Does Shaposhnikov & Wetterich 2009 have a hierarchy problem?

[mitchell porter]

A thread for discussing this issue (and related topics).

The first question I have is, how to define the theory under consideration? Asymptotic safety has only been proven for some truncations of general relativity; if we take one of those truncations, and couple it to one of those minimal extensions to the standard model, is that a context in which the hierarchy problem can be meaningfully analyzed?

 

[kodama]

also relevant

Gauge hierarchy problem in asymptotically safe gravity--the resurgence mechanism
Christof Wetterich, Masatoshi Yamada
(Submitted on 9 Dec 2016 (v1), last revised 28 Apr 2017 (this version, v2))
The gauge hierarchy problem could find a solution within the scenario of asymptotic safety for quantum gravity. We discuss a "resurgence mechanism" where the running dimensionless coupling responsible for the Higgs scalar mass first decreases in the ultraviolet regime and subsequently increases in the infrared regime. A gravity induced large anomalous dimension plays a crucial role for the required "self-tuned criticality" in the ultraviolet regime beyond the Planck scale.
Comments: Version published in Phys.Lett. B; 5 pages, 1 figure
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
Journal reference: Phys.Lett. B770 (2017) 268-271
DOI: 10.1016/j.physletb.2017.04.049
Cite as: arXiv:1612.03069 [hep-th]

 

[mitchell porter]

The argument that there is a finetuning problem usually goes like this. The standard model implies that the observed Higgs mass is a bare mass plus quantum corrections. To make this concrete, we assume that the standard model is valid up to some energy scale Lambda; then we can talk about the bare mass and the quantum corrections as evaluated at Lambda. It turns out that the quantum corrections are enormous, but the observed mass is small, so the bare mass must be another enormous quantity finetuned so that the quantum corrections leave only the small observed mass.

This line of reasoning says nothing about what the physics above Lambda is. But S & W 2009 does present such a hypothesis: physics above Lambda consists of the standard model (or rather its nuMSM extension) coupled to asymptotically safe gravity. What I would like to do, is to spell out the argument that there is a finetuning problem, given this particular assumption about the UV physics.

Here's what I envisage. I would want to consider nuMSM, or SM or something simpler (like a toy model in which the S & W mechanism still works), coupled to the simplest truncation or concrete formulation of gravity for which asymptotic safety has actually been proven. That might allow us to be concrete about the graviton interactions that give rise to the quantum corrections in the standard model effective theory at scale Lambda.

An example of what I am talking about would be graviton exchange between two electrons. In the effective theory that should correspond to a new point interaction between two electrons, in the same way that Fermi's theory of the weak interaction can be obtained by integrating out the heavy weak gauge bosons of the standard model.

So if the true ultraviolet physics is nuMSM plus asymptotically safe gravity, the effective theory at scale Lambda shouldn't just be the standard model, it should be the standard model augmented with a large number of effective interactions due to graviton exchange, which will contribute to the quantum corrections to the Higgs mass.

I actually have no idea what happens if this analysis is carried through. Do you find that all of those effective interactions are inherently minuscule, because of powers of Lambda in the denominator, except for just those corrections at work in the scenario which predicts the Higgs mass? Or will we find that some type of finetuning magic will still be needed? Or is an analysis in terms of gravitons mistaken, and one needs to use some nonperturbative method?

 

[ohwilleke]

I think that first the graviton interaction modifications turn out to be very small since the gravitational coupling constant is small relative to the other forces, and second, that it is relatively straightforward to slightly tweak the bare value before quantum corrections to make it match the empirically measured value after considering gravitational interaction corrections.

Also, the whole point of asymptotic safety is to derive the value of something like the Higgs mass via its beta function from a boundary condition at the GUT mass. There is nothing unnatural (even assuming that "naturalness" is a meaningful concept) about that derivation of the Higgs mass. The fine tuning comes from a different process that should also produce the Higgs mass. But, in AS you get at least a good justification for why an "unnatural" value might be appropriate since you have an independent principal for determining the same thing that is natural.