# Electron charge vs quark charge

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## Main Question or Discussion Point

I have been trying to understand some of the basic differences in the fundamental nature of leptons and quarks. One article on this issue compares leptons and quarks as "oranges vs apples" to which I basically agree except for one aspect. How can the charges of the quarks be 1/3 or 2/3 the "exact" value of the electron if the leptons and quarks are supposed to be so fundamentally different?? I don't think this is serendipity working.

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Staff Emeritus
2019 Award
How can the charges of the quarks be 1/3 or 2/3 the "exact" value of the electron if the leptons and quarks are supposed to be so fundamentally different?
In unified theories this comes about naturally. Quarks and leptons sit in the same multiplets.

In unified theories this comes about naturally. Quarks and leptons sit in the same multiplets.
Can you provide a reference for further reading. Thanks.

Staff Emeritus
2019 Award
Georgi, Howard; Glashow, Sheldon. "Unity of All Elementary-Particle Forces". Physical Review Letters 32 p.438. (1974)

Georgi, Howard; Glashow, Sheldon. "Unity of All Elementary-Particle Forces". Physical Review Letters 32 p.438. (1974)

https://en.wikipedia.org/wiki/Grand_Unified_Theory

"The fact that the electric charges of electrons and protons seem to cancel each other exactly to extreme precision is essential for the existence of the macroscopic world as we know it, but this important property of elementary particles is not explained in the Standard Model of particle physics. While the description of strong and weak interactions within the Standard Model is based on gauge symmetries governed by the simple symmetry groups SU(3) and SU(2) which allow only discrete charges, the remaining component, the weak hypercharge interaction is described by an abelian symmetry U(1) which in principle allows for arbitrary charge assignments.[note 1] The observed charge quantization, namely the fact that all known elementary particles carry electric charges which appear to be exact multiples of ⅓ of the "elementary" charge, has led to the idea that hypercharge interactions and possibly the strong and weak interactions might be embedded in one Grand Unified interaction described by a single, larger simple symmetry group containing the Standard Model. This would automatically predict the quantized nature and values of all elementary particle charges. Since this also results in a prediction for the relative strengths of the fundamental interactions which we observe, in particular the weak mixing angle, Grand Unification ideally reduces the number of independent input parameters, but is also constrained by observations."

What if there is really no GUT (the same reference says evidence for GUT is lacking)? Is there another alternative explanation how the charges of the quarks can be 1/3 or 2/3 the "exact" value of the electron if the leptons and quarks are supposed to be so fundamentally different??

Or is GUT (or other symmetry groups) the only explanation?

ohwilleke
Gold Member
I have been trying to understand some of the basic differences in the fundamental nature of leptons and quarks. One article on this issue compares leptons and quarks as "oranges vs apples" to which I basically agree except for one aspect. How can the charges of the quarks be 1/3 or 2/3 the "exact" value of the electron if the leptons and quarks are supposed to be so fundamentally different?? I don't think this is serendipity working.
I would not favor the oranges and apples analogy for leptons and quarks. An analogy more like screws, bolts, nuts and washers that come in three sizes each, or maybe different kinds of legos, might be more apt. Heck, even Pokemon types would be a better analogy.

Fundamental particles are subtly different interchangeable parts that can be transmuted into other kinds of interchangeable parts in the right interactions. All fundamental fermions have the same spin and propagate in essentially the same way, except for color charge, electrical charge and mass and behave in a very particular way with W bosons. The three generations of four fundamental fermions each are identical exception for the fact that they have normal hierarchy masses (with an increasingly improbable exception given experimental data of an inverted neutrino mass hierarchy) and different W boson transformations.

The nature of fundamental quantum physics is that lots of quantities come in discrete rather than continuous increments, Plank's constant, for example, measures that granularity.

The 1/3 and 2/3 increments, recall, are just reverse engineered from the fact that all hadrons have integer electric charges just as all leptons do. Three color charges (which are only stable if you have one of each or a color and an anticolor of the same type in a hadron, of both) and electric charges of +/- 1/3 and +/- 2/3 is the most parsimonious way to get there and happen to work.

Some of the intuitive ways to get a system of fermions and/or fundamental particles like this are preons (more fundamental subparts) or strings (where different twists or standing waves translate into fundamental particles of a single indivisible kind of fundamental particle) or different kinds of field excitations (resonnances) in a quantum field theory. It has also long been noted that various Lie groups/Lie algebras correspond rather neatly to the Standard Model particle spectrum, but this was mostly an after the fact realization rather than a predictive tool.

The trouble is that anything that explains the Standard Model particle spectrum and the properties of its "fundamental" particles is beyond our power to observe apart from the Standard Model that we observe. We haven't found the tool that allows us to look under the hood of this part of the Standard Model yet. At a minimum there is a big "desert" of new phenomena between the Standard Model particle electroweak scale and the next deeper "under the hood" energy scale at which phenomena revealing the nature of the mechanism behind this might be revealed.

To some extent, all possible combinations of a set of discrete properties are realized in fundamental particles with the notable exceptions of electrically neutral quarks, and particles with rest mass that do not interact via the weak force. The patterns hiding in the constants of the Standard Model are another set of clues. Those omissions and those constants are pretty much the best clues that we have to what is going on at a deeper level, and alas, they aren't a complete enough set of clues to solve the mystery.

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bluecap
Demystifier
Gold Member
How can the charges of the quarks be 1/3 or 2/3 the "exact" value of the electron if the leptons and quarks are supposed to be so fundamentally different?? I don't think this is serendipity working.
That's needed for anomaly cancellation. See e.g. Ryder's QFT, Eq. (9.275).

haushofer
Can you provide a reference for further reading. Thanks.
Zee has a very clear exposition of GUT's in his "QFT in a Nutshell".

ohwilleke
Gold Member
I have been trying to understand some of the basic differences in the fundamental nature of leptons and quarks. One article on this issue compares leptons and quarks as "oranges vs apples" to which I basically agree except for one aspect. How can the charges of the quarks be 1/3 or 2/3 the "exact" value of the electron if the leptons and quarks are supposed to be so fundamentally different?? I don't think this is serendipity working.
One other relevant thought that doesn't rely on preon type reasoning, and illustrates that leptons and quarks are part of a common scheme rather than being "oranges and apples."

Because the W boson has a charge of +/- 1 and because the W boson converts up-type quarks to down-type quarks and visa versa, the difference in charge between an up-type quark and and a down-type quark must be exactly one.

And, because charged leptons and neutrino transitions also occur via W boson exchanges, the difference in charge between an up-type quark and a down-type quark must also be exactly one.

And, because W boson exchanges mediate both flavor changes in quarks and flavor changes in leptons, the difference between up-type quark and down-type quark charge, and the difference between charged lepton charge and neutrino charge must be the same.

So, in any case where neutrinos are electrically neutral, the difference between the up-type quark charge and the down-type quark charge must be equal in magnitude to the charge lepton charge. And, if any one of the four categories of fundamental fermions is electrically neutral, you difference between the other kind of fundamental fermions in charge must be the same as the charged version of the kind of fermion that has one category with zero charge.

Quarks and leptons are actually much alike. Quarks and charged leptons are both described with Dirac fields, though neutrinos may instead be Majorana fields. Quarks and leptons have very similar electroweak couplings, including very similar Higgs-mechanism mass generation for quarks and charged leptons. Quarks have QCD couplings, something that leptons do not have, but those couplings are much like their electroweak couplings. In Grand Unified Theories, quarks and leptons are typically side by side in the same multiplets.