Neutrino Physics -...
Transcript of Neutrino Physics -...
Neutrino Physics
陆锦标 Kam-Biu Luk Tsinghua University
andUniversity of California, Berkeley
andLawrence Berkeley National Laboratory
Lecture 6, 11 June, 2007
2
Outline
• Neutrino interactions - elastic scattering - inelastic scattering
• Background - cosmic ray - natural radiation - spallation neutron• Reduction of background
3
νe Interactions• νe interacts with atomic electrons: elastic scattering
!
"(#ee$#
ee) =
GF
2s
%
1
2+ sin
2&W
'
( )
*
+ ,
2
+1
3sin
4 &W
-
. /
0
1 2
3 9.5 410545 E#
1MeV
'
( )
*
+ , cm
2
It can take place at any energy.
νe + e- → νe + e-
!
sin2"
W= 0.23
GF = Fermi constant
=1.167x10-5 GeV-2
ν eeν
4
νe Interactions• νe interactions with atomic electrons: elastic scattering
!
"(# ee$#
ee) =
GF
2s
%
1
3
1
2+ sin
2&W
'
( )
*
+ ,
2
+ sin4 &
W
-
. /
0
1 2
3 4.0 410545 E#
1MeV
'
( )
*
+ , cm
2
It can also take place at any energy.
νe + e- → νe + e-
νe νe
e- e-
Z0
e-
W-
νeνe
e-
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νµ Interactions• νµ interactions with atomic electrons: elastic scattering
!
"(# µe$# µe) =G
F
2s
%
1
2& sin
2'W
(
) *
+
, -
2
+1
3sin
4 'W
.
/ 0
1
2 3
41.6 510&45 E#
1MeV
(
) *
+
, - cm
2
νµ + e- → νµ + e-
νµ νµ
e- e-
Z0 W+
νµ
e-
e-
νµ
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νµ Interactions• νµ interactions with atomic electrons: elastic scattering
!
"(# µe$# µe) =G
F
2s
%
1
3
1
2& sin
2'W
(
) *
+
, -
2
+ sin4 '
W
.
/ 0
1
2 3
41.3510&45 E#
1MeV
(
) *
+
, - cm
2
νµ + e- → νµ + e-
νµ νµ
e- e-
Z0
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Inelastic νµ Interactions• νµ interactions with atomic electrons:
!
"(# µe$# eµ) =GF
2
%
s&mµ
2( )2
s for low energies
=GF
2s
% for high energies
'17 (10&45 E#
1MeV
)
* +
,
- . cm
2
νµ + e- → νe + µ-
W+
νµ
e-
µ-
νe
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Inelastic νe Interactions• νe interactions with atomic electrons:
µ-
W-
νµνe
e-
νe + e- → νµ + µ-
!
"(# µe$# eµ) =GF
2
3%
s&mµ
2( )2
s for low energies
=GF
2s
3% for high energies
' 5.7 (10&45 E#
1MeV
)
* +
,
- . cm
2
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Tau Neutrino Interactions
The cross sections of ντ and ντ with electron are identical
to those of the muon neutrinos.
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Neutrino-nucleon Interactionsνe + n → e- + p
ν pe-
n
dud
duu
W-
e-νe
In the laboratory,
For less than 1 GeV,
!
"(# en$ e%
+ p) =GF
2E#
2(hc)
2
&(gV
2+ 3gA
2) 1+
Q
E#
'
( )
*
+ , 1+ 2
Q
E#
+Q
2 %me
2
E#2
= 9.3-10%44 E#
1MeV
'
( )
*
+ ,
2
1+Q
E#
'
( )
*
+ , 1+ 2
Q
E#
+Q
2 %me
2
E#2
cm2
where gv = 1, vector coupling constant, gA = 1.23, axial-vector coupling constant, Q = mn - mp = 1.3 MeV
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Neutral-current Interaction With Nucleon
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Antineutrino-nucleon Interactions
νe + p → e+ + nInverse beta-decay reaction:
In the laboratory,
pνe+
n
For less than 1 GeV,
!
"(# e p$ e+
+ n) =GF
2E#
2(hc)
2
%(gV
2+ 3gA
2) 1&
Q
E#
'
( )
*
+ , 1& 2
Q
E#
+Q
2 &me
2
E#2
-(E# &Q)
= 9.3.10&44 E#
1MeV
'
( )
*
+ ,
2
1&Q
E#
'
( )
*
+ , 1& 2
Q
E#
+Q
2 &me
2
E#2
-(E# &Q) cm2
where θ(Eν-Q) = 1, for Eν > Q threshold function
= 0, for Eν < Q
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Cross Sections Of Low-energy ν Scattering
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Interactions With Nucleons At High-energy• For 50 GeV < Eν < 350 GeV, the inelastic cross sections are:
!
"(#lN$ l
%+ X) & 6.7 '10
%39 E#
GeV
(
) *
+
, - cm
2
!
"(# lN$ l
++ X) % 3.4 &10
'39 E#
GeV
(
) *
+
, - cm
2
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How Many Neutrino Events?For observing solar neutrino events with the electrons in the water molecule as the targets
Ndet = σνe•Φν•Ntgt
where Φν = 7 x 1010 cm-2s-1,
σνe ~ 10-45 cm2
For the target, the number of electrons in 1 mole of H2O:
(6 x 1023 molecules) x 18 e-/molecule ~ 1025 e-
If 1000 tonne of water is used, then the number of e- is
Ntgt = (103 x 103 x 103/18) x 1025 ~ 1032
Thus, the event rate is: Ndet ~ 0.01 s-1 or 1000 per day !!
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Dark Side Of Cosmic Ray• At sea level, the intensity of cosmic ray is ~1 cm-2min-1, and has an angular distribution given by
!
dI
dcos"= I
0cos
2"
Most are muons with an average energy of ~4 GeV.
µ- > 1 GeV
• Muons can ionize the target along their path, and can emit Cherenkov photons:
µ− + N → µ− + N+ + e-
or µ− + N → n + X µ− + N → N1 + X
→ N2 + β + νe
which can mimic the neutrino reactions.
• For a 1000 t water cube at sea level, the number of muons going through is ~(10 x 100)2 x 1 min-1 = 1.7 x 104s-1
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Go Underground
Muons lose energy as they go through rock. Hence they getattenuated.
10-13
10-11
10�-9
10-7
10-5
10-3
10 -1
0 1000 2000 3000 4000 5000 6000 7000 8000
Muon FluxNeutron ProductionMuon Flux
(cm-2 s-1)
Neutron Production(g-1s-1)
Boul
by
Soud
an
Gra
n Sa
sso
Kam
ioka
Frej
us
Mon
t Bla
nc
Sudb
ury
m.w.e.
1 m of granitic rock ≈ 2.6 m of water = 2.6 m.w.e.
metre waterequivalent
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Natural Radioactivity• The common radioactive isotopes in the environment are:
Gamma rays from 238U, 232Th, and 40K chains
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More Headache Due To Radioactivity• All materials used in the detector potentially can have natural radioactivity as well, for example, for a low background photomultiplier tube:
2530170Plastic
0300Metal
207030Ceremic
303060Glass
238U (ppb)*232TH (ppb)*40K (ppm)*
* Mass of radioactive nuclide/mass of the material• The number of gamma rays emitted is:
1 mg of natural K gives 285 γ/day with Eγ > 0.1 MeV1 µg of Th gives 958 γ/day with Eγ > 0.1 MeV1 µ g of U gives 2310 γ/day with Eγ > 0.1 MeV
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Problem With Background Gamma Rays
photon
Atomicelectron
λθ
λ’
• Since the energies of many of the gamma rays from natural radioactivity are more than 1 MeV, they can Compton-scatter to give energetic electrons:
• The electrons can look like those coming from ν or ν interactions.
• A gamma ray could also combine with a low-energy n to appear as a inverse beta-decay event (gamma ray looks like e+ as far as the detector is concerned).
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Beating Down The Background• The intensity of radiation after passing through a thickness x of material is given by:
!
I(x) = I0e"x /#
where I0 is the initial intensity, λ is the absorption length (for photon, this is also called radiation length)
!
" cm[ ] =
"g
cm2
#
$ % &
' (
)g
cm3
#
$ % &
' (
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Beating Down The Background (cont.)• The other background is the neutrons produced by muons.• Neutrons can be attenuated with hydrogen-rich materials, e.g. water, paraffin, borated polyethylene.• If water, cheap and easily available, is used:
Neutron absorption vs thickness of water
Fast
neu
tron
s pe
r da
y
water thickness (m)
0.05
0.10
0.15
0.20
0.25
0.30
0. 1. 2.
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Shielding Neutrino Detector ForNon-accelerator Experiments
targetvolume
buffer
shield
detector
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Summary• Neutrino interactions have small cross sections at low energies, hence, low event rate.
• Cosmic ray and natural radioactivity are major background in non-accelerator neutrino experiments
• Need large, clean, and well-shielded detectors placed underground to reduce unwanted events