Transcript Neutrinos
Neutrino Physics
• Three “active” neutrino flavors (from Z
width measurements). Mass limit from beta
decay
m e 3 eV
m 0.2 MeV
m 18 MeV
mex2 104 eV 2 x or
m2x 103 eV 2 x (or inactive)
• Probably have non-zero masses as they
oscillate
• Only have weak interactions and can be
either charged or neutral currents
e
W
charge
e
e
e
en e p
n p
e e e e
n e
n,p,e e p e p
neutral
e
p
Z
n,p,e
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ee ee
e e
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Neutrino Cross Sections
• Use Fermi Golden Rule
Rate
2
| M |2 phase space
• M (matrix element) has weak interaction
physics…W, Z exchange ~ constant at
modest neutrino energies. Same G factor as
beta decay
1
1
2
G
g
2
2 8M W
q M
2
2
W
M
2
W
E M W
• cross section depends on phase space and
spin terms. Look at phase space first for
charged current. Momentum conservation
integrates out one particle
e e e e (CC )
phase space pe2 dpe p2 dp
pcm pe p
4G 2
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pcm
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Neutrino Cross Sections II
• Look in center-of-momentum frame
s M 2 Etot2 ptot2
pe p ptot 0 Etot E Ee 2 p
s (2 p) 2
4G 2 p 2 G 2 s
• s is an invariant and can also determine in
the lab frame
ptot p E
Etot E me
s E2 2me E me2 p2 2me E
G 2 2m E
• cross section grows with phase space (either
neutrino energy or target mass)
(p) m p
2000
(p) me
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Neutral Currents
• The detection of some reactions proved that
neutral current (and the Z) exist
e e
p p
• the cross section depends on the different
couplings at each vertex and measure the
weak mixing angle
e
16 4
sin W )
3
G 2 me E 1 4 2
16
( sin W sin 4 W )
3 3
3
e
G 2 me E
(1 4 sin 2 W
• about 40% of the charged current cross
section due to Z-e-e coupling compared to
W-e-nu coupling
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Neutrino Oscillations
• Different eigenstates for weak and mass
weak : e , , 1, 2 , 3 : mass
• can mix with a CKM-like 3x3 matrix with
(probably) different angles and phases then
quarks. The neutrino lifetime is ~infinite
and so mix due to having mass and mass
differences (like KL and KS)
• example. Assume just 2 generations (1
angle)
1 cos 2 sin
e 1 sin 2 cos
• assume that at t=0 100% muon-type
(t 0) 1 e (t 0) 0
1 (t 0) cos 2 (t 0) sin
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Neutrino Oscillations II
• Can now look at the time evolution
• from the Scrod. Eq. And assuming that the
energy is much larger than the mass
1, 2 (t ) 1, 2 (0)e
mi2
Ei p
2p
iE1, 2t
c 1
• probability of e/mu type vs time (or length
L the neutrino has traveled) is then
2
(t ) cos e
2
iE1t
sin e
2
iE2t 2
2
4
m
Lc
1 sin 2 2 sin 2
4 Ec
• where we now put back in the missing
constants and use a trig identities
LE
t
c p
2 sin cos sin 2
( E2 E1 )t
cos(E2 E1 )t 1 2 sin
2
2
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Neutrino Oscillations III
• Oscillation depends on mixing angle and
mass difference (but need non-zero mass or
no time propagation)
2
4
m
Lc
(t ) 1 sin 2 2 sin 2
4 Ec
2
e (t ) 1 (t )
2
2
• so some muon-type neutrinos are converetd
to electron type. Rate depends on neutrino
energy and distance neutrino travels L/E
• go to 3 neutrino types and will have terms
with more than one mixing angle. Plus
neutrinos can oscillate into either of the
other two (or to a fourth “sterile” type of
neutrino which has different couplings to
the W/Z than the known 3 types)
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Detecting Neutrino Oscillations
• Disappearance: flux reduction larger L/E
• Solar Neutrinos. Measure rate for both
electron neutrinos and all neutrinos (using
neutral current). Low energies (for MeV)
cause experimental thresholds for some
techniques. Compare to solar models.
rate( e n e p)
Rate( e, , pn e, , p n)
• Atmospheric neutrinos. Measure rate as a
function of energy and length (from angle)
e e
# e 1
production
# 2
• also electron or muon neutrinos produced at
reactors or accelerators. Compare flux near
production to far away L/E >> 1
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Detecting Neutrino Oscillations
• Appearance: start with one flavor detect
another
• Ideal. Tag nu production by detecting the
lepton. Then detect neutrino interaction.
Poor rates (considered pi/K beams and
muon storage rings)
• Real. Tau neutrino very difficult to detact
sources of pure electon neutrinos (reactors)
are below muon/tau threshold
• ---> use mostly muon neutrino beam
e
K e e
0.003
• can measure neutrino energy in detector (if
above 1 GeV. Below hurt by Fermi gas
effects). Can usually separate electron from
muon events with a very good ~100%
active detector
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