Talk:Hierarchy problem

Diagrams

The diagrams in the figures are incorrect and should be removed because the second diagram does not exist (count the number of doublets at each vertex)! The correct set of diagrams for the cancellation of the quadratic divergence from the Higgs quartic coupling involvings the gauginos and gauge bosons (as the quartic coupling arises from the D-terms). The diagram could in principle be related to the top quark quadratic divegence, but would require relabelling (and then technically it would require both the left handed and right handed top squarks in seperate diagrams, but that is splitting hairs). -- jay 00:48 & 21:04, 1 February 2006 (UTC)

I think you're right. How about this as a replacement?

File:Hqmc600.png

Cancellation of the Higgs boson quadratic mass renormalization corrections due to stop squarks between fermionic top quark loop and scalar stop squark tadpole Feynman diagrams in a supersymmetric extension of the Standard Model

-- Xerxes 18:08, 1 & 17:48, 2 February 2006 (UTC)

  (I've restored, via strikeout and bolding, the removed revision of the discussion of the diagram.
  (IMO the apparent deletion of a diagram that has figured in a talk discussion is unacceptable, but i leave any investigation and restoration of it to others whose wiki-graphics savvy extends beyond my own.)
--Jerzy•t 06:27, 19 September 2014 (UTC)

I think that the first diagram should be tops (rather than stops). The original figure is used in several different places, so it would be great if it could be updated globally.
— Preceding unsigned comment added by Jgwacker (talk • contribs) 21:04, 1 February 2006‎

I mean to indicate that these are the diagrams that cancel the equivalent top diagrams. -- Xerxes 21:22, 1 February 2006 (UTC)

I don't believe that the first diagram cancels any diagram in the fermionic sector. It arises from a trilinear scalar coupling (ie a dimensionful coupling) that only gives rise to a log divergence and contributes to the top yukawa's renormalisation of the mu term (this diagram in the susy limit arises from the cross term in the Higgs' F-term potential). Although I could be being myopic... -- jay 02:56, 2 February 2006 (UTC)

I don't really know that much about this subject. I just tried to pick up enough from some papers to put together a better diagram. How's this one? -- Xerxes 17:48, 2 February 2006 (UTC)

Perfect! -- jay 21:04, 2 February 2006 (UTC)

Diagram as SVG

I made a vector version of the diagram. Please ensure that it is an accurate copy. VermillionBird (talk) 23:02, 20 January 2008 (UTC)

Relative strength of the weak force

"the weak force is 10³² times stronger than gravity."

Fundamental interaction shows the relative strength of the weak force (compared to gravity) as 10²⁵. Although it also mentions that the strengths are approximate, 10⁷ is quite a difference. How can these numbers be reconciled?
— Preceding unsigned comment added by ‎ 212.59.24.222 (talk) 21:35, 14 June 2007

The strength relative of forces is not well defined and depends on the distance and how the force is being measured. The 10³² is the ratio of G_N to G_F. I don't know where 10²⁵ arises from, but it could be the strength of gravity at the weak scale relative to the strength of the weak force at the weak scale. I personally don't like these quantifiers, they give a rather misleading impression and can vary largely (because the functional forms of the forces are different) jay 02:37, 15 June 2007 (UTC)

If gravity is weaker than the other forces because it "leaks" into other dimensions, then why don't the other forces also leak into other dimensions ? And second question - could gravity leaking explain the Pioneer Anomaly ? If the other dimensions are small, then their effects would be proportionally less over the huge (three dimensional) distances pioneer has traveled, thus producing a slightly stronger gravitational pull than would be expected. Salsa man (talk) 04:15, 18 January 2010 (UTC)

Difference of problems

Are the two problems mentioned in the particle physics section the same problem or different problems? The first being the difference in scale between the weak force and gravity and the second being the stability of the Higgs mass to radiative corrections. For example, can I imagine solutions that solve one problem and not the other? I know it is fashionable in these days of extra dimensions to consider the two as being solved by the same mechanism, but what, for example, does supersymmetry have to say about the relative weakness of gravity? --Eujin16 (talk) 06:16, 7 December 2007 (UTC)

Technically they are the same problem, but they mean two different things. the Higgs mass corrections asks why the Higgs mass does not shoot up to the Planck Scale when there are quantum corrections, while the other asks about the weakness of gravity. Both problems ask why the Planck Scale is so large (Planck Scale being very large implies that Gravity is very weak). Extra Dimensions solve 'both' problems since the fundamental scale is actually quite smaller, meaning that Gravity is actually a lot stronger. Because the fundamental scale is a lot smaller, then the cutoff is a lot smaller, producing quantum corrections that are reasonable, and dont let the Higgs mass shoot up (I think this is what you meant). Supersymmetry on the other hand treats the problem pertaining to the Higgs mass, and does not actually explain why Gravity is weak. However, unlike extra dimensional models, Supersymmetry actually explains gravity!! If you hold Supersymmetry locally, (well the Super-poincare group, which does include the poincare group), then you get a spin 2 tensor field which couples to energy, also known as the graviton -- Drgnrave (talk) 05:44, 9 September 2008 (UTC)

If I'm understanding right, a Higgs mass near the Planck scale would imply that the weak force was much weaker. Fermi's constant $G_{F}$ is proportional to $1/m_{W}^{2}$ where $m_{W}$ is the mass of the W boson. If I remember right, $m_{W}$ is related to the Higgs mass, so if the Higgs mass were close to the Planck mass you'd expect the W mass to be very large, and thus $G_{F}$ would be almost as small as the gravitational constant G. So in explaining why the Higgs mass isn't close to the Planck mass, you explain why $G_{F}$ is so much larger than G. (But I don't think this explains why G is so small -- and thus the Planck mass so large -- in the first place. That's where other ideas like large extra dimensions come in.) -- Tim314 (talk) 07:37, 12 September 2008 (UTC)

Just rediscovered my old comment on this. I think I was a bit off base; for one thing, $M_{W}$ depends on the Higgs vev ($v$), not the Higgs mass ($M_{h}$): $M_{W}^{2}=g^{2}v^{2}/4$. However, there are radiative corrections to the electroweak parameters which vary logarithmically with $M_{h}/M_{W}$, so we know (from precision measurements of those parameters) that the Higgs mass can't be more than a few times the W mass. I found this reference helpful: http://arxiv.org/abs/hepph/9901280 — Preceding unsigned comment added by Tim314 (talk • contribs) 21:17, 5 June 2011 (UTC)

Citations Please

I actually do not know how to cite on Wikipedia, and I don't have time to learn (sorry if it is really easy to do, and I seem lazy because of that). But, for the new sections (SUSY corrections and ADD) I have listed the sources of the 'proofs', so in case anyone wants to clean up/ add to this article, can they please also do the citations:

--Drgnrave (talk) 23:28, 9 September 2008 (UTC) Drgnrave

Hierarchy problem and Cosmological constant problem

Can someone please help me spell out the common source of both Hierarchy problem and Cosmological constant problem? I seem to see a clear connection here.Mastertek (talk) 08:52, 5 December 2011 (UTC)

Is this the same problem, or a different problem with the same name? I'm having trouble understanding how gravity and other force's strength relate to a cosmological constant. --99.245.28.74 (talk) 23:06, 3 March 2016 (UTC)

Missing link for "cancellation"

I feel "cancellation" should have a link. Not sure it should be Cancellation property or that might even be misleading so I didn't dare put it (I'm not a physicist). Leaving the next step for somebody more in the know for the sake of correctness, cheers --217.81.173.136 (talk) 23:49, 21 March 2014 (UTC)

How is this a hierarchy problem?

From the lede:

In theoretical physics, the hierarchy problem is the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on, for example, why the weak force is 10^32 times stronger than gravity.

From the technical definition (note I reworded this, and my rewording might be wrong):

A hierarchy problem occurs when the fundamental value of some physical parameter, such as a coupling constant or a mass, in some Lagrangian is vastly different from its effective value, which is the value that gets measured in an experiment.

How is the discrepancy between the weak force and gravity a hierarchy problem in the sense given in the technical definition? Wouldn't that only be the case if the weak force and gravity exist inside the same theory and one is the renormalized-corrected version of the other?

My understanding is that they don't exist inside the same theory. There are only speculative proposals for such a theory. But the statement that the weak/gravity ratio is a hierarchy problem is only meaningful relative to such a proposed theory. So the name of this theory should be mentioned. "Within the framework of grand unified theory X, the large weak/gravity ratio becomes a hierarchy problem."

Furthermore, enough explanation should be given -- at least on an abstract, cocktail-party-conversation level -- so that we can see how the weak force constant is the effective value of the gravity constant, or vice versa. (It's hilarious that I don't know which direction this might go, isn't it?) 178.38.171.5 (talk) 09:25, 20 April 2015 (UTC)

On top of this, I found these words under little hierarchy problem: According to quantum field theory, the mass of the Higgs boson must be rather light for the electroweak theory to work. However, the loop corrections to the mass are naturally much greater; this is known as the hierarchy problem.

This seems to give a definition of the hierarchy problem entirely within the sphere of electroweak theory.

There is also a paragraph about the hierarchy problem in the article on the Higgs boson. Here the mass of the Higgs boson is compared with both the Planck mass and the grand unification energy to illustrate how small it is (or must be?), and this is identified as the hierarchy problem. It also asserts that there is (or must be?) an inordinately large amount of cancellation in the QED calculation leading to its effective mass.

As a result of these paragraphs, it appears that the lede of the current article misses the point about the hierarchy problem. It seems to be mostly about the unexpectedly small size of the Higgs boson mass as it is (or must be?) within the Standard Model, compared to the size of the quantum corrections that go into the calculation. (I assume from context that the effective Higgs mass is linked to the effective Fermi constant.) The comparison with gravity seems to be another way of expressing the smallness, but according to the "technical definition", it is not the main point.

I'd correct it myself if I knew anything about the subject ;-).

178.38.171.5 (talk) 10:16, 20 April 2015 (UTC)

Unclear sentence about why we would (?) expect Fermi constant to be smaller (?)

Furthermore if the Standard Model is used to calculate the quantum corrections to Fermi's constant, it appears that Fermi's constant is surprisingly large and is expected to be closer to Newton's constant, unless there is a delicate cancellation between the bare value of Fermi's constant and the quantum corrections to it.

I can't tell what counterfactual leads to what, and therefore what is supposed to surprise me, partly because I don't know the factual background, which in any case is not reported in this sentence.

If the Standard Model is used to calculate the quantum corrections to Fermi's constant, what comes out? Please state this background result first, before expressing an assessment of it or surprise about it.

Furthermore if the Standard Model is used to calculate the quantum corrections to Fermi's constant, it appears that Fermi's constant is surprisingly large and is expected to be closer to Newton's constant...

Why it it expected to be closer to Newton's constant? The phrasing of the sentence suggests that this is due to a calculation using the Standard Model. But the description of a hierarchy problem suggests that such an expectation arises from fundamental intuitions about what is natural in a physical theory.

...it appears that Fermi's constant is surprisingly large and is expected to be closer to Newton's constant, unless there is a delicate cancellation between the bare value of Fermi's constant and the quantum corrections to it.

Wouldn't a delicate cancellation make the effective value of Fermi's constant much smaller, so there'd be a chance that it would be closer to Newton's constant? I'm lost concerning the dependencies of the counterfactuals. 178.38.171.5 (talk) 08:54, 20 April 2015 (UTC)

I'm starting to understand this better, but it is not really very well-said. How about:

Furthermore if the Standard Model is used to calculate the quantum corrections to Fermi's constant, the calculations are not conclusive, but they appear to make Fermi's constant surprisingly large, and indeed, closer to Newton's constant, unless there turns out to be a delicate cancellation between the bare value of Fermi's constant and the quantum corrections to it. On the other hand, there needs to be such a cancellation for some other aspects of the theory to work correctly.

Awkward, but perhaps more correct than what was there before?

It bothers me that Newton's constant is large here instead of small, but perhaps someone got it mixed up with the Planck mass?

178.38.171.5 (talk) 10:27, 20 April 2015 (UTC)

Hierarchy of what?

Apparently there's a problem in the hierarchy. If only we knew what hierarchy we were talking about in the first place... — Preceding unsigned comment added by 75.139.254.117 (talk) 20:47, 8 January 2017 (UTC)

In other words, a hierarchy problem is when we don't know why two things that seem similar are not the same size? Seems like a lot of jargon to convey this idea... Student298 (talk) 00:49, 1 March 2019 (UTC)

Monster group

The attempt to connect the hierarchy problem to the size of the Monster Group seems unconvincing. This section also doesn't cite any sources. Is this something any published papers discuss, or is this just the speculation of whoever wrote this section? John Baez (talk) 07:04, 31 December 2020 (UTC)

I agree. At the very least, the section does not hold encyclopedia quality. Since no one has defended or improved it, I will just go ahead and remove it right now. Presupposing innocence does not work on Wikipedia, especially for physics articles. The field seems to attract and harbor many eccentrics, arguably a great asset in the big scheme of things. Mad geniuses are a thing, and balancing on the edge is hard. Elias (talk) 10:09, 12 October 2021 (UTC)

Arxiv sources

Most of the sources here are papers published via Arxiv. Per WP:ARXIV, these likely aren't all valid. Should we add bsn, cn, etc after some of the sections for various hypothesis, or are these good cites? Big Money Threepwood (talk) 21:59, 21 January 2024 (UTC)