What is Dimensional Transmutation?

[cube137]

The May 2014 issue of Scientific American has the cover:
Supersymmetry and the Crisis in Physics
by Joseph Lykken and Maria Spiropulu with the prologue "For decades physicists have been working on a beautiful theory that has promised to lead to a deeper understanding of the quantum world. Now they stand at a crossroads: prove it right in the next year or confront an epochal paradigm shift"

Inside the article is written: "If supersymmetry is not a true description of the world, what
might take its place? Here are three different speculative answers. All of them imply profoundly new directions for thinking about basic physics and cosmology:"

They are enumated as:

1. Multiverse
2. Extra Dimensions
3. Dimensional Transmutation

The Extra Dimensions have been refuted already and Multiverse silly so we are left with one option which is Dimensional Transmutation.

In the Search option at physicsforums. The word "Dimensional Transmutation" has zero hit. The Scientific American article has the only layman reference to it in the whole world. Now with Supersymmetry almost refuted and other candidates. The concept of "Dimensional Transmutation" would become popular.

Quoting Sci-Am intro to Dimensional Transmutation:

"Dimensional transmutation: Instead of invoking supersymmetry
to suppress virtual particle effects, a new idea is to embrace
such effects to explain where mass comes from. Consider for a
moment the proton. The proton is not an elementary particle. It is
made up of an assembly of three quarks, which have a minuscule
mass, and gluons, which have no mass at all. The proton is much
heavier than the sum total of the quarks and gluons inside of it.
Where does this mass come from? It comes from the energy fields
generated by the “strong” force that holds the proton together.
Our understanding of these fields allows us to accurately predict
the proton’s mass based on just ordinary numbers such as pi.
It’s an odd situation in particle physics. Usually we can compute
masses only by starting with other masses. For example, the
Standard Model gives us no way to predict the mass of the Higgs
boson—we have to measure it. This seems like an obvious mistake,
given how cleverly we can predict the mass of the proton.
Building on seminal work by William A. Bardeen, a physicist at
Fermilab, a few radical theorists are now suggesting that the
Higgs mass scale is generated through a similar process called
dimensional transmutation."

Physicforums members. Can you give in your own words the meaning of dimensional transmutation? I know it is related to renormalization, coupling constants, perturbations in QFT, etc. I know what they mean.. but the scientific american article falls short of saying how it is related to the Higgs bosons. I know the meaning of the Hierarchy Problem and Naturalness and how the Higgs mass should have been pulled up to the Planck Mass because of virtual particles contribution.. but how is Dimensional Transmutation related to this... is it saying the Standard Model particles didn't get the mass from the Higgs. If not.. what is the function of dimensional transmutation? Is it related to new physics in the Electroweak Sector.. and what kind of hidden physics would support the process of Dimensional Transmutation?

The following are the professional references about it.

http://lss.fnal.gov/archive/1995/conf/Conf-95-391-T.pdf
https://arxiv.org/pdf/1301.4224v2.pdf
http://indico.cern.ch/event/217732/contributions/1518949/attachments/350025/487960/lykken_MITP.pdf

Please dumb it down for us laymen because Dimensional Transmutation will become popular as serious alternative to Supersymmetry. Thank you!

 

[Simon Bridge]

More laymans discussions:
http://www.math.columbia.edu/~woit/wordpress/?p=6836
... old blog post but links off it can be useful.

Possible accessible:
http://cds.cern.ch/record/408940/files/9911421.pdf
... describes what is meant by "dimensional transmutation" very early on.
https://books.google.co.nz/books?id...ymmetry and dimensional transmutation&f=false
... look for "gauge hierarchy problem".

You have probably seen:
https://en.wikipedia.org/wiki/Dimensional_transmutation
... at the most basic level it is how a dimensionless parameter changes to a dimensionful one ... "dimension" here refers to the measurable qualities of an object or phenomenon ... like mass, length, or duration. In a nutshell, Nature is messy.

 

[cube137]

More laymans discussions:
http://www.math.columbia.edu/~woit/wordpress/?p=6836
... old blog post but links off it can be useful.

Possible accessible:
http://cds.cern.ch/record/408940/files/9911421.pdf
... describes what is meant by "dimensional transmutation" very early on.
https://books.google.co.nz/books?id=FXsGCwAAQBAJ&pg=PA1165&lpg=PA1165&dq=supersymmetry+and+dimensional+transmutation&source=bl&ots=PU4pEBtIZc&sig=lP0B_4ASbBszTxJZYbgMj1cn1LI&hl=en&sa=X&ved=0ahUKEwimlMGZ-cnOAhWDVZQKHQO4CIQQ6AEIRTAG#v=onepage&q=supersymmetry and dimensional transmutation&f=false
... look for "gauge hierarchy problem".

You have probably seen:
https://en.wikipedia.org/wiki/Dimensional_transmutation
... at the most basic level it is how a dimensionless parameter changes to a dimensionful one ... "dimension" here refers to the measurable qualities of an object or phenomenon ... like mass, length, or duration. In a nutshell, Nature is messy.

I've actually read them over and over (for a day already).. but couldn't seem to get the core mechanism that handles the Hierarchy Problem and Naturalness problem (after we say goodbye to Supersymmetry).
If Supersymmetry has the supersymmetric particles that the LHC was looking for.
In Dimensional Transmutation. What are the new particles or forces involved that the LHC was looking for? Or is it a new vacuum dynamics perhaps involving something akin to Inflaton or other extra vacuum stuff?

 

[MathematicalPhysicist]

Extra dimensions have been refuted, how exactly? perhaps you just need the energy of the big bang; if you ask me it's not falsifiable.
Also Multiverse isn't falsifiable hypothesis but not necessarily silly.

We just don't know.


 

[cube137]

Extra dimensions have been refuted, how exactly? perhaps you just need the energy of the big bang; if you ask me it's not falsifiable.
Also Multiverse isn't falsifiable hypothesis but not necessarily silly.

We just don't know.


Have you heard about KK particles? Here's Lisa Randall last 2 paragraphs of her book Warped Passages:

"All of the models that address the hierarchy problem have visible weak-scale consequences. The signatures of
the warped geometry that addresses the hierarchy problem are particularly amazing. If this theory is right, we
will detect KK particles and measure their properties from the clues they leave behind. If, instead, other extradimensional
models describe the universe, energy will disappear into extra dimensions and we'll ultimately
detect those dimensions through the resulting unbalanced energy accounting.

We certainly don't yet know all the answers. But the universe is about to be pried open. Astrophysical
observations will explore the cosmos earlier, further away, and in more detail than ever before. Discoveries at
the LHC will tell us about the nature of matter at distances smaller than any physical process ever observed. At
high energies, truths about the universe should start to explode.

Secrets of the cosmos will begin to unravel. I, for one, can't wait."

 

[cube137]

to bump up this thread... I saw the following definition in net search about "dimensional transmutation":

"It's just the process of going from dimensionless couplings in a classical field theory to couplings that have dimensional dependence in a quantum field theory after renormalisation. Therefore you have the inevitable introduction of an energy(/mass/distance/...) scale."

1. What is the meaning of energy/mass/distance scale?
2. How does it cancel the Planck mass virtual particle loop that can pull the Higgs mass to Planck mass?
3. In the Hierarchy problem.. how does this really replace the supersymmetric particles? How is Dimensional Transmutation connected to it?

With LHC exclusion of Extra Dimensions reaching nearly 3 TeV already. It's already very cornered. For decades.. we have many pop sci books and articles about Supersymmetry and how it can solve the Hierarchy problem. If it's gone and we will replace it with Dimensional Transmutation. What's the best way or best description to describe it to the public?

I'm very interested because I'd like to share it to public. So how will I describe it? Please use your own words if you were to describe the concept to laymen. Thanks.

 

[David Neves]

Extra dimensions have certainly not been refuted or even "cornered" in any way. String theory predicts that the extra dimensions would be compactified close to the Planck scale, well out of reach of the LHC. Let's say you are walking home, and realize you lost your keys. The first place you check is under the lamp post, even though there is no particular reason to think that they are more likely to be there, simply because that is where they would be most easy to spot. If they are not there, does that mean that you have proven that the keys do not exist?

The multiverse is required for the anthropic principle which is required to explain the fact that biological life would not be possible if many fundamental parameters did not have the precise value they have. If the electromagnetic force were slightly weaker, life would not be possible. If the electromagnetic force were slightly stronger, life would not be possible. If gravity were weaker, life would not be possible. If gravity were stronger, life would not be possible. There are many other examples. How would you explain this without the anthropic principle? I am not asking, "How else would you explain the values of the fundamental constants?" That is not what I'm asking. I'm asking a different question. I am asking, "How else do you explain the specific fact that all of the fundamental constants have the specific values that they would need to have in order for biological life to exist, and if any were slightly different, life would not exist?" The likelihood of that happening by random chance is stupendously remote. The only answer to this specific question is the anthropic principle, which requires the multiverse.

There is a specific argument in favor of the anthropic principle that goes beyond the mere fact that the values of various parameters have the values they would need to have in order for life to exist. In the second and third generation of fermions, the quark with -1/3 charge has less mass than the quark with 2/3 charge. The first generation is unusual in that the the quark with -1/3 charge has greater mass than the quark with 2/3 charge. In physics, you normally expect a pattern or symmetry to be true throughout, and if it doesn't, there must be a reason. What would happen if the pattern did hold throughout, and the first generation had the same pattern of quark masses as the second and third generation, where the quark with -1/3 charge had less mass than the quark with 2/3 charge? If that were the case, the neutron would be stable outside the nucleus, and the proton would not, instead of the other way around, as in the real world. All of the protons in the early universe would have quickly decayed into neutrons, and there would be no atoms in the Universe. This would be same as dozens of other examples of the anthropic principle if it wasn't for the fact that the second and third generations indicate what the pattern of quark masses is "supposed to be", or more likely to be, or probably are in the vast majority of universes. This is very strong evidence for the multiverse.

 

[cube137]

Extra dimensions have certainly not been refuted or even "cornered" in any way. String theory predicts that the extra dimensions would be compactified close to the Planck scale, well out of reach of the LHC. Let's say you are walking home, and realize you lost your keys. The first place you check is under the lamp post, even though there is no particular reason to think that they are more likely to be there, simply because that is where they would be most easy to spot. If they are not there, does that mean that you have proven that the keys do not exist?

The multiverse is required for the anthropic principle which is required to explain the fact that biological life would not be possible if many fundamental parameters did not have the precise value they have. If the electromagnetic force were slightly weaker, life would not be possible. If the electromagnetic force were slightly stronger, life would not be possible. If gravity were weaker, life would not be possible. If gravity were stronger, life would not be possible. There are many other examples. How would you explain this without the anthropic principle? I am not asking, "How else would you explain the values of the fundamental constants?" That is not what I'm asking. I'm asking a different question. I am asking, "How else do you explain the specific fact that all of the fundamental constants have the specific values that they would need to have in order for biological life to exist, and if any were slightly different, life would not exist?" The likelihood of that happening by random chance is stupendously remote. The only answer to this specific question is the anthropic principle, which requires the multiverse.

There is a specific argument in favor of the anthropic principle that goes beyond the mere fact that the values of various parameters have the values they would need to have in order for life to exist. In the second and third generation of fermions, the quark with -1/3 charge has less mass than the quark with 2/3 charge. The first generation is unusual in that the the quark with -1/3 charge has greater mass than the quark with 2/3 charge. In physics, you normally expect a pattern or symmetry to be true throughout, and if it doesn't, there must be a reason. What would happen if the pattern did hold throughout, and the first generation had the same pattern of quark masses as the second and third generation, where the quark with -1/3 charge had less mass than the quark with 2/3 charge? If that were the case, the neutron would be stable outside the nucleus, and the proton would not, instead of the other way around, as in the real world. All of the protons in the early universe would have quickly decayed into neutrons, and there would be no atoms in the Universe. This would be same as dozens of other examples of the anthropic principle if it wasn't for the fact that the second and third generations indicate what the pattern of quark masses is "supposed to be", or more likely to be, or probably are in the vast majority of universes. This is very strong evidence for the multiverse.

In the constants of nature of the Standard Model. I heard the higgs were involved or related to it in many ways. Could the Higgs be what decide whether the electrons or quarks have certain mass or is it the electrons or quarks that set the values of the mass? What are the few contants where the Higgs were not involved, maybe fine structure constant or others. Does anyone have good articles about this?

About dimensional transmutation. I think I'll review concepts in QCD because the idea is originally gotten from it. My question is just how it is reflected in QFTs as general.

 

[cube137]

I tried to spend a couple of hours more to understand Dimensional Transmutation. Here are peer references for those also interested.

https://arxiv.org/pdf/1606.03738.pdf
http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-16518.pdf
http://www.lepp.cornell.edu/rsrc/Home/Research/GradTheses/Reece_Matthew.pdf

What I seemed to understand was that it tried to make some kind of Technicolor to the Higgs to avoid the quadratic loop and Planck mass Higgs.. but the LHC seemed to have ruled out Technicolor? But I know dimensional transmutation is more than it.
I really seriously suggest someone here at Physicsforums to write and contribute Scientific American article about it. Let it become cover page at SciAm with title like "LHC Nightmare Scenerio and Dimensional Transmutation". I'm sure it will encourage interests in many educational community. You can earn a few hundred dollars for the article and share the basic of it to scientific advanced laymen (which consist of the readership of Sci-Am versus Discover Magazine). Who will do it here?

 

[nikkkom]

From what I read, the meaning of term "dimensional transmutation" is not hard to grasp. It describes how in some QFTs dimensionless constants of coupling strength give rise to dimensionful constants.

In QCD, coupling strength value (current experimental value at mZ energy scale) is 1.221 - a dimensionless quantity.
Then QCD math derives from it that color confinement occurs at 220 MeV energy scale. This is a dimensionful quantity.
A dimensionless quantity "transmutes" into a dimensionful one.

 

[cube137]

From what I read, the meaning of term "dimensional transmutation" is not hard to grasp. It describes how in some QFTs dimensionless constants of coupling strength give rise to dimensionful constants.

In QCD, coupling strength value (current experimental value at mZ energy scale) is 1.221 - a dimensionless quantity.
Then QCD math derives from it that color confinement occurs at 220 MeV energy scale. This is a dimensionful quantity.
A dimensionless quantity "transmutes" into a dimensionful one.

Prior to this. I always heard it explained that more than 90% of mass of proton came from kinetic energy of the constituent quarks. Do you
still call the description correct that it's the kinetic energy of the constituent quarks or is this wrong because the real explanation is "the gluon coupling, which becomes the hadronic mass scale after dimensional transmutation"?

http://particleadventure.org/where-does-most-of-the-mass-of-the-universe-come-from.html
"It turns out that the mass of a proton is mostly due to the kinetic energy of its constituent quarks. As you'll remember by now, mass and energy are related by the equation E=mc2."

 

[David Neves]

It's not the kinetic energy. It's the binding energy.

http://physics.bu.edu/~duffy/sc546_notes10/mass_defect.html

 

[cube137]

Back to the Hierarchy Problem of the Higgs where they need Supersymmetry to avoid the Higgs from reaching Planck mass. With Supersymmetry almost gone. They need radical thing and propose dimensional transmutation.. for us the keyword (or punchline)
is binding energies.

So the Higgs mass is binding energies of what?? At the end of this technical paper http://indico.cern.ch/event/217732/contributions/1518949/attachments/350025/487960/lykken_MITP.pdf
It is mentioned in the summary part that "All masses come from dimensional transmutation
and whatever is going on in the dark sector". In other words, it's correct to mention the Higgs mass is binding energies of what is
going on in the dark sector? (does dark means dark matter sector or just the unknown sector between Higgs mass or GUT/Planck mass).

The Hierarchy Problem is the most important purpose of the LHC. We are now like in the days when the MMX experiment produced
null results, then came Relativity and Quantum Mechanics.. the new few years or decades will see another stunning revolution in physics.

 

[cube137]

From what I read, the meaning of term "dimensional transmutation" is not hard to grasp. It describes how in some QFTs dimensionless constants of coupling strength give rise to dimensionful constants.

In QCD, coupling strength value (current experimental value at mZ energy scale) is 1.221 - a dimensionless quantity.
Then QCD math derives from it that color confinement occurs at 220 MeV energy scale. This is a dimensionful quantity.
A dimensionless quantity "transmutes" into a dimensionful one.

In the Bardeen paper in first message (note William Bardeen is son of John Bardeen, Nobel Prize inventor of the Transistor), it was mentioned "In perturbation theory, the scale symmetry would protect the Higgs mass from quadratic divergences and the convensional statement of the fine tuning problem. Dimensional transmutation would be required to generate quadratic divergences from the logarithm divergences of the perturbative expansion"

What is the context of the Dimensional transmutation used above? Why is it required to generate quadraic divergences? I thought it was supposed to suppress it in the electroweak sector.