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I Higgs field couples to Planck quantum black holes?

  1. May 26, 2017 #1
    current proton decay experiments disfavor popular GUT like SU(5)

    Does the hiearchy problem for the higgs field require that the higgs couple to a GUT scale, if it exists, or to a planck scale?

    does this require the higgs couples to Planck mass quantum mechanical black holes?

    since the Higgs only couples to fundamental particles, not composite, does a higgs coupling to a Planck mass quantum mechanical black holes
    imply Planck mass quantum mechanical black holes are fundamental particles?

    if the higgs does NOT couple to Planck mass quantum mechanical black holes, and there is no GUT scale, does this imply there is no hiearchy problem?
  2. jcsd
  3. May 29, 2017 #2
    It would be nice to see an answer to this question from someone who is really expert in "conventional" ways of thinking about this issue (let's say, the relation between quantum gravity and the hierarchy problem).

    My own philosophy is that I don't care very much about the hierarchy problem, instead I care about what could be called the criticality problem: why is the Higgs boson mass so close to a "critical" value? This proximity is what allowed Shaposhnikov and Wetterich to predict the correct mass in 2009, because they had a theoretical framework (asymptotically safe gravity plus some technical details) capable of causing the mass to take the critical value.

    Here is why the criticality problem trumps the hierarchy problem. Worrying about the hierarchy problem means you want to know why the Higgs boson mass is small compared to, say, the Planck scale. Worrying about the criticality problem means you want to know why the Higgs boson mass is exactly what it is. You need a mechanism or a reason why the Higgs quartic self-coupling goes to zero at high energies. So the first priority is to identify such a mechanism. Once you have one, then you can see if its operation also needs to be protected from other high-energy effects, i.e. if there is still a hierarchy problem.

    Wetterich and Yamada wrote a paper on solving the hierarchy problem in asymptotically safe gravity. But it's unclear to me if their hierarchy problem is meant to include the finetuning problem which is the real reason why mainstream theorists care; or if they are just trying to explain why the electroweak scale is small compared to the quantum gravity scale, and don't think they have to worry about finetuning.

    In fact, I generally don't understand what their paper is saying - when it talks about self-tuning, and resurgence from a phase transition, as the reason for the difference in scales - but then I haven't tried too hard, because I remain fundamentally skeptical about asymptotically safe gravity. I regard asymptotically safe gravity as a serious theory that deserves attention and analysis, but I rate string theory much much higher because of its many other virtues.

    Indeed, if I could somehow know for sure that asymptotic safety of gravity is the cause of Higgs criticality, my first thought would be, how could I mimic asymptotically safe gravity within string theory? But the mechanism of Higgs criticality may be something else entirely.

    Regarding your questions, just a few comments. The non-gravitational interactions of the standard model Higgs occur because it is charged under the SU(2) and U(1) symmetries of the standard model, as are the other particles with which it directly interacts. If there are other particles not charged under those groups (a right-handed neutrino would be an example), it will not interact with them.

    One expects that it will interact with gravity because all forms of mass-energy do so. The only indication that there might be something odd here, is the smallness of the cosmological constant: the Higgs field is a constant nonzero energy density throughout space, whose gravity should be dominating the universe, yet it isn't. You might suppose that all the contributions to vacuum energy, positive and negative, almost cancel because of an unknown symmetry, or for anthropic reasons; or you might suppose that there is some unknown quantum gravity effect that screens out the gravitational force of the vacuum.

    Regarding the Higgs boson particle (I was just talking about the energy that's in the Higgs field, even in a zero-particle state), there seems to be much less reason to think that it would be screened from gravitational interactions somehow, or would otherwise not behave like every other particle, and interact with gravitons. One can write out a field theory of gravitons easily enough, and it's quite tractable in the usual ways, if you just stick to the few-graviton interactions.

    Something I would like to know - and this is where expertise in the conventional wisdom would be appreciated - is whether a Higgs boson perturbatively coupled to gravitons, has a hierarchy problem (in the finetuning sense). And is it even legitimate to ask that question, while ignoring the many-graviton vertices?

    Theorists of asymptotically safe gravity ought to have answers to those questions, as well as questions about virtual black holes, but I don't know if they are that far along in their research program. As for string theory... in string theory, a black hole is just another type of composite system (e.g. a bound state of branes), so having virtual black holes isn't a great novelty. Similarly, a graviton is just another string state, so gravitons, virtual black holes, and other objects from the gravitational sector, should naturally be subsumed into the path integral over all string states.

    That said, I am not at all sure what the usual field-theoretic reasoning about the hierarchy problem looks like, when transposed to string theory (let alone what it would look like, in the context of a string-theoretic mechanism enforcing Higgs criticality). I should probably give that question some thought.
  4. May 31, 2017 #3
    I think non-zero VEV of a field does not by itself mean that there is a non-zero energy density in that field.
  5. Jun 1, 2017 #4
    Yes, it's the potential energy of the field value that matters, see section 3 of Sola 2013, or part III of Weinberg 1989.
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