# Why is the up quark is lighter than the down quark, while top is heavier than bottom?

Up, charm and top seem to be similar in terms of electric charge (+2/3e) while down, strange and bottom have also same charge (-1/3e). In the second and third family, positively charged quark has higher mass, while in the first family, negatively charged quark is heavier.

Is there a particular reason why up quark is lighter than down quark, while in other two families, charm is heavier than strange, and top is also heavier than bottom?

• I'm almost sure that there is no reason up to now. Quark masses in QCD sector of SM are parameters of the theory and SM is called 'model' and not 'theory' because it cannot determine by itself those parameters. They are obtained by experimental measuring: this is named the 'naturalness' problem (see en.wikipedia.org/wiki/Naturalness_(physics)) Apr 3, 2019 at 20:50

In the standard model, the quark masses are proportional to their coupling to the Higgs field; but the magnitudes of those couplings (called yukawa couplings) are unexplained.

A theory which goes beyond the standard model, by explaining why the values of the yukawa couplings are what they are, has the potential to explain why the tilt of the quark masses is different in the first generation, compared to the other two generations.

For example, in some "vacua" of string theory, the yukawas depend on the surface area that quark strings have to cross in order to interact with the Higgs string - as the area to be crossed increases, the yukawa will be exponentially smaller. The distances and areas in turn depend on the resting configuration of the extra dimensions, and of any branes that they may contain.

A model like that has the potential to deliver an explanation, e.g. in terms of how the various branes arrange themselves when at rest. Although in practice, these geometric equilibria cannot presently be calculated in anything like the necessary detail, and it is counted a success if one can just show that one quark (the top quark) will be much heavier than the rest.

For now all this is speculation. Even if one believes that string theory is definitely the theory of everything, one has to admit that it encompasses vastly many possibilities, and we do not know at all which of them corresponds to our world.

I have, over the years, seen one or two theories of mass in which the tilt of the first generation had a clear and specific explanation. I will link them here if I can find them again.

• In short, we have no idea. Apr 16, 2022 at 0:08

We have absolutely no idea. Within the Standard Model there is no explanation, it just is. There have been speculative attempts to explain this kind of structure, but my impression is that they mostly focus on explaining why each family is much heavier than the last, not on the small differences within each family.

Within the first family, you can provide some anthropic "explanation". Since the up quark is lighter than the down quark, the proton ($$uud$$) is lighter than the neutron ($$udd$$). That means isolated protons are stable, while isolated neutrons will decay, via $$n \to p + e^- + \bar{\nu}_e.$$ Note that neutrons in atoms don't decay because of the stabilizing effect of the rest of the nucleus.

On the other hand, if the masses of $$u$$ and $$d$$ were swapped, then the proton would be heavier, and hydrogen would be unstable against the reaction $$p + e^- \to n + \nu_e$$ Since almost our entire universe is made of hydrogen, we'd just be left with a universe of mostly neutrons, far too bland to sustain chemistry and therefore life.

If you liked this explanation, see the paper Why the Universe is Just So for much more. If you didn't, join the club!

• I've always seen the anthropic explanation as the how is possible our existence but not the why is our existence as it is, which is the OP's question Apr 3, 2019 at 21:27
• @Vicky Absolutely, that's why I called it an "explanation" instead of an explanation. Whether or not it really is one is probably one of the most controversial things in high energy physics today. Apr 3, 2019 at 21:34
• You might call it a "significant property of the world we know"... Apr 3, 2019 at 22:51
• Is there actually theoretical explanation in the SM of the stabalizing effect? Apr 4, 2019 at 15:53
• @lalala Yes, the stabilizing effect of the nucleus on neutrons is well understood. Jun 23, 2019 at 2:03