All charged particles discovered so far have mass although theoretically nothing prohibits the existence of massless charges. There may be a very fundamental reason for this.
Actually, massless particles are quite few in number. Only the photon, the gluons, and (if it exists) the graviton are massless. Everything else is massive, so charged particles are not in any way special in this regard.
All charged particles do not have mass. Charge and mass are distinct attributes: the first is an ``internal'' label, the second a ``spacetime'' label for a particle.
The particles that make up matter, quarks and leptons, for instance the electron, that are fermions, in fact, acquire their mass through the Yukawa couplings to the scalar, that was introduced through the Brout-Englert-Higgs mechanism.
The neutrinos, however, that are leptons and carry weak charge are now (since 1998) known to have mass. However, how *they* acquire their mass is an open issue, since only left-handed neutrinos are observed to exist, so the B-E-H mechanism isn't, directly, applicable.
The particles that mediate the interactions, that are vector bosons, are massless, due to gauge invariance. The W+, W- and Z, all of whom carry weak charge, are massive through spontaneous breakdown of the electroweak symmetry, through the B-E-H mechanism, therefore gauge invariance is ``hidden'' in this case. The photon, that does mediate the electromagnetic interactions, but is electrically neutral, remains massless, since the gauge invariance, that expresses electric charge conservation, remains manifest.
The gluons and graviton are massless and do carry ``charge'': the gluons do carry ``color'', the charge of the strong interactions and the graviton does couple to the energy-momentum tensor (the gauge invariance is local coordinate invariance).
So the statement as made is not true.
Stam, I presumed (perhaps wrongly) that the question was about _electric_ charge. You are of course correct that gluons carry color charge. As to the graviton, I'd hesitate to call its self-interaction "charge"; the gravitational "charge" would be rest mass, which the graviton (as far as we know) does not have. Anyhow, perhaps this is simply a matter of semantics, nothing more.
One small correction: fermions do not acquire mass through the Higgs-mechanism. Under the Standard Model, they interact with the Higgs field directly through Yukawa terms in the Lagrangian. This is distinct from the Higgs mechanism, in which the presence of a quartic potential causes symmetry breaking and once the Lagrangian of the (originally massless) SU(2)xU(1) gauge boson field is rewritten with respect to the true vacuum, the bits corresponding to the SU(2) part, namely the W and Z bosons, acquire mass.
No, the charge the graviton couples to isn't rest mass, since this isn't ``gauge invariant''. The charge would be the ADM mass, defined through the energy-momentum tensor at infinity. As usual, you can see this by looking how it couples: the graviton couples to the energy-momentum tensor, the ``current'' and the ADM mass is the charge.
Incidentally, to write down the Yukawa couplings at all, you need to introduce a scalar field. *This* field, in the Standard Model *is* the field that is used in the Brout-Englert-Higgs machanism, so the statement I made is correct. As noted, the neutrinos,don't seem to obtain their masses from Yukawa couplings, whereas the others do, because it is possible to write them at all, with the physical fields.
Stam, to quote Wikipedia (https://en.wikipedia.org/wiki/Higgs_mechanism), "[i]n the Standard Model, the phrase 'Higgs mechanism' refers specifically to the generation of masses for the W±, and Z weak gauge bosons through electroweak symmetry breaking." This is distinct from the Yukawa coupling between the Higgs scalar and fermions.
That said, just yesterday a public press release by CERN that announced the Higgs decay into taus did refer to the mechanism behind fermion masses as the "Brout-Englert-Higgs mechanism" (http://atlas.ch/news/2013/higgs-into-fermions.html). I don't like it but who am I to argue with CERN?
Your main point, namely that the Higgs field is not responsible for neutrino masses (as far as we know), is of course correct regardless of terminology.
I don't care what something is called, I care what it does. In the Standard Model, the *same* scalar, that interacts with the gauge bosons of the elecrroweak sector to give, some of them, a mass (leaving the photon massless), through Yukawa terms, gives the fundamental fermions, save the neutrinos, mass. That's the important point.
(Both the coupling of this scalar to the gauge fields and to the fermions is determined by gauge invariance.) That's why the decay into fermions of this scalar is important to measure-and it's much harder than the two ``discovery'' channels.
Incidentally we do know, from the discovery channels that it *does* couple to fermions, as expected, through loop effects, because, for instance, the decay h->2 photons proceeds through gluon fusion->top loop->higgs->vector boson loop->2 photons.
Same scalar but two distinct (albeit related) mechanisms. That was my point. I am not hung up on names either, it's just that I think that the mechanisms for bosonic vs. fermionic masses are rather different (even though the same scalar field is involved).
The difference lies in the Yukawa couplings. So the exercise is: if you have a theory, with gauge fields, scalars and fermions, such that the tree-level Yukawa couplings are zero, whether they can be generated by radiative corrections, in the broken phase, where the scalar has a vacuum expectation value. One example, where this can be realized, is in this paper: http://arxiv.org/abs/hep-ph/9805314 that explores physics beyond the Standard Model.
There has been work by others, within the Standard Model. As far as I understand, however, these include additional assumptions. So yes, as historically occurred (Weinberg and Salam introduced, in particular, the Yukawa couplings of the B-E-H scalar to the leptons-the quarks were a more complicated story), one does seem to need, for the Standard Model, the tree-level Yukawa couplings-else the scalar would be ``fermiophobic'' (wouldn't decay so readily to fermions)--and that is what is being tested by measuring its decays into fermions, that, in fact, it isn't and decays into them readily enough that more than radiatively induced couplings are necessary, as in the Standard Model
(as already mentioned, the decay into two photons, already tests the top Yukawa coupling). So there is a compression, in merging the existence of the Yukawa couplings with the existence of the scalar itself, in this context.
Neutrino is a mass less particle in standard model. It does have weak charge, even though it is electrically neutral. This is a Fermion example.
Similarly, gluons have color charges, and they are mass less. They are mass less
because QCD is unbroken. This is a boson example.
In standard model, Q=T^3_l + Y/2, for Fermions and Higgs scalar.
That means T^3_L must cancel with Y/2 to make the particle
electrically neutral. This happens for the neutrino and one neutral
component of Higgs doublet only.
Neutrinos have been known to be massive (to be more precise: at least two out of the three neutrino species have been known to be massive) ever since neutrino oscillations were confirmed in solar neutrinos in the late 1990s/early 2000s. So we've known for some time that the Standard Model needs to be modified, with a neutrino mass mechanism. Moreover, this mechanism needs to be different from the Yukawa mechanism for other fermion masses due to neutrino handedness.
Hi Everybody!
Thank you all for your responses and interaction. Neutrinos are massive anyway. So no fermionic example so far.
Photons (chargeless) have been assumed to be massless and an upper bound is placed on their possible mass, if any, at 10^ (--57) kg or some such value.
Now, do the gluons (charged) not have some such upper bound? Since they are not available freely, their Self-interaction and and interaction amongst themselves will presumably make them massive also.
In that case we have no massless charges finally!
Photons, gluons and gravitons are massless from gauge invariance that is manifest (not spontaneously broken). The upper bound is just for calibrating the apparatus and providing a background check for *other* effects. The difficulty with photons is that they don't carry charge. Were gluons massive, the effects would be much stronger, that is how we can check they are massless.
The self-interaction of the gluons, just as for W and Z bosons and gravitons, cannot give rise to a mass for them, since it respects manifest gauge invariance. That was the reason that the B-E-H mechanism was necessary for the W and Z.
The reason is that mass and electric charge are related quantities. See my paper for details:
https://www.researchgate.net/publication/236260413_Electromagnetic_Mass_Charge_and_Spin
Article Electromagnetic Mass, Charge and Spin
A charged particle is always interacting with the electromagnetic field of the vacuum and is also self-interacting, so even if this particle does not have a bare mass it will always have a renormalized mass.
Not necessarily. This is, indeed, the case if you have a charged, massless, scalar, in interaction with the electromagnetic field, cf. S. Coleman and E. Weinberg, Phys. Rev. D7 (1973) 1888. If you had a charged, massless, fermion,in interaction with the electromagnetic field, it would stay massless, in perturbation theory (i.e. weak coupling), at least, due to (global) chiral symmetry: the Lagrangian splits into the sum of two, corresponding to each chirality separately interacting with the gauge field, so you can't write a term mixing the two chiralities, which would, thereby, generating a mass term.
In the Standard Model you can't write a mass term for the fermions because the two chiralities have different electroweak interactions: the right handed fermions are singlets, while the left-handed fermions are doublets-that's why you need the (Brout-Englert-Higgs) scalar field, which, through its Yukawa couplings with the fermions, when it acquires a non-zero expectation value, gives rise to a mass term for them.
A general rule, we know, is that unless masses are protected by some
symmetry, loop corrections involving standard model particles
will push up the mass to a scale M. This scale M is the mass
scale up to which standard model is valid. Then we can ask
why electron has a small mass ?
The answer would be that electron and positron transform
differently under the standard model gauge symmetry. The
electron transforms under SU(2)_L in a doublet, whereas
positron is a singlet under SU(2)_L. You can say left handed
electron is in a doublet where as the right handed projection
is in a singlet.
In this way symmetries can protect mass terms. When this
symmetry is broken by Higgs mechanism, one obtains
electron mass. If we could not break standard model
gauge symmetry electron would have remained mass less.
Then we could have found a mass less charged particle.
No, you're confusing antiparticles with chiralities. The electron has two chiralities, left and right, so has the positron. The left *chirality* of the electron transforms, together with the neutrino, as a doublet, while the right *chirality* of the electron as a singlet under the gauge group of the electroweak interactions. The positron, also, has *two* chiralities and the requirement that the positron be the antiparticle of the electron implies that the chiralities transform correspondingly. One chirality of the positron thus *must* transform, along with the antineutrino, as a doublet, while the *other* chirality will transform as a singlet under the gauge group. Since antiparticles have opposite chiralities to particles, this means that it's the *right* chirality of the positron that, along with the right chirality of the anineutrino, transforms in a doublet, while the *left* chirality of the positron transfoms as singlet.
If you want to write a mass term for the electron, what you're after is a term that contains *both* chiralities of the *electron*. Since these don't belong to the same representation of the gauge group in the Standard Model, you need a scalar, with the appropriate quantum numbers to make a term for the Lagrangian that is a Lorentz scalar and is gauge invariant-and for this scalar to acquire a non-zero vacuum expectation value. Corresponding statements hold for the positron.
@ Stam,
I still have some concerns.
At the level of the electroweak interactions U(1)_{em} is not
a good symmetry. Thus we cannot label fermions by their electric
charges, and so we cannot use terms electron or positron.
So let us say we have e_L and e_R and their antiparticles
at the level of unbroken electroweak symmetry.
e_L is in a doublet, and so is the antiparticle of e_R.
e_R is a singlet, and so is the antiparticle of e_L.
So we cannot write mass terms for them.
When electroweak symmetry is broken we
need not worry about doublets and singlets.
Now e_L can pair up with antiparticle of e_L
which was in a singlet. And, antiparticle
of e_R which was in a doublet can pairs up
with e_R which was in a singlet.
Do you agree with this description ?
All this is textbook stuff. Once more, you're confusing antiparticles with chiralities. You have a left handed doublet and a right handed singlet. The ``up'' component of the doublet is well-defined-it's the e_L. The ``down'' component is the neutrino. and so on. This is how SU(2) x U(1) is realized. This U(1) is *hypercharge* *NOT* electric charge.
Once SU(2) x U(1) gets broken to U(1)_em, the electric charge, which is defined as a combination of U(1)_Y and one of the generators of SU(2), is a good quantum number.
No this time I am sure.
gamma_5 e_L = - e_L
whereas
gamma_5 (e_L)^c = + (e_L)^c
This solves the problem. Thanks.
Dear Stam Nicolis,
From the reference that you mention before.
"We investigate the possibility that radiative corrections may produce spontaneous symmetry breakdown in theories for which the semiclassical (tree) approximation does not indicate such breakdown. The simplest model in which this phenomenon occurs is the electrodynamics of massless scalar mesons. We find (for small coupling constants) that this theory more closely resembles the theory with an imaginary mass (the Abelian Higgs model) than one with a positive mass; spontaneous symmetry breaking occurs, and the theory becomes a theory of a massive vector meson and a massive scalar meson. " . This reference is about scalar particles generating an "imaginary mass" . Chiral symmetry can protect a particle from acquiring mass, but chiral symmetry is not an exact symmetry in nature, as far as my knowledge goes. I think that a more conservative view is to say that chiral symmetry can keep the mass of particle from gaining large radiative corrections. If this is not so, then how come there are no fundamental charged particles in the real world? Charge means interaction, and interaction means energy, and energy is mass. In this article I don't see charged particles staying massless. I will appreciate if you can provide a little more explanations to sustain your point. I would really like to get your idea better. The topic is quite interesting.
No, the masses generated for the scalar and the photon are *real* masses in the paper by Coleman & Weinberg.
Regarding chiral symmetry: It is an exact symmetry for massless fermions, in the absence of gauge fields.
if massless fermions carry charge under a gauge symmetry then, in perturbation theory they do not acquire mass. However, since the axial current, in fact, is not conserved, an additional term appears in the Lagrangian. This term is a surface term and can give rise to a mass for the fermions; non-perturbatively in four space-time dimensions, perturbatively, however, in three space-time dimensions (these statements refer to abelian gauge fields, things get more complicated for non-abelian gauge fields).
The statements about charges, interactions, energy and mass are imprecise and the assertion that there are no fundamental charged particles in the real world is false: the leptons are, one, counterexample.
Charged particles can stay massless, despite interactions, if the mass terms are incompatible with the interactions. This is what happens for leptons in the Standard Model: Since the left handed leptons transform in a different representation than the right handed leptons, it is not possible to write down a mass term for them-so the only way for them to acquire a mass is through the interaction with a scalar field, with the appropriate quantum numbers, whose Yukawa couplings can give rise to the mass terms, if the scalar field does acquire a vacuum expectation value. This is, indeed, what happens.
@ Stam
Dear Stam'
Your words are "Regarding chiral symmetry: It is an exact symmetry for massless fermions, in the absence of gauge fields" But the electromagnetic field is a gauge field so you are saying that chiral symmetry is respected exactly in the absence of EM, but the question is if charged particles can be massless in the presence of the EM field (This is equivalent to the statement of the particle being charged!) . The second point is that charged leptons are massive in nature. Your counter example is not valid. Remember this equation E=mc^2? This is not imprecise is real! Standard model of particles is not even consistent without the Higgs model. But you most remember from your QFT course that not only correction to mass due to interaction exists is actually an infinite number! You are also saying at the end of you last statement that this is what actually happens, but this assumption is a little bit too absolute for a model that is not completely understood. Please I don't mean to be rude but your arguments are not strong enough. Please forgive my sincerity I do want to understand you better. If you can explain to me what is your point without the use of absolutes "no" the you are allowing for convincing arguments. Please remember also that the standard model is still a flawed theory, so arguments are more powerful without always invoking perturbation theory. You can use, for example, arguments based on more general principles.
Once more: If you write the classical action of a massless Dirac fermion, you will find that it can be written as the sum of the actions of each chiral projection. The interaction term with a gauge field (e.g. EM) can be split that way too. The action is invariant under global chiral transformations. Therefore, it would seem that the fermion will remain massless-the mass term, that mixes left and right chiralities, is not compatible with the symmetries of the classical action.
Therefore, at the classical level there are two conserved currents, the vector current and the axial current. If you compute the quantum corrections, however, you find that they cannot be both conserved: if the vector current is conserved, the axial current receives a correction. The theory is renormalizable, so this correction is finite. It contributes a surface term to the action, that breaks invariance under chiral transformations, therefore, the effective action acquires a ``theta term''. (You can get the same result by noticing that the *measure* of the path integral is not invariant under chiral transformations. Therefore the Jacobian is not unity and its contribution to the action is the theta term.)
Therefore you must include in the action all terms with compatible symmetry properties-here this includes the mass term for the fermion(s). This is all well known material that can be found in textbooks on quantum field theory.
This is true if the chiral transformations are *global* transformations. If they are *local* transformations, then these statements are not true-since gauge invariance is broken, the theory, in fact is *not* renormalizable. This is what happens in the Standard Model, where *both* leptons and quarks are needed to have electroweak interactions for the theory to be consistent.
In the Standard Model, the reason the leptons, in the absence of a Higgs field, are massless, is because it is not possible to write down a mass term. The reason is that the left chirality and the right chirality transform in *different* representations of the gauge group, SU(2) x U(1): the left chirality belongs to a doublet, the right chirality (of the electrons) to a singlet. *That's* why a mass term can't appear. By introducing the Higgs field, however, it is possible to write Yukawa couplings for the fermions with this field. The Yukawa terms are consistent with the symmetries of the theory.
If this field then acquires a vacuum expectation value, then the fermions acquire masses, proportional to their Yukawa couplings and the vev of the Higgs. In the presence of the Higgs, and taking into account contributions from leptons *and* quarks, the theory is renormalizable, therefore the physical masses are *finite*. Once more, well known material.
@Sam
Is a theory of massless fermions, coupled to a vector with local gauge invariant, free of radiative mass corrections at the quantum level?
Once more: for a vector theory, in perturbation theory Yes, non-perturbatively, No. Chiral symmetry breaking is a non-perturbative effect.
Dr guynn,
Thank you very much for the answer for references to your articles. I hope to go through them in time. Spin can be related to rotational motion but how to consistently explain the 4 pi symmetry rather than 2pi for ordinary space? Hope you have tackled this issue.
Best Regards.
Rajat
in Nature, the number of charged particles is no longer conserved, but that total (net) charge is actually being conserved, always .... when explored in the theory of the power of will... of ideas.. how they have mass in that they actually hold space, transform..
From philosophical insights of the last century... that human interaction is the missing part to equation of mental determinism could provide the needed particle for causation. We already know that , when under observation, electrons are being "forced" to behave like particles and not like waves. Thus the mere act of observation affects the the observed reality.
Wilhelm Max Wundt (1897) https://psychclassics.yorku.ca/Wundt/Outlines/sec22.htm
Suggests that like the concepts of matter, that the concept of mind energy in the form of ideas, hold space, have a force, can shift energy to affect another space and time holds the property of motion and transformation.
excerpt here... " concept energy, which in the special form of mechanical energy is defined as half the product of the mass multiplied by the square of the velocity. Energy, however, must, just as well as force, have a position in objective space, and under certain particular conditions the points from which energy proceeds may, just as well as the .points from which force proceeds, change their place in space, so that the concept of matter as a substratum contained in space, is retained in both cases. The only difference, and it is indeed an important one, is that when we use the concept force, we presuppose the reducibility of all, natural phenomena to forms of mechanical motion, while when we use the concept of energy, we attribute to matter not only the property of motion without a change in the form of [p. 312]energy, but also the property of the transformability of qualitatively different forms of energy into one another without a change in the quantity of the energy."
The view, for example, that all the contents of psychical experience are ideas, and that these ideas are more or less permanent objects, would hardly be comprehensible without such presuppositions. That this concept is really foreign to psychology, is further attested by the close interconnection in which it stands to the concept of material substance. It is regarded either as identical with the latter or else as distinct in nature, but still reducible in its most general formal characteristics to one of the particular forms of the concept matter, namely to the atom.
I have a very simple minded answer that may or may not be correct, but here it is: Imagine a negatively charged particle at rest above a positively charged plate. Because of the attraction of the two objects, the charged particle will begin to move towards the plate, picking up speed. As it moves towards the plate, the electronic energy of the system decreases. This energy has to go somewhere. The only option I see (and this may be the fatal flaw of the argument) is that it must transform into kinetic energy. For this to occur, the particle must have mass.
Dear Michael, i simply appreciate your simple but perfect answer based on energy conservation.
@Hinnerk Albert
We are talking of electric charges, not Colorado charge or any other charge.
OK, Michael Diebold answer based on energy conservation is true, but the conclusion is not. For massless particle, the kinetic energy is E=pc=hf. So, there need not that the velocity of massless particle, c, changes, but this is the frequency, f, that compensate it.
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