Supernova Detection via a Network of Neutral Current Spherical TPC's

0.16 MB·English

by  J. D. Vergados

SUPERNOVA DETECTION VIA A NETWORK OF NEUTRAL
CURRENT SPHERICAL TPC’S
J.D. Vergados1,2 and Y. Giomataris3
1University of Ioannina, Ioannina, GR 45110, Greece
2RCNP, Osaka University, Ibaraki,Japan.
3 CEA, Saclay, DAPNIA, Gif-sur-Yvette, Cedex,France.
Thecoherentcontributionofallneutronsinneutrinonucleusscatteringduetotheneutralcurrent
offersarealisticprospectofdetectingsupernovaneutrinos. Foratypicalsupernovaat10kpc,about
1000 eventsareexpected usinga spherical gaseous detector of radius4 m and employingXegas at
apressureof 10Atm. Weproposeaworld widenetwork ofseveral suchsimple, stableandlow cost
supernovadetectors with a runningtime of a few centuries.
6 PACSnumbers: 13.15.+g,14.60Lm,14.60Bq,23.40.-s,95.55.Vj,12.15.-y
0
0
2 INTRODUCTION.

n
a In a typical supernova an energy of about 1053 ergs is released in the form of neutrinos [1],[2].
J
These neutrinos are emitted within an interval of about 10 s after the explosion and they travel
2
to Earth undistorted, except that, on their way to Earth, they may oscillate into other flavors.
1
The phenomenon of neutrino oscillations is by now established by the observation of atmospheric

1 neutrino oscillations [3] interpreted as νµ ντ oscillations, as well as νe disappearance in solar
→
v neutrinos [4]. These results have been recently confirmed by the KamLAND experiment [5], which
3 exhibits evidence for reactor antineutrino disappearance. Thus for traditional detectors relying on
9
thechargedcurrentinteractionsthepreciseeventratemaydependcriticallyonthespecificproperties
0
of the neutrinos. The time integratedspectra in the case ofchargedcurrentdetectors,like the SNO
1
0 experiment, depend on the neutrino oscillations [6]. An additional problem is the fact that the
6 charged current cross sections depend on the details of the structure of the nuclei involved. With
0 neutral current detectors one exploits the fact that the vector component of the current can lead
/
h to coherence, i.e. an additive contribution of all neutrons in the nucleus (the proton component is
p tiny). Furthermorethededucedneutrinofluxesdonotdependontheneutrinooscillationparameters
- (e.g. the mixing angles). Even in our case, however, the obtained rates depend on the assumed
p
e characteristic temperature for each flavor,see sec. .
h Recentlyithasbecomefeasibletodetectneutrinosbymeasuringtherecoilingnucleusandemploy-
v: inggaseousdetectorswithmuchlowerthresholdenergies. Thusoneisabletoexploretheadvantages
i offered by the neutral current interaction, exploring ideas put forward more than a decade ago [7].
X
A description of the NOSTOS project and details of the spherical TPC detector are given in [8].
r We have built a spherical prototype 1.3 m in diameter which is described in [9]. The outer vessel is
a
madeofpureCu(6mmthick)allowingtosustainpressuresupto5bar. Theinnerdetectorisjusta
smallsphere,10mmindiameter[10]anddevelopmentsarecurrentlyunderwaytobuildaspherical
TPC detector using new technologies. First tests were performed by filling the volume with argon
mixtures and are quite promising. High gains are easily obtained and the signal to noise is large
enough for sub-keV threshold. The whole system looks stable and robustaaaaaaaaaaaaa made of
stainless steelas a proportionalcounter located atthe center of curvatureof the TPC.Furthermore
this interaction, through its vector component, can lead to coherence, i.e. an additive contribution
of all nucleons in the nucleus. Since the vector contribution of the protons is tiny, the coherence is
mainly due to the neutrons of the nucleus.
In this paper we will derive the amplitude for the differential neutrino nucleus coherent cross
section. Then we will estimate the expected number of events for all the noble gas targets. We will
show that these results can be exploited by a network of small and relatively cheap spherical TPC
detectorsplacedinvariouspartsoftheworld(foradescriptionofthe apparatusseeourearlierwork
[8]). The operation of such devices as a network will minimize the background problems. There is
noneedtogounderground,butonemayhavetogosufficientlydeepunderwatertobalancethehigh
pressure of the gas target. Other types of detectors have also been proposed [11],[12].
Large gaseous volumes are easily obtained by employing long drift technology (i.e TPC) that can
provide massive targets by increasing the gas pressure. Combined with an adequate amplifying
structure and low energy thresholds, a three-dimensional reconstruction of the recoiling particle,
electron or nucleus, can be obtained. The use of new micropattern detectors and especially the
novelMicromegas[13]provideexcellentspatialandtime accuracythatisaprecioustoolforpattern
recognition and background rejection [14],[15]. The virtue of using such large gaseous volumes
and the new high precision microstrip gaseous detectors has been recently discussed in a dedicated
workshop [16] and their relevance for low energy neutrino physics and dark matter detection has
beenwidelyrecognized. Suchlow-backgroundlow-energythresholdsystemsareactuallysuccessfully
usedintheCAST[17],thesolaraxionexperiment,andareunderdevelopmentforseverallowenergy
neutrino or dark matter projects [8],[18].
STANDARD AND NON STANDARD WEAK INTERACTION
The standard neutral current left handed weak interaction can be cast in the form:
G
∐ = F ν¯αγµ(1 γ5)να q¯γµ(gV(q) gA(q)γ5)q (1)
L −√2 − −
(cid:2) (cid:3)(cid:2) (cid:3)
(diagonal in flavor space).
At the nucleon level we get:
G
∐ = F ν¯αγµ(1 γ5)να N¯γµ(gV(N) gA(N)γ5)N (2)
L −√2 − −
(cid:2) (cid:3)(cid:2) (cid:3)
with
1 1 1 1.27
g (p)= 2sin2θ 0.04 , g (p)=1.27 ; g (n)= , g (n)= (3)
V W A V A
2 − ≃ 2 −2 − 2
Beyond the standard level one has further interactions which need not be diagonal in flavor space.
Thus
g (q) g (q)γ5
V A
− →
gSM(q) gSM(q)γ5 δ + λqLδ +ǫqL (1 γ5)
(cid:0) V − A (cid:1) αβ (cid:16) αβ αβ(cid:17) −
ν¯ γµ(1 γ5)ν ν¯ γµ(1 γ5)ν (4)
α α α β
− → −
(cid:2) (cid:3) (cid:2) (cid:3)
Furthermore at the nucleon level
g (N) g (N)γ5 gSM(N) gSM(N)γ5 δ
V − A → V − A αβ
(cid:0)+ λNLδ +ǫNL (1 (cid:1)1.27γ5)
αβ αβ −
ν¯ γµ(1 γ5)ν ν¯(cid:0)γµ(1 γ5)ν (cid:1) (5)
α α α β
− → −
(cid:2) (cid:3) (cid:2) (cid:3)
with
λpL = 2λuL+λdL , λnL =λdL+2λdL ,
ǫpL =2ǫuL+ǫdL , ǫnL =ǫuL+2ǫdL (6)
αβ αβ αβ αβ αβ αβ
In the above expressions λqL can arise, e.g., from radiative corrections, see e.g. PDG [19] and ǫqL
αβ
from R-parity violating interactions in supersymmetric models [20]-[21].
IndeedsinceR-parityconservationhasnorobusttheoreticalmotivationonemayacceptanextended
framework of the MSSM with R-parity non-conservation MSSM. In this case the superpotential W
acquires additional R-paity violating terms:
W = λ L L Ec +λ′ L Q Dc
R/p ijk i j k ijk i j k
+ λ′′ UcDcDc +µ L H (7)
ijk i j k j j u
Ofinterestto us here is the λ′ L Q Dc involvingfirst generationquarksands-quarks,i.e the term
ijk i j k
λ′ L Q Dc. From this term in four component notation we get the contribution
α11 α 1 1
λ′ d¯c ν u¯cα d˜c, α=e,µ, τ
α11 R αL− R L
(cid:0) (cid:1)
where ν = 1(1 γ )ν etc. Thus
αL 2 − 5 α
The first term at tree level yields the interaction
•
′ ′
λ λ
α11 β11ν¯ dcd¯c ν (8)
− m2 αL R R βL
d˜L
By performing a Fierz transformation we can rewrite it in the form:
′ ′
1λ λ
α11 β11ν¯ γµν d¯c γ dc (9)
2 m2 αL βL R µ R
d˜L
The previous equation can be cast in the form:
G
= Fǫd ν¯γµ(1 γ5)ν d¯γ (1 γ5)d ;
Ld −√2 αβ α − β µ −
(cid:2) (cid:3)(cid:2) (cid:3)
m2
ǫd = λ′ λ′ W (10)
αβ α11 β11m2
d˜L
There is no such term associated with the u quark, ǫu =0.
αβ
Proceeding in an analogous fashion the collaborative effect of the first and second term, for
•
α,β =e,µ,τ, yields the charged current contribution:
G
= Fǫd α¯γµ(1 γ5)ν u¯γ (1 γ5)d (11)
Ldu √2 αβ − β µ −
(cid:2) (cid:3)(cid:2) (cid:3)
Finallythesecondterm,forα,β =e,µ,τ,leadstoaneutralcurrentcontributionofthecharged
•
leptons:
G
= Fǫd α¯γµ(1 γ5)β u¯γ (1 γ5)u (12)
Lu √2 αβ − µ −
(cid:2) (cid:3)(cid:2) (cid:3)
The above non standard flavor changing neutral current interaction have been found to play an
importantrolein the in the infallstageof a stellarcollapse[22]. Furthermore precisemeasurements
involvingtheneutralcurrentneutrino-nucleusinteractionsmayyieldvaluableinformationaboutthe
non standard interactions [23]. They are not, however, going to be further considered in this work.
COHERENT NEUTRINO NUCLEUS SCATTERING
The cross section for elastic neutrino nucleon scattering has extensively been studied [1],[24].
The energy of the recoiling paricle can be written in dimensionless form as follows:
2cos2θ T E
recoil ν
y = , y = ,x = (13)
(1+1/x )2 cos2θ m ν m
ν recoil recoil
−
The maximum energy occurs when θ = 0, y = 2 , in agreement with Eq. (2.5) of ref.
max (1+1/xν)2−1
[1]. One can invert Eq. 13 and get the neutrino energy associated with a given recoil energy and
scatteringangle. Fromtheaboveexpressionsweseethatthevectorcurrentcontribution,whichmay
lead to coherence, is negligible in the case of the protons. Thus the coherent contribution [25] may
come from the neutrons and is expected to be proportional to the square of the neutron number.
The neutrino-nucleus coherent cross section takes the form:
dσ G2Am
= F N (N2/4)F (A,T ,E ),
coh A ν
(cid:18)dT (cid:19) 2π
A weak
A 1T T
F (A,T ,E )= 1+ − A +(1 A)2
coh A ν
(cid:18) A E (cid:19) − E
ν ν
A 1 T 1 Am T
A N A
1 − (14)
(cid:18) − A m E /T 1(cid:19)− E2
N ν A− ν
SUPERNOVA NEUTRINOS
The number of neutrino events for a given detector depends on the neutrino spectrum and the
distance of the source. We will consider a typical case of a source which is about 10 kpc, l.e.
D =3.1 1022 cm ( of the orderof the radius ofthe galaxy)with anenergy output of 3 1053 ergs
× ×
with a duration of about 10 s. Furthermore we will assume for simplicity that each neutrino flavor
is characterized by a Fermi-Dirac like distribution times its characteristic cross section and we will
not consider here the more realistic distributions, which have recently become available [26]. This
is adequate for our purposes. Thus:
dN E2 Λ x4 E
=σ(E ) ν = , x= ν (15)
dE ν 1+exp(E /T) JT 1+ex T
ν ν
with J = 31π6, Λ a constant and T the temperature of the emitted neutrino flavor. Each flavor is
252
characterized by its own temperature as follows:
T =8 MeV for ν ,ν ,ν˜ ,ν˜ and T =5 (3.5) MeV for ν˜ (ν )
µ τ µ τ e e
The constant Λ is determined by the requirement that the distribution yields the total energy of
each neutrino species.
ΛT ∞ x5 U
ν
U = dx Λ=
ν J Z 1+ex ⇒ T
0
We will further assume that U =0.5 1053 ergs per neutrino flavor. Thus one finds:
ν
×
Λ=0.89 1058 (ν ), 0.63 1058 (ν˜ ) ,0.39 1058 (all other flavors)
e e
× × ×
The emitted neutrino spectrum is shown in Fig. 1.
The differential event rate (with respect to the recoil energy) is proportional to the quantity:
dR λ(T) ∞ x4
= dxF (A,T ,xT) (16)
dT J Z coh A 1+ex
A 0
with λ(T) = (0.89,0.63,0.39) for ν ,ν˜ and all other flavors respectively. This is shown in Figs. 2
e e
and 2. The total number of expected events for each neutrino species can be cast in the form:
No of events = C˜ (T)h(A,T,(T ) ),
ν A th
(17)
F (A,T,(T ) )
fold A th
h(A,T,(T ) ) = (18)
A th
F (40,T,(T ) )
fold A th
with
A (TA)max dT
A
F (A,T,(T ) ) =
fold A th
J Z 1MeV ×
(TA)th
∞ x4
dxF (A,T ,xT) (19)
Z coh A 1+ex
0
0.01
0.008
0.006
8V
510Me
0.004
→
dNdEν 0.002
20 40 60 80
Eν → MeV
FIG. 1: The supernova neutrino spectrum. The short dash, long dash and continuous curve correspond to
νe,ν˜e and all other flavors respectively
0.3 0.06
0.25 0.05
0.2 0.04
0.15 0.03
0.1 0.02
0.05 0.01
0.01 0.02 0.03 0.04TA→MeV 0.01 0.02 0.03 0.04TA→MeV
FIG. 2: The differential event rate as a function of the recoil energy TA, in arbitrary units, for Xe. On the
left we show the results without quenching, while on the right the quenching factor is included. We notice
that theeffect of quenchingis moreprevalent at low energies. Thenotation for each neutrinospecies isthe
same as in Fig. 1
and
G2m 1MeV N2 1 PV
C˜ (T)= F N Λ(T) (20)
ν 2π 4 4πD2kT
0
Wherek isBoltzmann’sconstant,P the pressure,V the volume,andT the temperatureofthegas.
0
Summing over all the neutrino species we can write:
K(A,(T ) )
A th
No of events=C Qu(A) (21)
ν
K(40,(T ) )
A th
with
N 2 U 10kpc 2 P R 3 300
ν
C =153 (22)
ν (cid:18)22(cid:19) 0.5 1053ergs(cid:18) D (cid:19) 10Atm(cid:20)4m(cid:21) T
0
×
K(A,(T ) )isthe rateatagiventhresholdenergydividedbythatatzerothreshold. Itdepends
A th
on the threshold energy, the assumed quenching factor and the nuclear mass number. It is unity
at (T ) ) = 0. From the above equation we find that, ignoring quenching, the following expected
A th
number of events:
1.25, 31.6, 153, 614, 1880 for He, Ne, Ar, Kr and Xe (23)
respectively. Forotherpossibletargetstheratescanbefoundbytheaboveformulasorinterpolation.
ThequantityQu(A)isafactorlessthanonemultiplyingthetotalrate,assumingathresholdenergy
(T ) = 100eV, due to the quenching. The idea of quenching is introduced, since, for low emery
A th
recoils, only a fraction of the total deposited energy goes into ionization. The ratio of the amount
of ionization induced in the gas due to nuclear recoil to the amount of ionization induced by an
electron of the same kinetic energy is referred to as a quenching factor Q . This factor depends
fac
mainly on the detector material, the recoiling energy as well as the process considered [27]. In our
estimateofQu(T )weassumedaquenchingfactorofthe followingempiricalformmotivatedbythe
A
Lidhard theory [27]-[28]:
T r2
A
Q (T )=r , r 0.256 , r 0.153 (24)
fac A 1 1 2
(cid:20)1keV (cid:21) ≃ ≃
Then the parameter Qu(A) takes the values:
0.49, 0.38, 0.35, 0.31, 0.29 for He, Ne, Ar, Kr and Xe (25)
respectively. Theeffectofquenchingislargerinthecaseofheavytargets,since,foragivenneutrino
energy, the energy of the recoiling nucleus is smaller. Thus the number of expected events for Xe
assuming a threshold energy of 100 eV is reduced to about 560.
The effect of quenching is exhibited in Fig 3 for the two interesting targets Ar and Xe. We should
0.0005 0.001 0.0015 0.002 0.0005 0.001 0.0015 0.002
0.95
0.98
→ → 0.9
))Ath00..9964 ))Ath0.85
T T 0.8
A,( 0.92 A,( 0.75
K( 0.9 (TA)th→MeV K( 0.7 (TA)th→MeV
FIG.3: ThefunctionK(A,(TA)th)versus(TA)thforthetargetArontheleftandXeontheright. Theshort
and long dash correspond to no quenching and quenching factor respectively. One sees that the effect of
quenchingis less pronouncedat higher thresholds. The differencesappearsmall, since wepresent hereonly
theratio of therates to that at zero threshold. The effect of quenchingat some specific threshold energy is
not shown here. Forathreshold energy of100 eV theratesare quenchedbyfactors of 3and3.5 for Arand
Xerespectively (see Eq. (25).
mention that it is of paramount importance to experimentally measure the quenching factor. The
above estimates were based on the assumption of a pure gas. Such an effect will lead to an increase
in the quenching factor and needs be measured.
CONCLUSIONS
Inthepresentstudyithasbeenshownthatitisquitesimpletodetecttypicalsupernovaneutrinos
in our galaxy,providedthat sucha supernova explosiontakes place (one explosionevery 30 yearsis
estimated[29]). TheideaistoemployasmallsizesphericalTPCdetectorfilledwithahighpressure
noble gas. An enhancement of the neutral current component is achieved via the coherent effect of
all neutrons in the target. Thus employing, e.g., Xe at 10 Atm, with a feasible threshold energy
of about 100 eV in the detection the recoiling nuclei, one expects between 600 and 1900 events,
depending on the quenching factor. We believe that networks of such dedicated detectors, made
out of simple, robust and cheap technology, can be simply managed by an international scientific
consortium and operated by students. This network comprises a system, which can be maintained
for several decades (or even centuries). This is is a key point towards being able to observe few
galactic supernova explosions.
acknowledgments: One of the authors (JDV) is indebted for support and hospitality to the
OMEG05organizingcommitteeduringtheOMEG05conferenceandtoProfessorHiroshiTokiduring
a visit to RCNP.
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