The basic intuitive gist of the proposal of this paper is one that I've entertained myself, although I don't have the theoretical physics chops to spell it out at this level of formality and technical detail (and I'm really not qualified to evaluate the merits to this proposal at that level). I've seen one or two other papers (not recent ones) that take a similar approach.
The ratio of the electron mass to the lightest neutrino mass eigenstate is roughly the same as the ratio of the electromagnetic coupling constant to the weak force coupling constant, and both are masses are similar to what would be expected from the self-interactions of electrons and neutrinos via the electromagnetic and weak forces with themselves. Electrons interact via both of these forces, while neutrinos interact only via the weak force.
The down quark mass is about twice as much as the up quark mass, just as the absolute value of the down quark electromagnetic charge is twice the absolute value of the up quark electromagnetic charge. All quarks have the same magnitude of strong force color charge. And all of the fundamental fermions of the Standard Model have the same magnitude of weak force charge. Quarks interact via the strong force, the electromagnetic, and the weak force, so their self-interactions might be expected to be larger than for the electron which doesn't interact via the strong force.
Figuring out how this can work in concert with the three fundamental fermion generations is particularly challenging. I'm inclined to associate it with a W boson mediated dynamic process that sets the relative values of the Higgs Yukawas. This paper doesn't attempt to look beyond the first generation of fundamental fermions in implementing its model.
I'm not thrilled with the "leptoquark" component of this theory, but the fact that it gives rise to neutrino mass without either Majorana mass or a see-saw mechanism is very encouraging.
In the Standard Model of elementary particles the fermions are assumed to be intrinsically massless. Here we propose a new theoretical idea of fermion mass generation (other than by the Higgs mechanism) through the coupling with the vector gauge fields of the unified SU(2) ⊗ SU(4) gauge symmetry, especially with the Z boson of the weak interaction that affects all elementary fermions. The resulting small masses are suggested to be proportional to the self-energy of the Z field as described by a Yukawa potential. Thereby the electrically neutral neutrino just gets a tiny mass through its Z-field coupling. In contrast, the electrically charged electron and quarks can become more massive by the inertia induced through the Coulomb energy of the electrostatic fields surrounding them in their rest frames.
According to the common wisdom of the Standard Model (SM) of elementary particle physics, the fermions are intrinsically massless, but they gain their masses via phase transition from the vacuum of the Higgs field. However, this notion introduces many free parameters (the Yukawa coupling constants) that are to be determined through measurements. These have been made at the LHC only for some members of the second and third family of heavy leptons and quarks, yet not for the important first family of fermions, of which the stable and long-lived hadrons form according to the gluon forces of quantum chromodynamics (QCD).
Here we just consider the first fermion family of the SM and propose a new idea of the fermion mass generation. The key assumption is that their masses may be equal to the relevant gauge-field energy in the rest frames of these charged fermions carrying electroweak or strong charges. Their masses are suggested to originate from jointly breaking the chiral SU(2) symmetry combined with the hadronic isospin SU(4) symmetry, as described in the recent model by Marsch and Narita, following early ideas of Pati and Salam and their own work. Unlike in the SM, in their model both symmetries are considered as being unified to yield the SU(2) ⊗ SU(4) symmetry, which then is broken by the same procedures that are applied successfully in the electroweak sector of the SM.
The outline of the paper is as follows. We briefly discuss the extended Dirac equation and its Lagrangian including the Higgs, gauge-field and fermion sectors. Especially, the covariant derivative is discussed and the various gauge-field interactions are described. Also the different charge operators (weak and strong) are presented. Then the CPT theorem is derived for the extended Dirac equation including the gauge field terms. The remainder of the paper addresses the idea of mass generation from gauge field energy in the fermion rest frame. Finally we present the conclusions.
The paper's conclusion states:
In this letter, we have considered a new intuitive idea of how the elementary fermions might acquire their finite empirical masses. We obtained diagonal mass matrices as Kronecker products within the framework of the unified gauge-field model of Marsch and Narita. The mass matrices still commute with the five Gamma matrices of the extended free Dirac equation without gauge fields. However, when including them the chiral SU(2) and the hadronic SU(4) symmetries both are broken by the mass term. Thus, the breaking of the initial unified SU(2) ⊗ SU(4) symmetry by the Higgs-like mechanism gives the fermions their different charges as well as specific masses.
In the SM the initial common mass m is assumed to be zero, and then the Dirac spinor splits into two independent two-component Weyl spinors. But when the gauge fields are switched on, their self-energy gives inertia and thus mass to the fermions in their rest frame. The breaking of gauge symmetry yields the electromagnetic massless photon field E(µ) and the weak boson field Z(µ), which becomes very massive via the Higgs mechanism. It also induces inertia for all eight fermions, yet the resulting masses are rather small owing to the very small Compton wavelength of the Z boson. The neutrino and electron can acquire masses in this way, which yet differ by six orders of magnitude. The hadronic charge of the leptons is zero, and thus they decouple entirely from QCD. It is responsible by confinement through the gluons for the mass of the various resulting composite fermions, in particular for the proton mass.
The masses of the light fermions are thus argued to originate physically from the major self-energy of the electrostatic field as well as from the minor self-energy of the Z-boson field, which is proportional to the Higgs vacuum that determines the Z-boson mass. It is clear, however, that the masses of heavy composite hadrons, in particular of the proton and neutron, involve dominant contributions from the energy of the binding gluon fields, as the QCD lattice simulations have clearly shown.
In conclusion, the extended Dirac equation contains a physically well motivated mass term. It remedies the shortcoming of the SM that assumes massless fermions at the outset, whereas the empirical reality indicates that they are all massive. Therefore, the neutrino cannot be a Majorana particle, as it has often been suggested in the literature. This notion is in obvious contradiction to the observed neutrino oscillation, implying clearly finite masses. Chiral symmetry is broken in our theory, yet the parity remains intact.
Finally, we like to mention the masses of the heavy gauge bosons involved in the above covariant derivative and related matrix. In the reference of the particle data group we find in units of MeV/c^2 the values: M(Z) = 91.2 and M(W) = 80.4. For the “leptoquark" boson V we obtain M(V) = 35.4. For the sum of these masses we find the following surprising results: M(V) + M(Z) = 126.6, which equals within less than a one-percent margin the measured mass of the Higgs boson, M(H) = 125.3. Also, M(W) + M(Z) = 171.6, which again equals within less than a one-percent margin the measured mass of the top quark, M(T) = 172.7. Whether this is just a fortuitous coincidence or indicates a physical connection has to remain open.
4 comments:
if true how would you explain why the second and third generation are heavier, in principle. my theory is that flavor is a kind of charge, and second and third generation has more flavor and therefore more charge.
mitchell porter
your thoughts about
arXiv:2508.04220 (gr-qc)
[Submitted on 6 Aug 2025]
Null infinity as SU(2) Chern-Simons theories and its quantization
This paper studies the quantization of the future null infinity ( ) of an asymptotically flat spacetime. Based on the observation by Ashtekar and Speziale that can be regarded as a weakly isolated horizon, we adopt the quantization framework developed for weakly horizon to quantize . We first show that the symplectic structure of is equivalent to the sum of the symplectic structures of two Chern-Simons theories with opposite levels. Based on this observation, we apply Chern-Simons quantization approach to quantize . Finally, we compute the entropy of by counting the microstates, showing that it is proportional to the area of , a spacelike cross-section of . Our result is consistent with the universal entropy formula in the framework of (weakly) isolated horizon.
Comments: 15+8 pages, 1 figure
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:2508.04220 [gr-qc]
5 Quantization and entropy of I +
In this section, we first quantize I + with the quantization scheme of Chern-Simons theory. Based
on this result, we compute its entropy by counting the microstates
We adopt Witten’s quantization scheme for Chern-Simons theory [47]. At each puncture, we impose
the following two constraints
Conclusions and outlooks
In this work, we show that the null infinity of the asymptotically flat spacetime (I +) can be
dynamically described by a pair of SU (2) Chern-Simons theories, based on the recent developments
by Ashtekar and Speziale
We then quantize
I + using the Chern-Simons quantization scheme and compute its entropy by counting the number
of the microstates.
This work represents a first step toward developing a quantum theory of I +.
"if true how would you explain why the second and third generation are heavier, in principle."
My heuristic, non-rigorous logic runs something like this:
Hadrons have discrete excited states, in principle, infinitely many of them although the mass increments from one excited state to the next get smaller with each higher state (this is a much bigger deal with mesons than with baryons). In the context of hadrons, excited states always have more mass-energy because they have excitation energy beyond their ground state.
Due to the mathematical structure of the electroweak model and the Standard Model, any given generation has to be complete (i.e. it must have one up-like quark, one down-like quark, one charged lepton, and one neutrino). So, if any member of that generation can't exist, then the entire generation can't exist.
Fundamental fermions change generation only via W boson interactions.
The mean lifetime of the top quark is just slightly longer than the W boson mean lifetime.
The mean lifetime of a particle is a derived quantity in the Standard Model, so we can determine what the mean lifetime of a hypothetical fourth generation fundamental fermion would be if it existed.
We know that a fourth generation quark would have a mean lifetime much shorter than a W boson.
But it can't have a mean lifetime shorter than the particle whose existence facilitates the generation change.
Therefore, there cannot be a fourth generation of fundamental fermions.
An extended version of Koide's rule determines the relative masses of the quarks, and Koide's rule determines the relative masses of the charged leptons, and something similar like Brannen's variation of Koide's rule for neutrinos determines the relative neutrino masses.
All of these rules represent a dynamical balance of masses as a result of W boson interactions between particles that can transform into each other. Koide's rule for charged leptons is simpler than the extension for quarks, because neutrinos have approximately zero masses, unlike up-like and down-like quarks which all have significant masses.
The ground state masses are determined primarily by self-interactions and secondarily by W boson interaction balancing (which, for example, is the source of most of the up-quark mass).
The overall mass scale of the Standard Model fundamental particles, collectively, that provides boundaries to what would otherwise be only relative dynamical balancing is set by the Higgs vacuum expectation value which is a function of the weak force coupling constant.
The CKM matrix and PMNS matrix are logically prior to the SM constants for the masses (or equivalently the Higgs Yukawas) of the fundamental particles of the SM. These matrixes, in principle have four parameters each, although some of these parameters can be derived (e.g. the probability of a first to third generation transformation via a W boson is the same as the probability of a first to second generation transformation times the probability of a second to third generation transformation). It is even possible that the CP violation phase has a distinct theoretical source from the other three parameters, even though we can't distinguish that observationally. I don't know where the CKM and PMNS matrix parameters come from.
Another way to rule out a fourth generation is that the Higgs field Yukawas need to add up to exactly one, and there isn't any room for a fourth generation of particles since that would bring the sum of the Yukawas about exactly one.
Now, this does leave a puzzle. The best fit values of the Yukawas of the SM fundamental particles actually sum up to slightly less than one (although the uncertainties in the top quark and Higgs boson masses mean that this result is only in mild tension with the data, i.e. slightly more than two sigma), as the combined top quark and Higgs boson masses are both on the light side from a value predicted by these means.
Now, given that the fundamental fermions in the SM appear to be complete, that is potentially a hint at BSM particles that interact, at least, via the weak force - potentially with a mass on the order of 3-10 GeV, if from a single particle, but much less (or zero) if the current estimate for the top quark or Higgs boson masses are lower.
On the other hand, the decays of the W and Z bosons strongly suggest that the SM set of fundamental particles that interact via the weak force is complete.
Another interesting piece of this analysis is that the sum of the Yukawas of the SM fundamental bosons is greater than the sum of the Yukawas of the SM fundamental fermions, at a statistically significant level, even though they are close to 50-50. Thus, we have a slightly bosonic leaning universe rather than one that is evenly balanced between fermions and bosons (which would be one way to imagine "supersymmetry"). This is basically just trivia and is just how the universe is, but it's one more of those "close but not perfect" features of the SM, a bit like how the CP violation phase in a parameterization invariant form, isn't quite maximal.
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