Download Hadron energy resolution as a function of iron plate thickness

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 unitvectors (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
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[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