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11

Dimensional regularization (i.e., dim-reg) is a method to regulate divergent integrals. Instead of working in $4$ dimensions where loop integrals are divergent you can work in $4-\epsilon$ dimensions. This trick enables you to pick out the divergent part of the integral, as using a cutoff does. However, it treats all divergences equally so you can't ...


10

Whether you do your calculations using a cutoff regularization or dimensional regularization or another regularization is just a technical detail that has nothing to do with the existence of the hierarchy problem. Order by order, you will get the same results whatever your chosen regularization or scheme is. The schemes and algorithms may differ by the ...


6

The holographic principle tells us that the description of what happens in a volume of space can be encoded on a surface that surrounds it. This is related to the Bekenstein bound that tells us that the amount of information in a volume of space cannot be more than the area of the surrounding surface in units of a quarter of a planck area. This in turn as ...


6

One notable class of exceptions are what are called "hierarchy problems" in particle physics. For example, if you identify the Planck mass as a fundamental energy scale, you end up with huge dimensionless numbers which don't have an obvious explanation (i.e. ratio of Planck to electroweak scale, etc.). Explaining these large (or small depending on how you ...


5

Let's look at the forces in nature, there are four of them as far as we know (note that I am not very precise in the numbers I give, but for the comparison I make this is enough): the strong force is very strong, it's coupling constant (which is a measure for its strength) is about 0.1 the weak force is not actually all that weak. It can be unified with ...


4

Well, of course you have to pick the quantities in your dimensional analysis right. Example: Use dimensional analysis to estimate the potential energy of a star, hold together only by gravitation. Solution: Newtons gravitational constant $G$ better show up somewhere. This requires us to include something with units $kg^2 / m$. We can get this by inserting ...


4

The argument for fine tuning is far broader than just the Higgs. For example it's argued that the existance of any elements heavier than lithium relies on a fine tuned resonance in the carbon 12 nuclues that allows three helium nuclei to stay together long enough to form a carbon nucleus. There are lots of books that explore these ideas. A good start would ...


4

All we can do precisely is give a probability for some physical quantity to have its observed value. For example (subject to various assumptions!) the probability of the cosmological constant having it's observed value is around 1 in $10^{120}$. Since this is absurdly low we say it's fine tuned. But where you draw the line between fine tuned and not fined ...


4

The hierarchy problem is not only about big numbers, such as $M_{pl}/M_{EW}$, per se'. In fact in QCD there is no hierarchy problem associated to the ratio $M_{pl}/\Lambda_{QCD}$. The problem is actually about the quantum numbers of certain operators in a Wilsonian EFT. The point is that we understand the SM as an effective low-energy description of the ...


4

It's the same problem because the low scale matches in both definitions; and the high scale matches in both definitions, too. Both problems are the puzzle why the two scales are so much different. First, the low scale. In the Higgs fine-tuning, you define the low scale as the Higgs mass. But the Higgs mass can't be parameterically greater than the Z-boson ...


4

A fine tuning problem is only a problem if we require that the considered model is a good or complete model of how we think the universe behaves. In this case, it appears that we require the density of the universe to be as close as 1 part in $10^{64}$ to the exact density that will make it a flat universe that will expand forever, asymptotically coming to ...


3

The question is dealt with on pages 302 to 304 of Smolin's book The Life of the Cosmos. The reasoning is based on a proposal by Hans Bethe and Gerald Brown (I don't have the reference to hand) that in a neutron star kaons can become light (by a mechanism analogous to superconductivity), and indeed can become light enough for an electron to decay into a kaon ...


3

The difference between the $\mu$-problem and the hierarchy problem is that loop corrections to the value of $\mu$ in MSSM are small and convergent, because of supersymmetry, while the loop corrections to $m_h^2$ in the SM are divergent. So to explain why $\mu$ is small, it is enough to explain why its approximate – tree-level – value is small. (Well, the ...


3

The gauge bosons such as the photon and chiral fermions may be massless due to the symmetry – gauge symmetry and chiral symmetry, respectively. We may consistently require the theory to respect these symmetries at the exact level, including all quantum corrections. For the gauge symmetry, it means that $1+1=2$ polarizations of the photon or another particle ...


3

It is all about appropriate cancellations in the expansions when calculating the Feynman diagrams: The hierarchy problem Supersymmetry close to the electroweak scale ameliorates the hierarchy problem that afflicts the Standard Model. In the Standard Model, the electroweak scale receives enormous Planck-scale quantum corrections. The observed ...


3

Those who write than the Standard Model (SM) is natural interpret it as a fundamental theory, rather than an effective theory or effective field theory, with an unphysical cut-off taken to infinity, $\Lambda\to\infty$. The bare parameters and loop corrections diverge, but are in any case considered unphysical. Only renormalized Lagrangian parameters (...


3

If you assume pure QCD theta term, it becomes to make the contribution into the vacuum energy after QCD chiral symmetry spontaneous breaking. Really, since $G_{a}\tilde{G}_{a}$ term is the full derivative $G\tilde{G} = \partial_{\mu}K^{\mu}$, then it doesn't make the contribution into observed quantities. However, near the scale of QCD symmetry breaking the ...


2

It seems plausible that the probability of the universe being just right for human life by pure chance is pretty low, and possibly absurdly low. That means if the universe only had one chance at existing the probability we'd be around to see it is vanishingly small. The various multiverse theories suggest that huge numbers of disconnected universes get ...


2

The example of unnaturalness you describe is the example of the mexican hat for the higgs mechanism ( if you look at this page up on the left you will see the mexican hat in the PHYSICS logo). As all should know this symmetry is naturally broken at our energy levels, as in this the example, which is correct, that the pencil sits precariously and can break ...


2

For your first question: the physical mass is the measured mass. If $m$ is not the measured mass, don't call it the physical mass, because it isn't. If someone does, correct them. :-) For your second question, I think we should look at the physical interpretation of all those mathematical manipulations. The hierarchy problem (as I understand it) comes from ...


2

There are $20$ numbers which are of maximum importance in physics. Well, $20$ is probably not going to do it these days (maybe you were reading something written before the neutrino oscillation discovery of the late $1990$'s). Before the Super Kamiokande experiments in the $1990$'s, we all thought that neutrinos were massless and didn't mix with each other, ...


1

I believe you are "jumping to conclusions." The reason gravity is "an open problem in physics," is not because it is several orders of magnitude smaller than the others. It is only a problem for those trying to unify gravity with the other three forces, to come up with a TOE.


1

It is not a problem in the sense that it bothers anybody or causes trouble in certain calculations. In physics, however, we would like to find out whether there is an explanation for certain phenomena. In this case, the phenomenon is that there is a huge gap between the scales of interaction strengths of gravity and the other forces. This has no explanation ...


1

The upper mass limit for neutron stars depends both on general relativity and on the equation of state for dense nuclear matter. General relativity we seem to understand pretty well. Dense nuclear matter we understand less well, so estimates of the neutron star upper mass limit vary by about a factor of two. If Smolin's idea really does provide another, ...


1

Let us suppose that that the Standard Model is an effective field theory, valid below a scale $\Lambda$, and that its bare parameters are set at the scale $\Lambda$ by a fundamental, UV-complete theory, maybe string theory. The logarithmic corrections to bare fermion masses if $\Lambda\sim M_P$ is a few percent of their masses. The quadratic correction to ...



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