti)-neutrino interaction whereas RPCs detect the charged particles produced in these interactions. For the study of thickness dependence, 11 thicknesses in the range 1.5 cm – 8 cm, including the ICAL default thickness 5.6 cm and MINOS and MONOLITH iron plate thicknesses of 2.5 Mean hits (mean arith ) 40 σ arith 2.5cm Fe 5.6cm Fe 8cm Fe 16 mean arith 2.5cm Fe 5.6cm Fe 8cm Fe 14 12 ry 30 na mi 10 i O IN el Pr ry σarith 50 O IN 8 20 ina im el Pr 6 4 10 2 0 2 4 6 8 10 12 Eπ (GeV) 2 14 4 6 8 10 E π(GeV) 12 14 Figure 1. Variation of mean meanarith (left) and the width of the hit distribution σarith (right) with incident pion energy Eπ in GeV for three different plate thicknesses 2.5 cm, 5.6 cm, and 8 cm which represent MINOS, ICAL and MONOLITH respectively. cm and 8 cm, were used. Fixed energy, direction-averaged (both in θ and φ) single pions (π + ) of energies upto 15 GeV were propagated inside the detector volume with vertices randomized over the central volume of 2 m × 2 m× 2 m. For the direction resolution studies, the default ICAL configuration has been used. Here single pions with fixed energy and zenith angle (averaged over the azimuthal angle) are considered. 3. Hadron energy resolution as a function of iron plate thickness Since hadrons produce showers inside the detector, hadron energy is calibrated to the number of hits. The mean (meanarith ) and sigma (σarith ) of the actual hit distribution are used for the present analysis. As seen from Fig. 1, there is a systematic increase in meanarith and σarith with the decrease in thickness of the absorber. The mean hits as a function of energy can be expressed as n(E) = n0 [1 − exp(−E/E0 )], where n0 and E0 are the fit constants. Typically, E0 ≫ E, so that n/n0 ≃ E/E0 , or linear behavior is seen in the energy range of interest E ≤ 15 GeV . Energy resolution is expressed as (σ(E)/E) = (∆n(E)/n(E)) ≡ (width/mean hits) and is fitted to the form, σ(E) E 2 = a2 + b2 , E where E is in GeV. Here, a is the stochastic coefficient and b is a constant. The analysis is performed in three different energy ranges viz, 2–4.75 GeV, 5–15 GeV and 2–15 GeV. Thickness dependence of stochastic coefficient a is parametrized as a(t) = p0 tp1 + p2 , where p0 is a constant and p2 is the residual resolution. The thickness dependence of a in the 2–15 GeV energy range √ is shown in Fig. 2. It can be seen that it is not a t dependence as expected [3]; however, a increases significantly with thickness. Term b, as determined by the intercept, ranges from 0.23–0.29 with a small increase with thickness within 2–15 GeV. √ In comparison, MONOLITH (angle averaged) has √a resolution of ∼ 90%/ E ⊕ 30% [4] which is roughly comparable to our result of ∼ 98.5%/ √ E ⊕ 29.4% for 8 cm iron plate in the energy range 2–15 GeV. MINOS has reported ∼ 70%/ E resolution for gas based detectors and √ ∼ 50%/ E resolution for scintillator based detectors [5],[6] but this is with respect to beams, which agrees roughly with our results for 4 cm with pions propagated along the vertical direction. The thickness dependence of the stochastic coefficient a is a = p0 tp1 + p2 . It is seen that the thickness dependent term is always sub-dominant because of the small value of p0 for all t in all E ranges, while p2 represents the residual resolution for hadrons which is dominant compared 1 2 [2 - 4.75 GeV] [5 - 15 GeV] 0.95 0.9 ry ina 0.85 im rel 0.8 O χ2 / ndf 0.789 / 8 p0 0.03472 ± 0.02617 p1 1.13 ± 0.3182 p2 0.5988 ± 0.04758 χ2 / ndf 1.401 / 7 p0 0.08097 ± 0.06436 p1 0.7337 ± 0.2866 p2 0.5993 ± 0.08471 P IN 0.75 0.7 0.65 0.6 2 3 4 5 6 Plate thickness t(cm) 7 Stochastic coefficient (a) 0 Stochastic coefficient (a) 1 p Stochastic coefficient a vs plate thickness t (cm) fitted with p t 1 + p 0.95 Stochastic coefficient a vs plate thickness t(cm) p fitted with p t 1+p 0 0.85 0.8 ry na i lim e 0.75 O IN 0.7 Pr 0.65 [2 -- 15 GeV] χ / ndf 3.846 / 8 p0 0.04893 ± 0.01482 p1 0.937 ± 0.1209 2 0.6389 ± 0.02265 p2 0.6 8 2 0.9 2 3 4 5 6 7 Plate thickness t (cm) 8 Figure 2. Stochastic coefficient a as a function of thickness t (cm) in the energy ranges 2 – 4.75 GeV and 5 – 15 GeV (left) and in 2 – 15 GeV (right). to the first term. Hence there is only a slight improvement in a with decreasing plate thickness; the actual improvement also depends on the energy range of interest. 4. Hadron shower direction reconstruction The hadron shower hits are used to reconstruct their direction. Two methods viz raw hit method and orientation matrix method have been used for direction reconstruction. Raw hit (RH) method : Average x and y positions in the ith layer of an event are found separately and fitted with straight lines x = mx z + c1 and y = my z + c2 in the X-Z and Y-Z planes respectively. The slopes mx and my are used to reconstruct the shower direction by defining them in terms of spherical polar co-ordinates, θ and φ, which are then reconstructed. Due to the presence of trigonometric functions, there arises a quadrant degeneracy in θ. This is broken by using the timing information of hits; i.e., all events “up” (“down”) in time have θ in the first (second) quadrant. Hits only within a time window of 50 ns are taken to avoid randoms. Since this method does not require any prior vertex information to reconstruct the shower direction it can be used in both CC and neutral current (NC) interactions. The distribution of θrec at (E, cos θ) = (10 GeV, 0.9), is shown in Fig. 3. An excess is visible at θrec ∼ 150◦ due to reconstruction in the wrong quadrant. Preliminary results for the angle resolution as a function of the pion energy is also shown in Fig. 3. 24 600 22 cos cos θ θ = =0.9 0.9 500 Entries cosθ=0.3 18 400 Mean 27.32 RMS 12.56 ry 16 300 na mi 100 IN 0 50 O IN el Pr cosθ=0.7 12 eli r OP cosθ=0.5 ina im 14 ry 200 0 cosθ=0.1 20 9816 σθ rec(deg) Frequency Single pions, raw hit method 10 GeV, single pions, raw hit 10 100 θrec (deg) 150 200 8 cosθ=0.9 1 2 3 4 5 6 7 E π(GeV) 8 9 10 Figure 3. Distribution of θrec using RH method for 10 GeV single pions at an incident cos θ = 0.9 (left). Preliminary results for θ resolution for single pions with raw hit method is also shown (right). Orientation matrix (OM) method : This is useful for a CC process where the vertex of the event is known from the muon track. The orientation matrix T is defined (see Ref. [7] for details)for a collection of unitvectors (xi , yi , zi ), i = 1, · · · , n, is the symmetric maΣx2i Σxi yi Σxi zi trix: T = Σxi yi Σyi2 Σyi zi . Eigen analysis of T gives an idea of the shape of the Σxi zi Σyi zi Σzi2 underlying distribution. Distributions of the error angles (∆θ) are fitted with the function f (∆θ) = A∆θ exp(−B∆θ), where, A and B are the fit parameters. It is seen that the resolution obtained in this case is better than with the RH method, as expected. In general, angular resolution of about 10◦ are obtained for hadrons in the few GeV region. 250 10 GeV 200 Frequency Orientation Matrix Technique Entries 1600 Mean 0.1329 RMS 0.1574 χ2 / ndf 116 / 44 p0 1.201e+04 ± 6.100e+02 p1 19.67 ± 0.43 150 100 50 INO Preliminary 0 0 0.2 0.4 0.6 0.8 1 ∆θ (radian) 1.2 1.4 Figure 4. Illustration of orientation matrix method (left). The red circle shows the vertex. Perpendiculars are drawn with respect to an arbitrary axis to each hit point where a unit mass is assumed to be present. The direction which gives the least moment of inertia will be the net hadron direction. Distribution of (∆θ) for 10 GeV single pions is also shown (right). Acknowledgments The work on the thickness dependence of hadron energy resolution is in collaboration with Anushree Ghosh, Moon Moon Devi, Daljeet Kaur, D. Indumathi, M.V.N. Murthy, Sandhya Choubey, Amol Dighe and Md.Naimuddin; that on hadron direction is in collaboration with Moon Moon Devi, D.Indumathi and Amol Dighe. We thank Y.P. Viyogi, G. Majumdar, P.K.Behera, A. Redij for comments and inputs on the ICAL Code, and N.K. Mondal and members of INO collaboration for support. This research was supported by the Department of Atomic Energy (DAE) and Department of Science and Technology (DST). We thank NUFACT 2013 organisers for financial support. References [1] Athar M S et.al 2006 India-based Neutrino Observatory: Project Report Volume I [2] Devi M M et.al 2013 Hadron energy response of the Iron Calorimeter detector at the India-based Neutrino Observatory JINST 8 P11003 [3] Dan Green, 2000 Physics of Particle Detectors (Cambridge: Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology, Cambridge University Press) p 266–8 [4] Agafonova N Y et.al 2000 MONOLITH: A massive magnetised iron detector for neutrino oscillation studies Monolith Proposal LNGS P26/2000 CERN/SPSC 2000-031, SPSC/M657 p 41–2 [5] Schoessow P. et.al 1997 Results from an iron proportional tube calorimeter prototype NUMI-335, SLACREPRINT-1997-070, ANL-HEP-CP-98-02, NUMI-L-335 [6] Petyt D A 1998 A study of parameter measurement in a long-baseline neutrino oscillation experiment, FERMILAB - THESIS - 1998 - 66 p 73–4, www.physics.ox.ac.uk/neutrino/Petyt/Petyt.htm [7] Fisher N. I., Lewis T., Embleton B. J. J. 1993 Statistical Analysis of Spherical Data Reprint Edition (Cambridge: Cambridge University Press) p 33–4