6805: 1094 Activities 14
Write your name and answers on this sheet and hand it in at the
Work with others at your table on these activities. Argue about
the answers but work efficiently!
Neutrino masses and oscillations
Goal: Understand neutrino interactions at the microscopic level.
- Electroweak interactions
- Look at the diagrams on page 1 of the "Neutrinos 2" slides.
Which processes are shown in the first two diagrams?
(Hint: Draw appropriate time axes.)
- Draw the appropriate diagram for the beta decay of a proton.
- Draw an alternative for the second diagram with a different
- On the second slide, why does one redefine the down quark but
not the up quark?
- Why is the relation between mass and weak quark eigenstates for
two generations expressed in terms of a single angle?
(Hint: write the transformation in matrix form. What property does
the matrix have to have, yielding how many free parameters? Of these,
how many are physically significant?)
- Which factors should appear at the quark-W vertices in the
diagrams on pages 1 and 2 of the "Neutrinos 2" slides?
- Neutrino oscillations
- Page 4 of the "Neutrinos 2" slides shows the CKM matrix that
describes the mixing of quark eigenstates. What would an analogous
matrix for neutrino oscillations look like?
- Let us now take a more quantitative look at oscillations. For simplicity,
we work with only two flavors |να,β> (and thus two mass
eigenstates, call them 1 and 2). What does the mixing matrix look like in
this case? (Hint: recall what we had for two quark generations!)
- Mathematically, what does it mean to be a "mass eigenstate," and what determines
its time evolution?
- Suppose you start with an initially pure |να> beam. What
is its composition after a time t? In other words, what is
|να(t)>, expressed in terms of |ν1> and
- The relativistic energy-momentum relation is
E2 = p2 + m2.
What are the non-relativistic and ultra-relativistic limits, respectively, and which
one would you use here?
- Calculate the probability to measure a |νβ> after travelling a
distance L, i.e., derive the formula given in p. 5 of the "Neutrinos 2"
- Finally: Why does the observation of neutrino oscillations imply that they
have a nonzero mass? What can be inferred about the masses from
6805: 1094 Activities 14.
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