5 Higgs-like bosons -- natural supersymmetry required?

[fanieh]

The example given is a horrible one, because it poses the question as a question of probability. But, when it comes to the fundamental constants of nature, probability is not an appropriate way to frame the question.

"The Higgs mechanism gives mass to some fundamental particles, but not others. It interacts strongly with W and Z bosons, making them massive. But it does not interact with particles of light, leaving them massless."

This has a pretty obvious explanation. Fundamental particles that interact via the weak force have mass; fundamental particles that do not interact via the weak force do not. The Higgs field is deeply and fundamentally related to the weak force in electroweak unification, so this is no surprise.

Likewise, the question of whether there is one Higgs or more is an empirical one.

But, the fact that all of the constants of the SM interact in such a way that the Higgs mass arising from those interactions is exactly 125.___ GeV is a "so what?", not a problem. Because, there aren't a host of possible probable values for all of the SM constants only one set of which interacts just so. There is just one possible value for each of these constants and this happens to work.

I think that there are more useful ways to think about how the Higgs mass gets the value that it does than the conventional formulation in which it seems mysterious. For example, the sum of the square of the fundamental boson masses is almost exactly half of the square of the Higgs vev (which in turn is basically a function of the weak force coupling constant). Likewise, the sum of the square of the fundamental fermion masses is almost exactly the square of the Higgs vev, implying a balance between the fermions and the bosons.

In that frame of analysis, the Higgs mass has the mass it does in order to make the boson side of the contributions to the Higgs vev add up, and the top quark has the mass it does in order to make the fermion side of the contributions to the Higgs vev add up, and the Higgs vev has the value it does because of the magnitude of the weak force coupling constant. Not terribly mysterious.

More importantly, whether this particular example has a true and correct physical basis or not, the point is that if you are looking at the world from a perspective that makes the world look "unnatural", or "fine tuned" or like a "problem" you are probably looking at the universe from the wrong perspective and looking at the universe from another perspective will probably make it look like it makes sense (although there are absolute no guarantees of this. It's right in the user's manual. Life is not required to be fair or easy to understand, and neither is Nature. What, you mean they threw out your user's manual when you were born? Tough luck for you.)

Similarly, there is a heuristic argument for why the CP violation parameter theta of the strong force should be exactly zero, rather than of on the order of one, as "strong CP problem" advocates suggest. This is because CP violation calls for a broken time reversal symmetry. And, if you take the perspective of a massless gluon or massless photon, the carrier boson does not experience time, so it shouldn't know the difference between going forward in time and going backward in time. In contrast, the W boson which is massive, does experience time, so it knows the difference between going forward in time and going backward in time, and it therefore can implement a CP violation.

Again, the point is not that this heuristic answer really is the true and correct solution to the strong CP problem. Maybe it is, maybe it isn't. But, if you are looking at the problem from a perspective that makes the laws of nature look like a problem, or unnatural or finely tuned, then you are probably looking at the problem from the wrong perspective anyway, because the actual value of a physical constant is incapable of being a problem or being unnatural or being fine tuned. It simply is.

I think you simply misunderstand it. The Hierarchy Problem of the Higgs is not why it has the value it does. But more specifically.. why isn't it affected by the quantum corrections and and became Planck mass. Or in terms of this good intro site: http://www.quantumdiaries.org/2012/...why-the-higgs-has-a-snowballs-chance-in-hell/ "we expect its mass to be around 125 GeV (not too far from W and Z masses), but ambient quantum energy wants to make its mass much larger through interactions with virtual particles.".

Please read the site carefully.. You are a business lawyer so it would take more effort to understand the complexities of physics which is based on math.. not legal laws and linguistic based materials. Or just answer the direct question why the higgs is not affected by quantum corrections. Google the words "quadratically divergent contributions" and read it carefully then answer my question.

 

[ohwilleke]

I was a math major a class or two short of a physics minor in college (if I'd graduated in four years instead of three I could have done it) and all of the math courses that I took in college were upper division courses because I finished three semesters of calculus, linear algebra, discrete math, and abstract algebra before I started college, I understand the math perfectly well. I also read a dozen or more pre-prints in physics a week and have for at least six or seven years. Certainly, its been a while since I've solved a challenging differential equation or calculated a tensor product or written actual code to optimize traffic flow through a set of stoplights in a city. Law pays the bills, physics is a hobby that keeps my mind sharp. But, I understand perfectly well what the hierarchy problem is (hell, I wrote an explanation of it that was incorporated in a post on the subject at a successor blog to the one you link, Quantum Diaries Survivor). Matt Strassler sums it up this way: "Why is it at a value that is non-zero and tiny, a value that seems, at least naively, so unnatural?" https://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-hierarchy-problem/

(I'll also note his somewhat nit picky caveat and beg forgiveness for any sloppy wording: "By the way, you will often read the hierarchy problem stated as a problem with the Higgs particle mass. This is incorrect. The problem is with how big the non-zero Higgs field is. (For experts — quantum mechanics corrects not the Higgs particle mass but the Higgs mass-squared parameter, changing the Higgs field potential energy and thus the field’s value, making it zero or immense. That’s a disaster because the W and Z masses are known. The Higgs mass is unknown, and therefore it could be very large — if the W and Z masses were very large too. So it is the W and Z masses — and the size of the non-zero Higgs field — that are the problem, both logically and scientifically.")

He notes: "Others have argued that there is nothing to explain, because of a selection effect: the universe is far larger and far more diverse than the part that we can see, and we live in an apparently unnatural part of the universe mainly because the rest of it is uninhabitable — much the way that although rocky planets are rare in the universe, we live on one because it’s the only place we could have evolved and survived."

I think he is far too timid in saying that. There is nothing to explain, not because of a selection effect, but because there is just one universe and that is the way that it is.

Naturalness is an academic disease, not a legitimate part of the scientific method. It rests on the idea that Platonic concepts of what the laws of nature could be are really things that are up for debate and are chosen by lot. But, this simply isn't a sound way to think about the ideas explored with Naturalness which at best is a concept with a poor track record in its only marginally legitimate role as a hypothesis generator.

As is commonly understood, the issue isn't that quantum corrections can't provide the mass that it does (obviously that isn't the case). It is in essence, why the huge counterterms managed to cancel out to a value many, many orders of magnitude smaller. But, it is simply a category error to think of the problem in terms of probabilities. There is just one outcome that actually happens 100% of the time. And, as long as each input is exactly right (and those inputs never change), you get the result that we see. It is fundamentally an analytical issue not a probabilistic one. The hierarchy problem is a case where we have a formula (perhaps not the most elegant or illuminating one of those possible) to give us the output and we are too thick to see why it is that all of the inputs work out in the manner that they do. If the 125 GeV mass were impossible to achieve given the terms that go into it, that would be another thing entirely. But, you can no more say that a physical constant value which is possible is "improbable" than you can say that pi should be a rational number because it is derived from dividing circumference by diameter, rather than transcendental as it is in fact.

Many aspects of quantum physics are inherently stochastic. Certainly the outputs it gives you when you ask the theory a question are of that character. But, the physical constants, both directly calculated and experimentally measured with no even hypothetical derivation, are not. Every single charged pion in the universe has a rest mass of 139.571 MeV/c^2 (subject to some conditions related to renormalization which are deterministic as well).

The more I've thought about the issue over the years, the more I've ben convinced that thinking about it in terms of probabilities like "a snowballs chance in hell" is a misleading and inappropriate way to think about the issue involving a 100% probability event.

I'm certainly not alone among those who have questioned the appropriateness of problems like this among physicists. Sabine Hossenfelder has talked about it. Here's an excerpt from one of her most recent and thoughtful rants on the subject: http://backreaction.blogspot.com/2016/08/the-lhc-nightmare-scenario-has-come-true.html

During my professional career, all I have seen is failure. A failure of particle physicists to uncover a more powerful mathematical framework to improve upon the theories we already have. Yes, failure is part of science – it’s frustrating, but not worrisome. What worries me much more is our failure to learn from failure. Rather than trying something new, we’ve been trying the same thing over and over again, expecting different results.

When I look at the data what I see is that our reliance on gauge-symmetry and the attempt at unification, the use of naturalness as guidance, and the trust in beauty and simplicity aren’t working. The cosmological constant isn’t natural. The Higgs mass isn’t natural. The standard model isn’t pretty, and the concordance model isn’t simple. Grand unification failed. It failed again. And yet we haven’t drawn any consequences from this: Particle physicists are still playing today by the same rules as in 1973.

For the last ten years you’ve been told that the LHC must see some new physics besides the Higgs because otherwise nature isn’t “natural” – a technical term invented to describe the degree of numerical coincidence of a theory. I’ve been laughed at when I explained that I don’t buy into naturalness because it’s a philosophical criterion, not a scientific one. But on that matter I got the last laugh: Nature, it turns out, doesn’t like to be told what’s presumably natural.

The idea of naturalness that has been preached for so long is plainly not compatible with the LHC data, regardless of what else will be found in the data yet to come. And now that naturalness is in the way of moving predictions for so-far undiscovered particles – yet again! – to higher energies, particle physicists, opportunistic as always, are suddenly more than willing to discard of naturalness to justify the next larger collider.

Woit has talked about it. For example here: http://www.math.columbia.edu/~woit/wordpress/?cpage=1&p=8708

Jester a.k.a. Adam Falkowski has talked about it. (Not exactly on point but acknowledging the concept's declining relevance without giving up on it at http://resonaances.blogspot.com/2015/05/naturalness-last-bunker.html)

Gross is credited with acknowledging the failure of the naturalness paradigm, but supports SUSY anyway. http://www.math.columbia.edu/~woit/wordpress/?p=6737

Of course, Lubos Motl is a four square supporter of the ideas of naturalness and fine tuning and has articulated his view on this subject repeatedly.

If I wracked my brain for a few hours, I could probably identify three or four more who don't blog who have looked back on the last forty years and come to the same conclusion in the last couple of years as the "Nightmare Scenario" at the LHC has come to pass.

 

[kodama]

ohwilleke

so if you could earn a phd in a field of physics, and get a full position at a prestigious university one that pays the bills, what would your phd thesis and research interests be and why? i.e particle physics, strings, loops, QG etc? personally i wouldn't get one in low energy susy particle physics rn.

 

[fanieh]

I was a math major a class or two short of a physics minor in college (if I'd graduated in four years instead of three I could have done it) and all of the math courses that I took in college were upper division courses because I finished three semesters of calculus, linear algebra, discrete math, and abstract algebra before I started college, I understand the math perfectly well. I also read a dozen or more pre-prints in physics a week and have for at least six or seven years. Certainly, its been a while since I've solved a challenging differential equation or calculated a tensor product or written actual code to optimize traffic flow through a set of stoplights in a city. Law pays the bills, physics is a hobby that keeps my mind sharp. But, I understand perfectly well what the hierarchy problem is (hell, I wrote an explanation of it that was incorporated in a post on the subject at a successor blog to the one you link, Quantum Diaries Survivor). Matt Strassler sums it up this way: "Why is it at a value that is non-zero and tiny, a value that seems, at least naively, so unnatural?" https://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-hierarchy-problem/

(I'll also note his somewhat nit picky caveat and beg forgiveness for any sloppy wording: "By the way, you will often read the hierarchy problem stated as a problem with the Higgs particle mass. This is incorrect. The problem is with how big the non-zero Higgs field is. (For experts — quantum mechanics corrects not the Higgs particle mass but the Higgs mass-squared parameter, changing the Higgs field potential energy and thus the field’s value, making it zero or immense. That’s a disaster because the W and Z masses are known. The Higgs mass is unknown, and therefore it could be very large — if the W and Z masses were very large too. So it is the W and Z masses — and the size of the non-zero Higgs field — that are the problem, both logically and scientifically.")

He notes: "Others have argued that there is nothing to explain, because of a selection effect: the universe is far larger and far more diverse than the part that we can see, and we live in an apparently unnatural part of the universe mainly because the rest of it is uninhabitable — much the way that although rocky planets are rare in the universe, we live on one because it’s the only place we could have evolved and survived."

I think he is far too timid in saying that. There is nothing to explain, not because of a selection effect, but because there is just one universe and that is the way that it is.

Naturalness is an academic disease, not a legitimate part of the scientific method. It rests on the idea that Platonic concepts of what the laws of nature could be are really things that are up for debate and are chosen by lot. But, this simply isn't a sound way to think about the ideas explored with Naturalness which at best is a concept with a poor track record in its only marginally legitimate role as a hypothesis generator.

As is commonly understood, the issue isn't that quantum corrections can't provide the mass that it does (obviously that isn't the case). It is in essence, why the huge counterterms managed to cancel out to a value many, many orders of magnitude smaller. But, it is simply a category error to think of the problem in terms of probabilities. There is just one outcome that actually happens 100% of the time. And, as long as each input is exactly right (and those inputs never change), you get the result that we see. It is fundamentally an analytical issue not a probabilistic one. The hierarchy problem is a case where we have a formula (perhaps not the most elegant or illuminating one of those possible) to give us the output and we are too thick to see why it is that all of the inputs work out in the manner that they do. If the 125 GeV mass were impossible to achieve given the terms that go into it, that would be another thing entirely. But, you can no more say that a physical constant value which is possible is "improbable" than you can say that pi should be a rational number because it is derived from dividing circumference by diameter, rather than transcendental as it is in fact.

Thanks for your great elaborations. When you mentioned above that "It is in essence, why the huge counterterms managed to cancel out to a value many, many orders of magnitude smaller.". So you believe that there is really huge counterterms that managed to cancel out to a value many, many orders of magnitude smaller? What if tomorrow all those Susy particles suddenly appear or Lisa Randall Extra Dimensions pop out in the LHC. Then there is no longer any huge counterterms? Or in case I misunderstood you. Were you saying those counterterms don't exist at all? Then what canceled the huge quantum contributions?

 

[ohwilleke]

ohwilleke

so if you could earn a phd in a field of physics, and get a full position at a prestigious university one that pays the bills, what would your phd thesis and research interests be and why? i.e particle physics, strings, loops, QG etc? personally i wouldn't get one in low energy susy particle physics rn.

Probably quantum gravity and QCD with a focus within QCD on (1) scalar and axial vector mesons, (2) determining the values of fundamental constants, and (3) the mathematical similarities between graviton quantum gravity and QCD due to both involving self-interacting carrier bosons.

 

[ohwilleke]

Too many questions for one reply close to bedtime. I'll take a stab at the easiest one. Don't have the focus to write sufficiently precisely about quantum corrections to the Higgs vev while half awake without a grave risk of flubbing it.

What if tomorrow all those Susy particles suddenly appear or Lisa Randall Extra Dimensions pop out in the LHC.

I would be stunned/flabbergasted and highly skeptical.

Why?

Even if SUSY particles or Extra Dimensions do exist, they almost certainly can't be "just around the corner" such that they could appear clearly at the LHC in the near future. Those phenomena would pretty much have to start giving rise to experimental hints of their existence orders of magnitude before they were observed directly because there are multiple observables in HEP that are sensitive to physics at much higher energy scales.

While the direct exclusions on phenomena like these are in the low single digit TeV zone right now at the LHC, the indirect probes of higher energy scales pretty strongly disfavor this kind of phenomena much below 10 TeV. At best, you might can an inconclusive glimpse of it towards the end of Run 2.

What you would expect instead is a mosaic of correlated deviations from SM predictions in multiple channels. For example, if SUSY exists, we should be able to experimentally observe material differences between the SM beta functions and the running of the SM coupling constants that are observed long before we can actually discover a new SUSY particle. Anomalous magnetic moments are also a pretty powerful indirect probe of high energy scale physics.

Still, if that did happen, obviously I'd have to recalibrate my expectations just as physicists did decades ago when the muon suddenly appeared unheralded and unexpected, when SR and GR fundamentally altered our understandings of time, matter and energy, when the singularities predicted by GR turned out to be physically meaningful (even if they turn out not to be true classical singularities) instead of merely mathematical pathologies of the theory, when scientists discovered that quantum physics is inherently stochastic. It would dramatically change the entire field.

Probably the best prospects out there right now for new physics are the multiple experimental hints of lepton flavor non-universality in interactions involving charged leptons. But, that particular example is tainted by the fact that other experiments in which any reasonable kind of lepton flavor non-universality that really exists should also manifest place extremely tight bounds on that possibility. It is extremely hard to come up with a sensible way to distinguish experiments that hint at non-universality from those that rule it out strictly in any plausible way.

If the LHC or some other experiments do see BSM physics, it is more likely to be something that hasn't been analyzed to death by theorists because our currently event cuts, experimental designs, etc. are specifically calibrated to be as sensitive to those theories as possible and have, so far, come up with nothing. Some of the phenomena I think we might be more likely to stumble into more or less unexpectedly would include:

1. A new boson that mediates neutrino oscillation.
2. Definitive proof that space-time is not perfectly smooth and continuous and instead has quanta scale non-localities.
3. A gravity modification arising from an effort to develop a quantum gravity theory that explains most or all dark matter phenomena and at least some dark energy/cosmological constant phenomena. Put another way, I expect the biggest deviations from GR in a quantum gravity theory to be in the weak fields and not in the strong fields.
4. Extremely rare and short lived top quark hadrons.
5. Inconclusive early indications of a composite nature for one or more "fundamental" particles of the SM that overcomes previous "no go" evidence with a novel loophole of some kind.
6. A new unpredicted phase or state of matter analogous to Bose-Einstein condensate or quark-gluon plasma that emerges in some characteristic boundary conditions with surprising new properties.

 

[ohwilleke]

Thanks for your great elaborations. When you mentioned above that "It is in essence, why the huge counterterms managed to cancel out to a value many, many orders of magnitude smaller.". So you believe that there is really huge counterterms that managed to cancel out to a value many, many orders of magnitude smaller? What if tomorrow all those Susy particles suddenly appear or Lisa Randall Extra Dimensions pop out in the LHC. Then there is no longer any huge counterterms? Or in case I misunderstood you. Were you saying those counterterms don't exist at all? Then what canceled the huge quantum contributions?

Shorter answer: SUSY is a really crude and artificial way to tame quantum corrections. Its like a de eux machina resolution of a conflict in a play. I suspect that what really happens is more subtle than a crude one to one correspondence of SM particles and their superpartners. The insights that SUSY theories have provided to date (not a lot, but some) have more to do with the fact that they simplify the math in ways that still capture the essence of the actual high energy processes, than with their necessity or reality.

 

[fanieh]

Too many questions for one reply close to bedtime. I'll take a stab at the easiest one. Don't have the focus to write sufficiently precisely about quantum corrections to the Higgs vev while half awake without a grave risk of flubbing it.
I would be stunned/flabbergasted and highly skeptical.

Why?

Even if SUSY particles or Extra Dimensions do exist, they almost certainly can't be "just around the corner" such that they could appear clearly at the LHC in the near future. Those phenomena would pretty much have to start giving rise to experimental hints of their existence orders of magnitude before they were observed directly because there are multiple observables in HEP that are sensitive to physics at much higher energy scales.

While the direct exclusions on phenomena like these are in the low single digit TeV zone right now at the LHC, the indirect probes of higher energy scales pretty strongly disfavor this kind of phenomena much below 10 TeV. At best, you might can an inconclusive glimpse of it towards the end of Run 2.

What you would expect instead is a mosaic of correlated deviations from SM predictions in multiple channels. For example, if SUSY exists, we should be able to experimentally observe material differences between the SM beta functions and the running of the SM coupling constants that are observed long before we can actually discover a new SUSY particle. Anomalous magnetic moments are also a pretty powerful indirect probe of high energy scale physics.

Still, if that did happen, obviously I'd have to recalibrate my expectations just as physicists did decades ago when the muon suddenly appeared unheralded and unexpected, when SR and GR fundamentally altered our understandings of time, matter and energy, when the singularities predicted by GR turned out to be physically meaningful (even if they turn out not to be true classical singularities) instead of merely mathematical pathologies of the theory, when scientists discovered that quantum physics is inherently stochastic. It would dramatically change the entire field.

Probably the best prospects out there right now for new physics are the multiple experimental hints of lepton flavor non-universality in interactions involving charged leptons. But, that particular example is tainted by the fact that other experiments in which any reasonable kind of lepton flavor non-universality that really exists should also manifest place extremely tight bounds on that possibility. It is extremely hard to come up with a sensible way to distinguish experiments that hint at non-universality from those that rule it out strictly in any plausible way.

If the LHC or some other experiments do see BSM physics, it is more likely to be something that hasn't been analyzed to death by theorists because our currently event cuts, experimental designs, etc. are specifically calibrated to be as sensitive to those theories as possible and have, so far, come up with nothing. Some of the phenomena I think we might be more likely to stumble into more or less unexpectedly would include:

1. A new boson that mediates neutrino oscillation.
2. Definitive proof that space-time is not perfectly smooth and continuous and instead has quanta scale non-localities.
3. A gravity modification arising from an effort to develop a quantum gravity theory that explains most or all dark matter phenomena and at least some dark energy/cosmological constant phenomena. Put another way, I expect the biggest deviations from GR in a quantum gravity theory to be in the weak fields and not in the strong fields.
4. Extremely rare and short lived top quark hadrons.
5. Inconclusive early indications of a composite nature for one or more "fundamental" particles of the SM that overcomes previous "no go" evidence with a novel loophole of some kind.
6. A new unpredicted phase or state of matter analogous to Bose-Einstein condensate or quark-gluon plasma that emerges in some characteristic boundary conditions with surprising new properties.

Thanks a lot for your information above. We'd all be anxiously waiting for you in your sleep for the message about how exactly or approximately huge counterterms managed to cancel out to a value many, many orders of magnitude smaller to produce the Higgs mass.

 

[kodama]

Probably quantum gravity and QCD with a focus within QCD on (1) scalar and axial vector mesons, (2) determining the values of fundamental constants, and (3) the mathematical similarities between graviton quantum gravity and QCD due to both involving self-interacting carrier bosons.

what's your fav approach to QG ? strings loops asymsafe graviton or spacetime approaches?

 

[kodama]

Shorter answer: SUSY is a really crude and artificial way to tame quantum corrections. Its like a de eux machina resolution of a conflict in a play. I suspect that what really happens is more subtle than a crude one to one correspondence of SM particles and their superpartners. The insights that SUSY theories have provided to date (not a lot, but some) have more to do with the fact that they simplify the math in ways that still capture the essence of the actual high energy processes, than with their necessity or reality.

how do you feel about string theory, which 100% depend on susy

 

[ohwilleke]

what's your fav approach to QG ? strings loops asymsafe graviton or spacetime approaches?

Agnostic.

String theory provides some interesting mathematical insights but is a poor way to model what we see in Nature. Like SUSY it is probably not an accurate description of the real world.

 

[kodama]

Agnostic.

String theory provides some interesting mathematical insights but is a poor way to model what we see in Nature. Like SUSY it is probably not an accurate description of the real world.

which QG approach is most similar to your pet fav QCD = gravity? there is some overlap between spinfoam/lqg and lattice gauge theory used in QCD

 

[fanieh]

Let's take analogy of a skyscraper building constructions.
If the steel and concrete and other materials just grow from the ground up.. then we can say it is Natural because steel and concrete came from the seed.
But if steel and concrete are build by hands and by people. Then it is not natural or unnatural.
I think ohwilleke treats physics as only understanding the finished product and some relations (like the finished skyscraper and relations between elevators)
Then what occurred before like how the construction crew assembled the building is outside physics.
If it is outside physics. Then what should it be called "Hyperphysics" or "Off limit Beyond Standard Model" or simply philosophy?
But can we call the construction stages of the building as philosophy at all?

 

[lpetrich]

I wish to note some details.

The MSSM predicts two even-parity neutral Higgs particles, h and H0, one odd-parity Higgs particle, A, and two charged Higgs particles, H+ and H- (or two variants of one particle). The h and H0 have a 2*2 mass matrix, as one might expect.

If one of the MSSM parameters is high enough, then the H0, A, and H+- have masses close to each other, masses much greater than the h mass.

The MSSM has a "mu problem", from an interaction term (mu) * (Hu.Hd) (Hu and Hd are the two unbroken Higgs doublets in the MSSM). The problem with (mu) is lack of explanation of why it has an electroweak-scale mass rather than a GUT-scale mass. The NMSSM adds an additional Higgs particle, S, a Standard-Model gauge singlet. Electroweak symmetry breaking yields an additional even-parity neutral Higgs particle, an additional odd-party neutral Higgs particle, and an additional Higgsino. This means 3 even-party neutral Higgs particles, 2 odd-parity ones, and 5 neutralinos.

That additional particle S replaces the (mu) in the above mass term, and SUSY breaking makes an effective (mu) value. So in the NMSSM, all the electroweak-scale masses are due to SUSY breaking.

Turning to GUT's, SO(10) puts the Hu and the Hd in a single 10 (vector) multiplet H, and the elementary fermions into three generations of 16 (spinor) multiplets F. The S remains a gauge singlet in it.

However, going to E6, the H, the F, and the S can be part of a single fundamental 27 multiplet. The triplet interaction (27).(27).(27) is a gauge singlet and also symmetric in the fields. Breaking down to SO(10) gives interactions S.H.H and H.F.F -- what the NMSSM needs.

 

[kodama]

I wish to note some details.

The MSSM predicts two even-parity neutral Higgs particles, h and H0, one odd-parity Higgs particle, A, and two charged Higgs particles, H+ and H- (or two variants of one particle). The h and H0 have a 2*2 mass matrix, as one might expect.

If one of the MSSM parameters is high enough, then the H0, A, and H+- have masses close to each other, masses much greater than the h mass.

The MSSM has a "mu problem", from an interaction term (mu) * (Hu.Hd) (Hu and Hd are the two unbroken Higgs doublets in the MSSM). The problem with (mu) is lack of explanation of why it has an electroweak-scale mass rather than a GUT-scale mass. The NMSSM adds an additional Higgs particle, S, a Standard-Model gauge singlet. Electroweak symmetry breaking yields an additional even-parity neutral Higgs particle, an additional odd-party neutral Higgs particle, and an additional Higgsino. This means 3 even-party neutral Higgs particles, 2 odd-parity ones, and 5 neutralinos.

That additional particle S replaces the (mu) in the above mass term, and SUSY breaking makes an effective (mu) value. So in the NMSSM, all the electroweak-scale masses are due to SUSY breaking.

Turning to GUT's, SO(10) puts the Hu and the Hd in a single 10 (vector) multiplet H, and the elementary fermions into three generations of 16 (spinor) multiplets F. The S remains a gauge singlet in it.

However, going to E6, the H, the F, and the S can be part of a single fundamental 27 multiplet. The triplet interaction (27).(27).(27) is a gauge singlet and also symmetric in the fields. Breaking down to SO(10) gives interactions S.H.H and H.F.F -- what the NMSSM needs.

wouldn't all these additional higgs interact with one another and with SM particles that can be observed at LHC?

 

[lpetrich]

Yes they would, if their masses are low enough for them to be produced by the LHC.

They would likely be produced in much the same way that the SM Higgs is produced, and their production cross sections and decays are likely similar. That means that it may be hard to search for them, since they may not have decays that stand up above the background very much.

But that's why the LHC will eventually get its High Luminosity upgrade, to search for particles and decay modes that are less distinguishable from the LHC's background than what it can currently see.

 

[kodama]

I wish to note some details.

The MSSM predicts two even-parity neutral Higgs particles, h and H0, one odd-parity Higgs particle, A, and two charged Higgs particles, H+ and H- (or two variants of one particle). The h and H0 have a 2*2 mass matrix, as one might expect.

If one of the MSSM parameters is high enough, then the H0, A, and H+- have masses close to each other, masses much greater than the h mass.

The MSSM has a "mu problem", from an interaction term (mu) * (Hu.Hd) (Hu and Hd are the two unbroken Higgs doublets in the MSSM). The problem with (mu) is lack of explanation of why it has an electroweak-scale mass rather than a GUT-scale mass. The NMSSM adds an additional Higgs particle, S, a Standard-Model gauge singlet. Electroweak symmetry breaking yields an additional even-parity neutral Higgs particle, an additional odd-party neutral Higgs particle, and an additional Higgsino. This means 3 even-party neutral Higgs particles, 2 odd-parity ones, and 5 neutralinos.

That additional particle S replaces the (mu) in the above mass term, and SUSY breaking makes an effective (mu) value. So in the NMSSM, all the electroweak-scale masses are due to SUSY breaking.

Turning to GUT's, SO(10) puts the Hu and the Hd in a single 10 (vector) multiplet H, and the elementary fermions into three generations of 16 (spinor) multiplets F. The S remains a gauge singlet in it.

However, going to E6, the H, the F, and the S can be part of a single fundamental 27 multiplet. The triplet interaction (27).(27).(27) is a gauge singlet and also symmetric in the fields. Breaking down to SO(10) gives interactions S.H.H and H.F.F -- what the NMSSM needs.

Yes they would, if their masses are low enough for them to be produced by the LHC.

They would likely be produced in much the same way that the SM Higgs is produced, and their production cross sections and decays are likely similar. That means that it may be hard to search for them, since they may not have decays that stand up above the background very much.

But that's why the LHC will eventually get its High Luminosity upgrade, to search for particles and decay modes that are less distinguishable from the LHC's background than what it can currently see.

wouldn't a higher energy upgrade to 28-33TEV be even more useful?

 

[lpetrich]

True, but it would be difficult to keep the accelerated protons in the accelerator. The magnets' field strength would have to be over twice as great to steer them in place (Gyroradius - Wikipedia). The Large Hadron Collider has a radius of 4.3 km, and here's what magnetic field is necessary to get up to these energies:

• 6.5 TeV - 5.0 T (LHC now)
• 7 TeV - 5.4 T (LHC design)
• 14 TeV - 10.7 T
• 16.5 TeV - 12.7 T
• 28 TeV - 21 T
• 33 TeV - 25 T

The actual maximum field of the LHC's steering magnets is 7.7 T.

The synchrotron-radiation energy loss is proportional to (E⁴*v²)/(m⁴*r²) (E, v, m = particle energy, velocity, mass, r = radius of particle path). The previous occupant of the LHC's tunnels, the LEP, was an e-e+ collider. It was limited to 104.5 GeV per particle. If the LHC was limited by synchrotron-radiation losses, then it could go up to about 200 TeV.

That's why proposals for more energy involve building larger accelerators.

 

[kodama]

just replace the 5.4 T magnets with 25 T

 

[lpetrich]

just replace the 5.4 T magnets with 25 T

Has anyone ever built 25-tesla electromagnets? Is there any superconductor that won't be quenched by a magnetic field that strong?

 

[Dr.AbeNikIanEdL]

Well, https://en.wikipedia.org/wiki/Superconducting_magnet#History lists 26.8 T as world record. Of course, this does not mean you have this ready to use in an accelerator. Have a look at e.g. these slides https://indico.cern.ch/event/521926/attachments/1310549/1960888/160718_summer-students_II_final.pdf shown at a summer school this year. Anything above ~15 T seems be far in the future with time scales "beyond 2035". I am not in this field, and others might have different opinions on future developments, but I think it is clear that this is not as easy as "just replace the magnets"...

 

[arivero]

MSSM and nMSSM require 5 higgs like bosons

Is 5 the minimum?

From degrees of freedom I would expect some susy theory with only three, consider a neutral higgsino weyl, and a charged one dirac. Only six spartners. Three dof are eaten to give mass to the Z and W and the other three are H0 H+ and H-

Another look: a massive gauge supermultiplet is one spin 1 particle, two Weyl fermions, one scalar. We have three massive particles, so three scalars.

 

[kodama]

do these additional higgs fields also generate mass in elementary particles? and since the LHC hasn't seen them, do they have to have masses higher than energies LHC can probe?

 

[Vanadium 50]

Is 5 the minimum?

Yes. You need different Higgs fields to couple to u-type and d-type quarks. The problem isn't the quarks, strictly speaking: it's the squarks. In supersymmetric theories the scalars belong to chiral multiplets and their complex conjugates belong to multiplets of the opposite chirality; because multiplets of different chiralities cannot couple together in the Lagrangian, a single Higgs doublet is unable to give mass simultaneously to the u-type and d-type quarks. The same argument holds for leptons if the neutrino is Dirac.

 

[kodama]

Yes. You need different Higgs fields to couple to u-type and d-type quarks. The problem isn't the quarks, strictly speaking: it's the squarks. In supersymmetric theories the scalars belong to chiral multiplets and their complex conjugates belong to multiplets of the opposite chirality; because multiplets of different chiralities cannot couple together in the Lagrangian, a single Higgs doublet is unable to give mass simultaneously to the u-type and d-type quarks. The same argument holds for leptons if the neutrino is Dirac.

does this provide any predictions lhc can see with regards to the 1 higgs they see