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Neutrino Oscillation in matter

  1. May 11, 2015 #1

    ChrisVer

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    Hi, I have some problem in deriving [itex]\Delta m_M^2 [/itex] as given in eq.35 here:
    http://www.slac.stanford.edu/econf/C040802/papers/L004.PDF

    When I tried to derive the eigenvalues of [itex] H_M [/itex] (eq.33) I got:

    [itex] m^2 = (\cos 2 \theta -x)^2 + \sin^2 2 \theta [/itex]
    which is only one eigenvalue. Any help? In particular it seems he defines:
    [itex] \Delta m_M^2 = \Delta m_i^2 \times |m|[/itex]
     
  2. jcsd
  3. May 11, 2015 #2

    ChrisVer

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    Here's my solution
     

    Attached Files:

  4. May 11, 2015 #3

    ChrisVer

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    If I say:
    [itex] m_{1M} = m_1 + m \Rightarrow m_{1M}^2 = m_1^2 + m^2 + 2 m_1 m[/itex]
    [itex]m_{2M} = m_2 -m \Rightarrow m_{2M}^2 = m_2^2 + m^2 - 2 m_2 m[/itex]
    Then:
    [itex]\Delta m_M^2 =m_{1M}^2 - m_{2M}^2 = (m_1^2 - m_2^2 ) + 2 m (m_1 +m_2 ) = \Delta m^2 + 2 m (\Sigma m) [/itex]
     
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