I The Higgs Field and Fermion Generations: Stability and Mass

[kodama]

if there were no higgs field, would the second and third generation of fermions, such as the top quark, be exactly the same mass as first generation?

is the coupling between the top quark and the higgs field the sole reason the top quark is heaviest SM particle?

is there a reason the top quark, and second and third generation fermions couple to the higgs field more strongly than the first generation?

if there were no higgs field, would second and third generation fermions be stable and long-lived as first generation?

 

[arivero]

Could you elaborate about what alternative mass mechanism are you thinking about?

 

[nikkkom]

Related thread:

https://www.physicsforums.com/threads/imagining-a-higgsless-universe.882072/

 

[kodama]

Could you elaborate about what alternative mass mechanism are you thinking about?

why do third generation fermions interact more strongly with the higgs field than second, and second first. why does the top quark interact with the higgs field more strongly than an electron?

 

[Orodruin]

why do third generation fermions interact more strongly with the higgs field than second, and second first. why does the top quark interact with the higgs field more strongly than an electron?

The couplings of the Higgs field are free parameters in the Standard Model and directly related to the masses of the quarks. Therefore, a quark with a larger mass will interact more strongly with the Higgs field. In effect, it is the interaction with the Higgs field that provides the mass, implying that a quark that interacts more strongly with the Higgs field will have a larger mass.

 

[kodama]

i understand it is a free parameter, but are there any physics explanations why second and third generation fermions interact more strongly with the higgs, such as a degree of freedom

is there any reason why second and third generation fermions couldn't be lighter and couple less strongly than first generation to the higgs, since it is a free parameter and can take any value

 

[Orodruin]

i understand it is a free parameter, but are there any physics explanations why second and third generation fermions interact more strongly with the higgs, such as a degree of freedom

is there any reason why second and third generation fermions couldn't be lighter and couple less strongly than first generation to the higgs, since it is a free parameter and can take any value

The lighter quarks are what we define as the first generation.

 

[kodama]

The lighter quarks are what we define as the first generation.

since higgs coupling is a free parameter isn't it certainly conceivable that all 3 generations have the same coupling to the higgs and therefore same masses

 

[Orodruin]

since higgs coupling is a free parameter isn't it certainly conceivable that all 3 generations have the same coupling to the higgs and therefore same masses

Yes, but this would be a rather strange situation where we would probably suspect that some symmetry was in play because there is no a priori reason for this to be the case.

 

[arivero]

Yes, but this would be a rather strange situation where we would probably suspect that some symmetry was in play because there is no a priori reason for this to be the case.

In fact all the masses are almost zero compared to the top quark, so we could suspect a symmetry where all masses are null except the top quark, but this scenario is not asked/developed frequently, neither in literature nor even here in forums.

EDIT: AFAIK, of course

 

[ohwilleke]

Given that the W bosons are the means by which quarks and charged leptons, at least, change from one flavor to another at frequencies that show a some crude relationship to the mass differences involved, surely the Higgs boson couplings and the CKM matrix that governs W boson quark flavor transformations, have some deeper connection to which we are not yet privy.

Also, it isn't obvious that it is possible for particles to be distinct from each other in some means other than their propensity to change from one type to another (which would have no observable consequences if all other properties were the same) if they do not have some different properties, so it stands to reason that given that they are identical in everything else, that they ought to have different masses, and are assignment of those masses to particular generations in order of mass is something that can be done without loss of generality in every case where there are distinct masses.

 

[ohwilleke]

since higgs coupling is a free parameter isn't it certainly conceivable that all 3 generations have the same coupling to the higgs and therefore same masses

Not if the Higgs coupling is the source of masses in the universe. If all the couplings were the same the Higgs boson and field would be much simpler mathematically.

 

[nikkkom]

Also, it isn't obvious that it is possible for particles to be distinct from each other in some means other than their propensity to change from one type to another (which would have no observable consequences if all other properties were the same)

Pauli exclusion principle effects should be observable: in the "Higgsless Universe", electrons and muons would look the same, but you'd notice that sometimes you can cram two of them into the same state, and sometimes you can't.

 

[arivero]

Hmm if all the three masses are equal, does the CKM matrix still has the same physical components? Or does some component become unphysical?

 

[Orodruin]

surely the Higgs boson couplings and the CKM matrix that governs W boson quark flavor transformations, have some deeper connection to which we are not yet privy.

The mixing in the quark sector is directly given by the mismatch between the left-handed transformations that diagonalise the up and down type Yukawa couplings.

Hmm if all the three masses are equal, does the CKM matrix still has the same physical components? Or does some component become unphysical?

If all masses are equal the entire CKM matrix is unphysical. (In fact, it is sufficient that either the up or down type quarks have the same masses.)

 

[kodama]

Yes, but this would be a rather strange situation where we would probably suspect that some symmetry was in play because there is no a priori reason for this to be the case.

what would be a reason a priori they would be different? how can you tell apart a massless muon from a massless electron or tau

 

[kodama]

Not if the Higgs coupling is the source of masses in the universe. If all the couplings were the same the Higgs boson and field would be much simpler mathematically.

in a higgless universe is it possible that there is NO difference between an electron tau or muon? they are all the same particle, the only difference is that sometimes the higgs is more strongly attracted to muon or tau, or that a muon or tau are quantized excited versions of electron

 

[Vanadium 50]

electrons and muons would look the same, but you'd notice that sometimes you can cram two of them into the same state, and sometimes you can't.

Not exactly. What would be observed is you can get 3 electrons into the same state. Eventually it would be explained as a hidden quantum number called "infracolor" or "ultracolor" or something like that, in analogy with QCD color.

If all masses are equal the entire CKM matrix is unphysical.

I wouldn't say "unphysical". "Trivial" and "unnecessary" seem to be more descriptive.

 

[arivero]

Not exactly. What would be observed is you can get 3 electrons into the same state. Eventually it would be explained as a hidden quantum number called "infracolor" or "ultracolor" or something like that, in analogy with QCD color.

It is not gauge, so flavor is still a good name.

I wouldn't say "unphysical". "Trivial" and "unnecessary" seem to be more descriptive.

My vote is with "Trivial".

Is it right to think that while we need three different masses to have a full non trivial CKM matrix, we do not need six?

 

[Vanadium 50]

It is not gauge

I am not sure that people would immediately conclude that. I suspect they would start putting together "ultraweak" theories to try and explain flavor. We sort of do this today with topcolor-style theories.

Is it right to think that while we need three different masses to have a full non trivial CKM matrix, we do not need six?

Has to be the right three. All the +2/3 or all the -1/3. That allows you to change the basis so the CKM matrix is the identity. If you make e.g. two of the +2/3's degenerate with one of the -1/3's, you still have a nontrivial matrix. However, that matrix will be real, so there will be no CP violation.

 

[Orodruin]

I wouldn't say "unphysical". "Trivial" and "unnecessary" seem to be more descriptive.

I think unphysical nails it. The precedent here being that we call the Majorana phases unphysical as they can be reabsorbed in the definitions of the fields, the entire CKM matrix would be unphysical as you could reabsorb it in the field definitions or chose to work in a basis with an arbitrary CKM matrix and it would make no observable difference.

Has to be the right three. All the +2/3 or all the -1/3. That allows you to change the basis so the CKM matrix is the identity. If you make e.g. two of the +2/3's degenerate with one of the -1/3's, you still have a nontrivial matrix. However, that matrix will be real, so there will be no CP violation.

There is no requirement that a -1/3 has to be degenerate with the degenerate 2/3 pair. It is sufficient that a single 2D rotation in flavor space commutes with the up type Yukawas.

 

[Vanadium 50]

The question was 3 mass degeneracies. There are two ways to do this: 3 and 0 and 2 and 1 - i.e. all of the +2/3s, all of the -1/3's or one degeneracy within a charge and one across charges. In the 3-0 case you can adjust your basis so that the CKM matric is diagonal. In the 2-1 case you can't make it diagonal, but it is always real. That's all I am saying.

 

[Orodruin]

In the 2-1 case you can't make it diagonal, but it is always real.

To be specific: It does not need to be real, but you can absorb any of the complex phases in field redefinitions and even if you do not it does not the phases are unphysical and therefore do not lead to any CP violation