DAMA実験における中性子 バックグラウンドの季節変動２
名古屋大学
久野光慧 / 森下美沙希
2015/5/17
1
内容
•  muonとneutrinoはDAMAの示すシグナルとな
るような十分なneutronをつくるか
•  DAMAに注目した点
•  neutronとdark ma0erの区別
2
neutrino properties such as nonzero mass and mixing, because of the wide range of
density and the great distance from the Sun to the Earth.
The solar neutrinos are produced by some of the fusion reactions in the pp ch
CNO cycle. The combined eﬀect of these reactions is written as
neutron 破砕
4p → 4 He + 2e+ + 2νe .
•  detecterの周りのシールドと
してPbがよく使われる •  muon、neutrinoがPbに衝突
することでneutronをつくる
•  neutrinoのエネルギー Eν > 7 MeVで208Pbからneutron
がでる
• 
Figure 14.2: The
8B太陽neutrinoのエネル solar
model [103].
solar neutrino spectrum predicted by the BS05(OP) stand
The neutrino fluxes are given in units of cm−2 s−1 MeV−1
continuous spectra and cm−2 s−1 for line spectra. The numbers associated with
neutrino sources show theoretical
errors of the fluxes. This figure is taken from
late John Bahcall’s web site, http://www.sns.ias.edu/~jnb/.
ギーは7 MeVより大きい値
をもつ
8
5B
! 2 42He + e+ + ⌫e
ν
ν
> 7 MeV
Positrons annihilate with electrons. Therefore, when considering the solar therma
generation, a relevant expression is
3
−
4
4p + 2e → He + 2νe + 26.73 MeV − Eν ,
Pb n
neutron event rate
neutronの比率をR
R⇠
nV
8B太陽neutrinoのﬂuxと208Pbをターゲットとしたcross secBonより
R⌫ ⇠ 10
35
Rµ ⇠ 10
34
Φν 〜 106 cm-‐2 s-‐1 σν 〜 10−41 cm2
nV neutrons/sec
Φμ 〜 10-‐8 cm-‐2 s-‐1 σμ 〜 10−26 cm2
muonについて
nV neutrons/sec
これより、neutron比の関係は
R⌫
⇠ 0.1
Rµ
Φ：ﬂux σ：cross secBon n：ターゲットの数密度
V：体積
4
DAMAとの対応
• 
Pbについて、数密度n 〜 1029 m-‐3、ターゲットの体積V 〜 1000 m3 とする
–  Rν 〜 100 neutrons/days –  Rν + Rμ 〜 1000 neutrons/days –  〜 1 m3 of lead is present in the DAMA/LIBRA shield ????? • 
これはDAMAの検出比と似ている
– 
– 
– 
– 
• 
250 kg NaI(Tl), recoil energy 2-‐6 keV 3.5 × 106 events/keV, Exposure 1.33 ton × yr 〜2.6 x 103 event/keV/kg/yr 〜1700 event/keV/day 〜7000 event/day ????? (0.0112 ± 0.0012) cpd/kg/keV 〜 2.5 cpd/keV 〜 10 cpd ????? muonによるneutronの(n,p)反応のみを考えたときのmean free pathはλ = 2.6 m
–  このときの有効体積はVeﬀ 〜 450 m3 程度と見積もられる
• 
これはDAMAのシグナルを説明するために必要な体積Vに近い
• 
neutron生成の全ての過程を考えている訳ではない
–  V 〜 1000 m3 をより小さく補正できるかもしれない ⇒muon+neutrino modelでDAMAのシグナルを説明できるかも
5
DAMAに注目した点
ization based on the measureLUKA simulation.
.64Eµ0.02
−
0.74Eµ−0.12,
(10)
ed neutron multiplicity, Mmc is
ultiplicity in FLUKA and Eµ is
V. After correcting the neutron
KA simulation, good agreement
ta and the simulation as can be
Neutron Yield (n/µ g cm-2)
•  シールドの構造
nction• of しきい値
muon energy between
Pb
Au
Fe
10-3
Cd
NaCl
Na
C
CnH2n+2
10
2
10
Atomic Weight of a Medium
6
Aglietta
FIG. 12: Simulation of the muon-induced neutron product
2 of 11
Eur.
Mineral Oil
(30cm) &ofMuon
hardware
threshold
eachdet.
PMT is at
KIMS
DAMA
while a software energy threshold of 2
Lead (15cm)
lent (hereafter keV)
is used [1, 20]. E
X-rays/γ Polyethylene
sources are (5cm)
regularly carried
ning conditionCopper
down(10cm)
to few keV [1];
coincidences due to internal X-rays f
CsI(Tl)
ppt levels in the
crystals) provide (wh
crystal
over long periods) a calibration poin
the software energy threshold (for det
DAQ system records both single-hit e
of the detectors fires) and multiple-hi
than one detector fires) up to the MeV
timization is performed for the lowest
Cu/Pb/Cd-‐foils/polyethylene/paraﬃn/… The 25
the procedures and details are discus
1 Schematic
view of the DAMA/LIBRA apparatus.
y radiopure NaI(Tl) crystal scintillators (5-rows by 5-columns
and references therein.
•  neutronを遮断するためにPolyethyleneがよくきく
x), housed
in the sealed copper box continuously maintained
The data
of the former
DAMA/
WPAS2014,
Hyun Su Lee,
Ewha
igh Purity Nitrogen atmosphere, within low-radioactive passive
× yr) and, later, those of the first
d are visible. Mostly outside the installation, the DAMA/LIBRA
•  DAMAのシールドの構造をみると、neutronを多くつくるPbの外側に
DAMA/LIBRA (0.87 ton × yr) hav
ratus is also almost fully surrounded by about 1 m concrete made
Polyethyleneのシールドがある
e Gran Sasso rock. The copper guides of the calibration system
tive model independent evidence for
lso shown. For details see Ref. [1]
particles in the galactic halo with hig
•  DAMAの構造ではPbからでるneutronを遮断できない可能性がある
the basis of the exploited DM annual
7
[2, 3, 7, 22].
, very effective and, in addition, it allows to test a large
Fig. 9. Monte Carlo geometry model for a 250 kg liqu
50 cm of hydrocarbon scintillator (40 g/cm2 ) and 30 c
figure also shows a GEANT4 event in which a 280 GeV
(n1 , n2 ) in the lead shielding which are captured in the
•  muonが引き起こすneutronの
スペクトルは低いエネルギー
で現れることが知られている
•  muonとneutrinoが引き起こす
neutronは10-‐100 keVの運動
エネルギーをもつ
•  neutronがNaを散乱した時の
recoil energyは2-‐6 keV relative neutron flux, n/µ/MeV
しきい値
1
10
10
10
10
10
10
10
10
•  DAMAはdark ma0erによる
recoil energyを2-‐6 keVで見て
いる 10
rock→cavern
-1
air→lead
-2
lead→veto
-3
-4
-5
-6
-7
veto→air - GEANT4
-8
veto→air - FLUKA (Paper 3)
-9
10
-1
1
10
10
2
10
3
10
4
neutron energy, MeV
Fig. 10. Energy spectra of muon-induced neutron flux
The thick line represents the flux at the rock face for an
⇒neutronとdark ma0erのシグナルを区別できない
8 neutr
‘GEANT4 - F+R’ in Fig. 8). The spectrum of
veto obtained with FLUKA (Paper 3) is also shown.
区別の方法
•  2-‐4 keVのphaseのずれ
•  場所依存
9
phaseのずれで区別
13) 73:2648
on amplitude
π
) and phase
ting, with the
− t0 ), the
ate of the
RA–phase1,
he former
he results are
th
ignal in the
tion
Page 5 of 11
A (cpd/kg/keV)
T=
2π
ω
(yr)
t0 (days)
C.L.
134 ± 7
8.1σ
DAMA/LIBRA–phase1
2–4 keV
2–5 keV
2–6 keV
(0.0178 ± 0.0022)
(0.0127 ± 0.0016)
2–5 keV
2–6 keV
(0.996 ± 0.002)
137 ± 8
7.9σ
(0.0097 ± 0.0013)
(0.998 ± 0.002)
144 ± 8
7.5σ
(0.0190 ± 0.0020)
(0.996 ± 0.002)
134 ± 6
9.5σ
(0.998 ± 0.002)
144 ± 7
9.3σ
DAMA/NaI & DAMA/LIBRA–phase1
2–4 keV
(0.996 ± 0.002)
(0.0140 ± 0.0015)
(0.0112 ± 0.0012)
(0.996 ± 0.002)
140 ± 6
9.3σ
•  ここまではrecoil energyが2-‐6 keVの場合を考えてきた
accounted by the statistical spread expected from the used
• 
• 
sampling time. Moreover, fitting the time behaviour of R90
including a term with phase and period as for DM particles,
2-‐4 keVのエネルギーを使ったDAMAの見せたbest-‐ﬁt phaseは〜10daysだ
a modulation amplitude compatible with zero
has also been
found for all the annual cycles (see Table 5). This also exけ前にずれる
cludes the presence of any background modulation in the
whole energy spectrum at a level much lower than the effect
found
the lowest energy region for the single-hit events. In
このずれをmuon+neutrino minodelで説明できるれば信憑性があがる
fact, otherwise—considering the R90 mean values—a modulation amplitude of order of tens cpd/kg would be present
10
⇒neutronとdark ma0erの区別できるかも
for each annual cycle, that is ≃100σ far away from the mea-
WIPP
場所で区別
Soudan
-7
−7
−2 −1
(4.0 ± 1.1)×10
s fit
and
P1 = 0.86
± 0.05 km.
muon flux andcm
our global
function.
The horizontal
lines
Boulby
Homestake
WIPP
-2
Flat-overburdan sites
Soudan
10-7
Kamioka
-9
10
Gran Sasso
Sudbury
2Boulby
3
indicateare
the
root-mean-square
deviation
amongst the residStopping-muons
also
a source of background.
For
example, uals
µ− capture
on
a
nucleus
produces
neutrons
based upon the experimental uncertainties in the meaand radioactive
isotopes. The total stopping-muon rate
surements.
has contributions from cosmic-ray muons coming to
WIPP
the end of their
range, secondary muons generated locally through interactions
of the primary muons (due to
Soudan
B.
Stopping
Muon
Intensity
virtual-photo
interactions
with nuclei),
and local
muon
Kamioka
-8
10
production by real photons (π0 -decay in electromagnetic
showers). It is customary to quote results in terms of the
Boulbyto through-going
Stopping-muons
are also amuons.
source of background. For
ratio, R, of stopping muons
Gran Sasso A
−
example,is provided
µ capture
on aetnucleus
detailed calculation
by Cassiday
al. [13]. produces neutrons
The total
ratio,
R(h),
of
stopping-muons
to
through10-9 and radioactive isotopes. The total stopping-muon rate
going muons
direction) atfrom
diﬀerent
depths can muons coming to
has(vertical
contributions
cosmic-ray
be parameterized as [19]
-2
Total Muon Flux (cm s-1)
10-8
Neutron Flux (cm s-1)
-2
Total Muon Flux (cm s-1)
in Table
In intensities
order toare
circumvent
the misuse of vertical
P1 the−h
and I.
these
used hereafter.
0 /P1
FIG. 4: The relative deviation between data on
total
)e
,
φ
=
P
(
n
0
muon intensity in comparing sites with flat overburden
muon flux and-0.15
our global fit
function. The horizontal lines
Kamioka
h
0 the residindicate the root-mean-square deviation amongst
to those under mountains, we define the equivalent depth
2
3
4 mea- 5
6
uals based upon the experimental
uncertainties
in the
Flat-overburdan
sites
relative to a flat overburden by
the experimental
meaEquivalent Vertical Depth (km.w.e.)
surements.
where h0 is the equivalent vertical depth (in km.w
surements of the total muon Kamioka
intensity. This definition
10
Gran Sasso
relativeFIG.
to a4:flat
overburden.
The fit parameters are P
and these intensities are used hereafter.
The Muon
relative
deviation between data on the total
B. Stopping
Intensity
Frejus
Frejus
4
5
6
Equivalent Vertical Depth (km.w.e.)
Homestake
10-8 FIG. 3:
The total muon flux measured for the various underground sites summarized in Table I as a function of the
equivalent vertical depth relative to a flat overburden. The
smooth curve is our global fit function to those data taken
from sites with flat overburden (equation (4)).
-9
10
the end of their range, secondary muons generated lo∆Eeh/ξ
cally R(h)
through
of the primary
muons (due to
≈ γµ interactions
,
(7)
h/ξ − 1)ϵ
TABLE I:2 Summary 3of the total 4muon flux measured
at6 the
5
(e
-10
µ
virtual-photo interactions with nuclei), and local muon
10
Equivalentvertical
Verticaldepth
Depthrelative
(km.w.e.)
underground sites and the equivalent
(πkm.w.e.,
where γµ =production
3.77 for Eµ ≥ by
1000real
GeVphotons
[20], ξ = 2.5
0 -decay in electromagnetic
to a flat overburden.
Sudbury
∆E
≈
αh,
α
=
0.268
GeV/km.w.e.
[21]
for
E
≥ 1000
showers). It is customary to µquote
results in terms of the
Site
Total flux
Depth
FIG. 3: The total
muon
flux
measured
for
the
various
unGeV [20], ratio,
h is theR,
depth
of an underground
cm−2 sec−1
km.w.e.
of stopping
muonslaboratory,
to through-going muons. A
−7Table I as a function of the
derground
sites
summarized
in
and
ϵ
=
618
GeV
[20].
For
large
depths,
as can be seen
WIPP
(4.77±0.09) × 10 [6]
1.585±0.011
µ-11
10
−7
calculation
is provided
by Cassiday et al. [13].
Fig. 5, detailed
this ratio is
less than 0.5%
and is hereafter
Soudan
10 [15] to a flat1.95±0.15
equivalent
vertical(2.0±0.2)
depth ×relative
overburden. in
The
2
3
4
5
6
−7
†
(1.58±0.21)
10 function
[8]
neglected The
for thetotal
underground
considered
in this
ratio, sites
R(h),
of stopping-muons
to (km.w.e.)
throughsmooth Kamioka
curve is our
global×fit
to2.05±0.15
those data taken
Depth
−8
Boulby
(4.09±0.15) × 10 [9]
2.805±0.015
study.
going muons (vertical direction) at diﬀerent depths can
from sites
with flat overburden (equation (4)).
Gran Sasso (2.58±0.3) × 10−8 [this work] 3.1±0.2†
−8
†
be parameterized as [19]
(2.78±0.2) × 10 [16]
3.05±0.2
Sudbury
FIG. 14:
The total muon-induced neutron flux deduce
•  muonのﬂuxは実験場所の深さで異なる
the various underground sites displayed. Uncertaintie
each point reflect those added in quadrature from uncer
•  深いほど、neutronのﬂuxが少ない ties in knowledge of the absolute muon fluxes and neu
production rates based upon our simulations constraine
perimental
cavern.
Thehenergy
spectrum
isof
discussed
in
the
available
experimental
data.
GeV
[20],
is the
depth
an underground
laboratory,
(3.22±0.2) × 10−8 [17]
2.96±0.2†
C. Muon Energy Spectrum and Angular
−9
Distribution
Fr´ejus
(5.47±0.1) × 10 [14]
4.15±0.2†
∆Eeh/ξ
−9
†
R(h) ≈ γµ h/ξ
,
(7)
(4.83 ±0.5) × 10 [this work] 4.2±0.2
TABLE Homestake
I: Summary
of the total muon flux
measured at the
(e
−
1)ϵ
µ
(4.4±0.1 × 10−9 )[this work]
4.3±0.2
In addition to the total muon intensity arriving at a
underground
sites(3.77±0.41)
and the ×equivalent
depth relative
Sudbury
10−10 [12] vertical
6.011±0.1
given underground site, we require knowledge of the dif†
where
= 3.77
for Eµ ≥in1000
GeV
to a flat overburden.
Equivalent vertical depth with a flat overburden
ferential energy
andγµ
angular
distributions
order to
gen-[20], ξ = 2.5 km.w.e.,
11
determined
by the measured total muon flux.
∆E ≈ αh, activity
α = 0.268
≥ 1000
erate the muon-induced
withinGeV/km.w.e.
a particular ex- [21] for Eµ
Site
Total flux
Depth
−2
−1
場所で区別
rio
m
ne
co
ha
ne
of
fo
th
A
in
FIG.
4: Approximate peak day ofmthe
neutrino+muon signal
•  実験場所の違いでneutrino+muon odelのphaseがずれる
at four di↵erent labs. Deeper labs have a lower muon flux [38]
and so a phase closer to that of the solar neutrinos.
⇒neutronとdark ma0erを区別できるかも
our estimates imply R⌫ /Rµ ⇠ 0.1 which is encourag-
12
is
th
Summary
•  muonとneutrinoはdetectorの周りのPbで
neutronをつくる
•  muon+neutrino modelはDAMAのシグナルと
よくあう
•  このmodelのDAMAのシグナルの区別の方法
として、phaseのずれと場所依存を考える
13