Neutrino Physics - Lecture 2

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Neutrino Physics - Lecture 2

• Steve Elliott
• LANL Staff Member
• UNM Adjunct Professor
• 505-665-0068, elliotts_at_lanl.gov

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Lecture 2 Outline

• Neutrino detection
• Sources of neutrinos
• Neutrino Mixing
• Discussion

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Neutrino detection

• Targets
• H2O
• D2O
• Scintillator
• Ga
• Cl
• Emulsion
• Ice
• Iron
• Rock

ES on e- ?x e--gt ?x e- CC on Nucleus
?l A-gt A l NC on Nucleus ?x A-gt A ?x
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Cross sections

• 10,000 light years of Pb to stop half of solar
  neutrinos (few MeV ?e)
• Beta decay provides estimate of strength

Neutron beta decay
Anti-neutrino absorption
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Cross Sections
The small size of these cross sections is what
led early researchers to believe they had
postulated an undetectable particle.
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Hard experiments

• Rates are very low
• Big detectors
• Background difficulties
• Signal may not be very distinct
• Other more common processes can mimic signal
• Rare variations of common phenomena

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Sources of neutrinos
Big Bang Radioactive decays Stars Supernovas Cosmi
c rays Reactors Accelerators
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Big Bang

• Relic neutrinos contribute at least as much mass
  to the Universe as all the stars.
• There are as many leftover neutrinos as photons.
• N? 420/cc
• Photon energy 2.728 K
• Neutrino energy 2 K
• There are no viable ideas for detecting such low
  energy neutrinos.
• But they might have detectable effects for large
  scale structure
• Note that neutrinos are studied via their
  particle nature
• The microwave background was discovered by the
  wave nature of photons.

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Radioactive Decays

• MCi sources have been made
• Mostly for use by solar neutrino radiochemical
  experiments for efficiency measurements.
• Proposals for other neutrino property
  measurements
• Electron capture isotopes provide a monoenergetic
  neutrino.
• 51Cr
• 37Ar

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Stars (our Sun)
Features Produce only ?e through fusion
reactions Very long baseline, ?e disappearance,
?x appearance Low energy, spectral shape well
known L/E is large so sensitive to small
?m2 Large Flux Matter enhancement Data Rates
from several experiments Energy dependence Day
vs. Night Seasonal
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Supernovas
Features Very long baseline ??'s and ??'s
Complicated and poorly understood source Target
cross sections not all well understood Data
Not a common phenomenon once 30 years in our
galaxy SN1987A provided little n physics data
SN1987A did give hope for the future
My personal prediction is that neutrinos will
teach us a lot about supernovae, but the inverse
will be much harder.
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Supernovas
By using various targets with different energy-
and flavor-dependent cross sections, one may be
able to de-convolute the various fluxes. Its
difficult to get a dedicated supernova neutrino
experiment funded.
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Cosmic Rays
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Reactors
Features Complicated but well-understood
source. Low energy Short, medium, long
baselines Disappearance experiments Data Several
at short baselines 10-250 m CHOOZ/Palo Verde at
1 km KamLAND at 250 km
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Accelerators
Features Usually appearance Various baselines and
wide energy range Controlled experimental
conditions Data Oscillation limits for many
species Lots of experimental results
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A reminder of the questions

• Are neutrinos Majorana or Dirac?
• What is the absolute mass scale?
• How small is ?13?
• How maximal is ?23?
• Is there CP violation in the neutrino sector?
• Is the mass hierarchy inverted or normal?
• Is the LSND evidence for oscillation true? Are
  there sterile neutrinos?

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Present Values (from oscillation expts.)
hep-ph/0606054
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Neutrino Oscillations

• Or how we know most of what we know

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Outline

• Two-flavor vacuum oscillations
• Two-flavor matter oscillations
• Three-flavor oscillations
• The general formalism
• The rotation matrices

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Consider Two Mass States
?1 corresponding to m1 ?2 corresponding to
m2 Think of ? as a Vector
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? is a solution of H
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The Neutrinos
Consider the weak eigenstates ?e, ??. These are
not the mass eigenstates, ?1, ??. The mass
eigenstates are propagated via H.
The Mixing Matrix U
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Mixing
Weak eigenstates are a linear superposition of
mass eigenstates.
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In Vacuum, no potential in H
Denote c cos ? s sin ?
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UHU-1
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The energy difference (and Trig.)
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UHU-1 becomes
The algebra is going to get involved, so lets
define A, B, and D such that
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The Diff Eq
A solution to this equation should have the form
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Insert proposed solution
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Two Equations
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r solution
r- solution
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?? is a superposition of these 2 solutions
(D2A) is a constant so we sweep it into a
redefinition of the Cs.
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The solutions
To determine the Cs, use lt????gt1 and assume
that at t0, we have all ?e.
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The time dependent solution
What is the probability of finding all ??? at
time t?
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Transition probability
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The Answer
Complete mixing large sin2? and long R/L would
result in an average that is P1/2.