A Possible Method to Measure Small 13 in the
Detection of Supernova Neutrinos
Ming-Yang Huang
(Xin-Heng Guo, Bing-Lin Young)
Beijing Normal University
(hep-ph/0806.2720)
1
Contents
 Detection of SN neutrinos.
 Possible method to measure very small 13 at Daya
Bay.
 Apply this method to some other current experiments.
 Summary
2
I. Detection of SN neutrinos
 Supernova explosion: natural laboratory to study
fundamental issues of physics and astrophysics.
 Observation SN neutrinos can serve as an early warning
for the optical emission of a type II SN.
 SN neutrinos have valuable information of deep inside the
core; can be helpful to study of intrinsic properties of
neutrinos.
3
Energy spectrum
 Since cross section of interactions depend on neutrino energy, the
energy spectra of neutrinos are not simple blackbodies. As a result,
the energy spectrum has a pinched shape compared with the
Fermi-Dirac distribution.
 Lα(0) (Tα ): luminosity (temperature) of να ; ηα : pinching parameter;
ESN(0) : total energy release. Typical values from numerical
simulations are ( < E α > ~ 3.15 Tα):
4
SN neutrinos’ propagation in Earth
 Neutrinos from SN explosion will go through some portion of the
Earth before reaching detector. Earth effects have to be taken into
account.
 For Earth matter effects, we use the realistic matter profile:
5
Earth Matter Effect
 The treatment of the Earth matter effect has been discussed in detail
in Dighe and Smirnov, Phys. Rev. D62 (2000) 033007
Ioannisian and Smirnov, Phys. Rev. Lett. 93 (2004) 241801
Ioannisian, Kazarian, Smirnov, and D. Wyler, Phys. Rev. D71 (2005)
033006
Incident angle
Detector
AD
R: radius of Earth
h: depth of detector
Centre of Earth
OB
X=AB
6
Neutrino flux at detector
 Consider the MSW effect at SN and the matter effects on Earth,
one can obtain neutrino flux as follow (PH is the crossing probability
at the high resonance region inside the SN and P2e is the probability
that a neutrino mass eigenstate ν2 enters the surface of the Earth
and arrive at the detector as an electron neutrino):
 (Normal hierarchy)
 (Inverted hierarchy)
7
 The probability P2e has been calculated in Ioannisian and Smirnov,
Phys. Rev. Lett. 93 (2004) 241801 by applying Schroedinger Eq.
in low density matter (neglecting
):
the potential in the Earth:
V ( x)  2GF Ne ( x)
the electron number density:
and we defined:

m
a b
2
m21
  dx
[cos 212   ( x)]2  sin 2 212
2E
a
b
8
Event number
 Now we calculate the predicted numbers of event that can be observed
through various reaction channels at current neutrino experiments.
 Integrating the product of the target number NT, the cross section of
each channel σ(i) , and the neutrino flux function over the neutrino
energy,
D: distance between SN and Earth, i: different channels.
 At Daya Bay, liquid scintillator is Linear Alkyl Benzene (LAB), C6H5 –
CnH2n+1, n=9~14. Let ratio of C and H to be 0.6, then for total detector
mass 300 tons,
9
Cross sections
 Inverse beta decay has the largest cross section:
 neutrino-electron elastic scatterings:
 Charged-current capture of electron neutrino on Carbon:
10
 Charged-current capture of anti-electron neutrino on Carbon:
 Neutral-current inelastic scatterings on Carbon :
11
The event numbers observed at the Daya Bay experiment as a function of the
incident angle  when
12
It can learn from the above plot that:
 Earth matter effect depends on the incident angle of the neutrino,
the mass hierarchy, and the flip probability PH .
 When the incident angle of SN neutrino is smaller than a value 0 ~
90o (L < 100km), Earth matter effect can be ignored for all reactions.
 Earth matter effect becomes large and reaches a maximum for  ~
92o -- 95o .
 When  is larger than about 100o, the Earth matter effect is
insensitive to .
 The inverse beta decay could have the largest Earth matter effect
among all the channels: 7%.
 For neutrino-electron elastic scattering and reactions with 12C , the
maximum Earth matter effect could be as large as 2%.
13
II. Possible method to measure very
small 13 at Daya Bay
 Using Landau-Zener formula, the crossing probability at high
resonance region depends on neutrino energy, neutrino mass
difference, mixing angle 13 and density profile of SN:
 Take the matter density profile of SN as (the constant C depends on
the amount of electron capture during the star collapse and its
value between 1 and 10):
 For small 13, F≈1. Then
14





From the plot, when 13=0, PH=1.
When 13 varies between 0o and 1.5o, PH varies between 0 and 1.
When 13 > 1.5o, PH is nearly 0.
The variation of PH depends on neutrino energy and parameter C.
In the following, we will consider a possible method to measure small
13 by detecting the event numbers of SN neutrinos at Daya Bay. As
an example, we consider
15
16
17
18
 From the above figures, it is known that:
(1), when 13 is smaller than 1.5o, N is very sensitive to 13; when 13 is
larger than 1.5o, N is nearly independent of 13. Therefore, very small
13 can be measured by detecting the event numbers of SN neutrinos.
(2), At the Daya Bay experiment, the event numbers of SN neutrinos
can be measured in the inverse beta-decay. This will help us to get
information about 13 smaller than 3o.
(3), If the actual case is the normal hierarchy, we need to detect SN
neutrino event numbers in the processes of neutrino-electron scattering
and neutrino-carbon scattering. This, however, will be difficult for the
Daya Bay experiment.
 In order to reduce the uncertainties of the luminosity and distance of an
SN, we define Re which represents the ratio of the event numbers of
electron and anti-electron neutrino. Therefore, the mixing angle 13 can
be determined by Re .
19
20
III. Apply this method to some other
current experiments
 Similar to Daya Bay, for
Super-k, Kamland, LVD,
MiniBooNe, Double Chooze,
Borexino, SNO (H2O), the
main neutrino reactions are
inverse beta-decay.
Therefore, vary small 13
can be measured by these
experiments while the
hierarchy is inverted.
21
D2O
 It can be seen that in the
cases of both normal
hierarchy and inverted
hierarchy, event numbers of
reactions of neutrinos with
deuteron change obviously
when 13 changes between
0o and 1.5o.
 So in both cases one can get
information about small 13
by observing SN neutrinos.
 This is an unique advantage
of D2O.
22
Summary of current detectors. N (I) represents normal (inverted) hierarchy. We
list types of liquid scintillator, detector masses, total numbers of targets
(proton or deuterium), depth of detectors, location of detectors, and event
numbers for inverse beta-decay process except for D2O at SNO (in this case we
list the result for the heavy water reaction).
23
IV. Summary
In our work,
 we have calculated the realistic Earth matter effects on the detection of
type II SN neutrinos at Daya Bay experiment;
 using the relation between the event number of SN neutrinos and the
mixing angle 13 , we propose a method to determine very small 13 in
the range of 0o and 1.5o by detecting the event number of SN neutrinos;
 we also apply this method to some current neutrino detectors.
Therefore, very small 13 can be measured by detecting the event
numbers of SN neutrinos.
24