What Determines the Electric Charge of Fundamental Particles?

[Akhilesh Kumar]

We have been able to explain the reason for the mass of a particle to a great extend... But till now why are we not getting a clear idea of why does a particle has charge?? What gives a particle its charge??

 

[mfb]

We have been able to explain the reason for the mass of a particle to a great extend

Do we?
We have a theory that gives the correct results. The same is true for all types of charges. I guess you mean the electromagnetic charge here. You can just assume the existence of particles with a coupling to the electromagnetic field, and it works nicely and gives the correct results.
Physics cannot answer "why" questions on a fundamental level. It can only give descriptions that allow to predict measurements.

 

[Dr. Courtney]

Charge is a fundamental quantity. We know that it is and how it works, but I'm not sure we know why it exists.

Existential problems are challenging is science.

 

[ohwilleke]

We have been able to explain the reason for the mass of a particle to a great extend.

Not really. We have determined that fundamental particles derive their mass from their coupling constant to the Higgs boson, but we have no deeper understanding of why those coupling constants (called Yukawas) take the value that they do.

The most obvious and alluring way to answer to the question of why particles have the electric charge that they do, which would be that the fundamental particles of the Standard Model are made of smaller particles (conventionally called "preons") (just as protons and neutrons are made of more fundamental particles calls quarks whose mix explains the charge of the composite hadrons) with charges of 1/3 and their antiparticles with charges of -1/3 that combine to form various Standard Model particles has been explored at considerable length, but so far, the experimental evidence has pretty much ruled out that possibility. There is no experimental evidence to suggest that quarks, leptons, or fundamental bosons in the Standard Model are composite. The energy scales at which composite quarks and composite leptons are excluded are higher than almost any of the other exotic phenomena exclusions at the LHC (approaching 10 TeV), and preon theories with binding energies at these scales usually start to create paradoxes that could actually make them impossible.

We could reach a point sometime in the future when we can explain why fundamental particles in the Standard Model have the electric charges that they do (and theories that try to do that call "Grand Unified Theories" generally resort to the combinations allowed by various kinds of algebraic structures called "groups" to do so), but ultimately, any such explanation replaces one arbitrary set of charge values with another slightly more parsimonious set of arbitrary rules.

Before the Standard Model was invented, a number of theorists tried to link the mass of a fundamental fermion like an electron, to the energy created by its electric field, sacrificing the question of why a particle had electric charge to divine fiat, in exchange for an answer to the question of fundamental particle mass. This effort looked pretty promising at first. But, that effort crashed and burned when we learned, for example, that there are three particles (the electron, muon and tau) with exactly the same properties except for their mass, and that there appear to be not an infinite number of "generations" of quarks and leptons (the way that there are an infinite number of exited states of each kind of meson and baryon), but instead exactly three such generations.

We aren't entirely hopeless and we have some hints. We have, for example, learned that a quantity called CPT is conserved in all interactions and that this principle explains by particles and their antiparticles have exactly equal and opposite electric charges. We have also learned that quarks with different electrical charge can have identical strong force color charge, or visa versa. We know that all fundamental particles have electric charges of +1, + 2/3, +1/3, 0, -1/3, -2/3 or -1. We also know that no fundamental particle with color charge has electric charge of +1 or -1 (gluons, which have color charge have electric charge of zero). And, we know that the law of nature that says that all quarks are confined in a color neutral hadron implies that all free standing particles in nature have integer electric charges (in all cases experimentally observed +2, +1, 0, -1, -2). We know that particles with zero electric charge can have no rest mass (photons, gluons), tiny masses (neutrinos), or huge masses (Z bosons and Higgs bosons). We know that particles with non-zero electric charge always have some mass, although these masses vary over many orders of magnitude from the electron to the top quark.

Likewise, when it comes to mass hierachies, we know that higher generation quarks and charged leptons are heavier than lower level ones (we don't yet know if the same is true of neutrinos), that the ratios of the electron mass to the muon mass to the tau mass follows a phenomenological relationship called "Koide's rule" and that the ratio of quark masses approximate but don't exactly fit, formulas that extend Koide's rule and formulas linking quark masses to the probability of transforming into other kinds of quarks in weak force interactions. There is also an interesting empirical fact that the sum of all of the Yukawas of the Standard Model particles is exactly equal to 1 up to experimental error, and that the sum of the Yukawas of the quarks and leptons is very nearly identical to the sum of equivalent coupling constants for the Standard Model bosons.

Some theorists feel like it is meaningful to explain why we have the fundamental constants we do in nature with something called the "anthropic principle". The reasoning goes that if the fundamental constants weren't exactly or very nearly exactly what they are, that it would be impossible for life to exist and therefore no one like your or me could exist to think about what value those fundamental constants took. For example, if free standing particles had non-integer electric charges, it would be very hard to get exactly balanced electric charges in physical systems which would lead to massive electrical fields everywhere in the universe which would not be good for the existence of life. But, most scientists don't find resort to the anthropic principle to be an answer to what they are looking for when they ask "why" the world is the way that it is.

But, the bottom line is, we do not know why particles have charge, nor do we know why they have the masses that they do. The Standard Model of particle physics simply puts those values in by hand at experimentally measured values as physical constants whose values are arbitrarily determined at the beginning of time.

It isn't impossible that we could discovery a deeper reason for the electric charges that we observe. Indeed, most physicists that I have met, deep down, believe that there is some deeper reason which we just haven't figured out yet for the Standard Model constants. But we need more pieces to the puzzle than we have in our current box of experimental results to come up with such a reason.