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I Basic Kaluza-Klein towers

  1. Sep 11, 2017 #1
    - Does anyone know , why for instance a muon or a tau , can't be considered as Kaluza-Klein tower(s) ?
    M.
     
  2. jcsd
  3. Sep 13, 2017 #2

    mfb

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    If two leptons would be part of such a tower, then many more particles would be in the accessible mass range.
     
  4. Sep 13, 2017 #3
    Ok, but topology of the extra dimensions could be restricted; or have special properties; hence the mass ranges become
    restricted too.
     
  5. Sep 14, 2017 #4

    mfb

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    Do you have a publication discussing this?
    I don't see how you could get a finite Kaluza-Klein tower, and with just two states "tower" would be misleading anyway. Also, where is the partner of the other lepton then?
     
  6. Sep 14, 2017 #5

    Vanadium 50

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    Because they have different flavour quantum numbers.
     
  7. Sep 16, 2017 #6
    Ok, but what does it hint to us : perhaps that that vibrating modes aren't classical spatial dimensions , as
    we know them, but that an oscillation happens within 'other topologies' ?
    M
     
  8. Sep 16, 2017 #7

    mfb

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    Do you have a publication discussing this?

    Words are quite meaningless without mathematics backing them.
     
  9. Sep 17, 2017 #8
    Math is only a tool, it has bound us to certain visions and makes it very difficult to discover new idea's nowadays. In my review on Joseph Conlon's book 'why string theory' I wrote (amongst other ittems ):

    My major objection lies in the observation that with string theory, perhaps for the first time , math was no longer
    used to describe reality but was identified with it
    M.
     
  10. Sep 17, 2017 #9

    mfb

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    It is a tool, but it is a necessary tool. If you propose some mechanism it has to give the right quantitative predictions. "He was clearly killed by the impact of an object" loses its plausibility if the object had a mass of 1 gram and a speed of 10 cm/s.
     
  11. Sep 19, 2017 #10
    After a long search I did find papers claiming a finite KK tower or KK tower with irregular spacing. The finite tower is on a "fuzzy sphere", the irregular towers are obtained through special boundary conditions. And here is a reference on KK towers on general manifolds.

    Let's suppose you want to get fermion generations as the three lightest massive states in an irregular KK tower. What is the Higgs, in this picture? In the standard model, fermion mass is obtained from a yukawa coupling between left-handed particle, right-handed particle, and Higgs condensate. The higgs-tau coupling is now being measured. So it looks like your model will separately need a scalar that couples to the KK modes in proportion to their mass. Well, maybe you can build it out of the fermions themselves, by using some kind of four-fermion interaction.

    You also have to worry about "charged lepton flavor violation" - e.g. a muon emitting a neutral Z boson and becoming an electron. How is the Z supposed to discriminate between the KK modes with sufficient precision, that they can play the role of different flavors? Find or impose an A4 symmetry in the interaction, and maybe you could solve part of that problem.

    Such difficulties would be why people don't try to do this. Here is an unusual paper which does seek a kind of KK explanation for the generations, but deals with mass in the orthodox way. The extra dimension is "apple-shaped", with a cusp, and produces three massless KK modes. These then acquire mass through a version of the usual Higgs mechanism, and their higher excitations are posited to all be far above standard-model scales. This is also how things work in string phenomenology - the observed particles all come from massless states of the string.

    I haven't managed to understand the finite KK tower of the fuzzy sphere paper.
     
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