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Masses of elementary particles

  1. Aug 31, 2010 #1

    tom.stoer

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    I have a simple question regarding masses of elementary particles (in string theory).

    What is the mechanism proposed to explain the tiny but non-zero fermion masses?

    I know zero masses e.g. due to some symmetry (gauge, conformal) or symmetry breaking (Goldstone bosons). I know the huge masses at and beyond Planck-scale due to higher modes of the string. I know mass generation due to non-linear interaction like for hadron masses in QCD.

    But all these mechanism do not seem applicable for the generation of fermion masses.

    Of course one could assume a very complicated self-interaction a la Higgs and try to fit a potential that reproduces all these masses; but that seems to be unsatisfying, doesn't it?
     
  2. jcsd
  3. Aug 31, 2010 #2
    In terms of generations I believe current research is focused on understanding the geometry of compactified dimensions. For instance if you have a torus with three holes it is possible to generate 3 fermion generations.
     
  4. Aug 31, 2010 #3

    tom.stoer

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    Yes, but what about the masses?
     
  5. Aug 31, 2010 #4

    arivero

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    Nothing about the masses. The state-or-the-art keeps being the one of GUT theories. The yukawa couplings should run via the renormalisation group in a way able to justify the difference betwee the bottom and the top.

    My personal opinion is that the top yukawa coupling is one, all the others are zero.
     
  6. Aug 31, 2010 #5

    tom.stoer

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    How should running yukawa coupling account for all different fermion masses?
     
  7. Aug 31, 2010 #6

    arivero

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    Well, to be precise, to separate the mass of the charged lepton from its neutral partner, we invoke the see-saw. The yukawas could be unimportant in this cases.

    The masses of the three colored variants of any particle are the same, so it is clear that the mass generation procedure does not relate to SU(3) and it depends of SU(2)xU(1). Thus the yukawa coupling is the main suspect. Note also that SU(3) is non chiral.

    Of course, the meaning of the yukawa depends of the meaning of the Higgs field. All GUT theories, including those which shlould come from string theory, assume that the Higgs field is an elementary field at GUT scale.

    They are two different questions:

    1) Why different yukawa couplings (thus mass) for each generation?

    2) Why different yukawa couplings for the 2/3 and 1/3 particle of each generation?

    GUT theoretists unify each generation in a multiplet, but they do not unify different generations, so they are only forced to address (2). I believe to remember that some papers were done claiming a different running for the top - bottom multiplet respect to the other two. This was because SU(5) allowed for a unification of the top and bottom, obviously failing to do the same for the other couples. But then, naive SU(5) itself is ruled out by experiment, so it makes not sense to keep it as an esential piece of argument. Thus I'd think that most of the theoretical search on the topic stopped about 1984. The state of the art is preserved in the collection "Unity of Forces in the Universe", recopilated by A. Zee.

    For the small masses of the two first generations, Zee collects an argument from Barbieri Nanopoulos Wyler.


    About (1), nothing was told. But in SUSY GUT they are some work on "top infrared fixed point" where the mass of the third generation has some special role to generate the breaking of electroweak symmetry.
     
    Last edited: Aug 31, 2010
  8. Sep 1, 2010 #7

    tom.stoer

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    So the conclusion is that I should add "running Yukawa couplings" to my list. To be honest, the predictive power seems to be rather low in a model with 3 generations, u-d like splitting, massless neutrinos etc.

    That' why I was asking for string-inspired ideas.
     
  9. Sep 1, 2010 #8

    Haelfix

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    Mmm, the way I understand it, is that string theory will generate a set of effective field theory actions after compactification. So for instance it will generate a family of theories that might look like mSugra if the theorist is clever enough, where the superpotential will have some additional constraints and/or fields (moduli) that vary upon continous deformation of the geometry.

    The question, what generates the mass of the electroweak particles is essentially the same phenomenology as what we are typically accustomed to for all practical purposes. There is a higgs field (or as set of Higgs fields) that lives in a particular representation of the gauge group. The difference is certain things are now fixed (eg the representation often cannot be too large), various parameters and couplings will secretely have relations between them and the mechanism of how the symmetries break might be more or less specified.

    As to what solves the hierarchy problem.. Well, weak scale supersymmetry is usually considered the simplest and most natural solution and seems to be rather generic in the stringy landscape, but you'll notice the question shifts from 'why are fermion masses so tiny' to 'why is supersymmetry at the weak scale, and why and how does it break and why xyz GuT group'. Thats somethign that you expect for your theory to answer and I think that in some cases it actually does.
     
    Last edited: Sep 1, 2010
  10. Sep 1, 2010 #9

    tom.stoer

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    I am only interested in the general idea of the approach. What I get is that string theory may have a vacuum which determines generations, parameters as expectation values of fields, relations between them, potentials and symmetry breaking etc.

    So the masses of the particles are essentially determined by a specific solution of the theory. This was my expectation and it has been confirmed, thanks.
     
  11. Sep 1, 2010 #10

    Haelfix

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    Yes I think thats correct, given a particular vacuum of string theory all the masses, couplings and detailed phenomenology is completely fixed *in principle*.

    Of course in practise, in the phenomenology literature you will see real world solutions that are considerably more arbitrary. A lot of that is parametrizing one's ignorance, eg instead of doing some ridiculously complicated 10 point integral or working out tiny corrections arising from the superpotential, you simply write in a new parameter in the low energy eft and try to put bounds on it.
     
  12. Sep 1, 2010 #11

    tom.stoer

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    One main question which remains (if one accepts that one is not able to do all these calculations in practice) is whether string theory gives us some hint how to explain the mass scales, the tiny masses and mass differences "in principle". So why are u- and d-mass small and slightly different, why are b and t so much heavier, why is the mass spectrum so complicated etc. Shifting everything to a complicated enough symmetry breaking seems implausible.

    Every symmetry looks nice as long as it is realized, but as soon as you try to break it it becomes ugly. Now the problem witrh strings is that they have a huge symmetry, but that our world looks rather ugly. That means that the mechanism responsible for the symmetry breaking is expected to be ugly as well. Of course this is not a physical objection, but it seems reasonable to expect that there are some difficulties in claiming that "the correct vacuum + symmetry breaking will do the job" w/o trying to understand "how".

    That's why I am asking if string theory may provide a new principle which might help to understand mass generation.
     
  13. Sep 1, 2010 #12

    arivero

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    Straightforward string theory reduces to GUT, so it does not help.

    Of course, there are alternatives. You can hope for extra dimensions to appear already at TeV scale, and then you can use string theory to explain them.

    Also, you can buy my suggestion of going back to Physics. Letters. B 37 315 (1971) from J H Schwarz , "Dual quark-gluon model of hadrons". The original author changed his viewpoint and abandoned this line of approach to superstrings, but it is clear that if pursued, it should link all the masses of the terminated gluons (mesons and diquarks, and posibly barions too) via supersymmetry, down to the elementary particle level.

    One intriguing thing in the question of masses is why the QCD scale (the scale where the coupling of QCD becomes 1 ) lies about the quark and lepton mass scales. Of course, to a GUT it is just a random coincidence: the QCD coupling runs, the yukawas run, the higgs coupling runs, and when the higgs breaks electroweak symmetry the QCD coupling happens to be near of reaching its strong regime.

    Sorry to keep pestering on this line, but I feel that simply to say that "string theory does not predict anything about fermion masses" is not honest; it is true only if by string theory we refer to the developed corpus, which has extended in a very definite and narrow directions and even in this case is still under development. Other directions of string theory could travel differently.
     
    Last edited: Sep 1, 2010
  14. Sep 1, 2010 #13

    tom.stoer

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    Did I say that string theory predicts nothing regarding the mass scales? Then this was a mistake.

    All what I say is that breaking a highly symmetric theory usually makes this theory ugly - and that this applies to string theory as well. So I hope that there is a new principle (still to be discovered) which sheds new light on mass generation. This need not be restricted to string theory and could emergy in a different context as well (but this is a personal opinion w/o any support from other research programs; sp it could be completely wrong)
     
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