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How did the $SU(3)\times SU(2)\times U(1)$ come to be the standard model of particle physics? After years and years of experiments that showed up the quark model, which lead to the standard model. example of symmetries in the data: The meson octet. Note that even though the symmetry splits according to charge and strangeness, there is a mass dependence in ...

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It's definitely a legitimate question. The standard generation assignment $$(e, \nu_e, u, d)\\ (\mu, \nu_\mu, c, s)\\ (\tau, \nu_\tau, t, b)$$ is essentially arbitrary: the only rational of the above generation assignment is the relative magnitudes of masses. If we adopt an alternative generation assignment, say $$(\mu, \nu_\mu,u, d)\\ (\tau, \nu_\tau, c,... 1 You need the standard, but not obvious, integrals$$ \int_{-\infty}^\infty \frac{d\epsilon}{2\pi}\frac 1{2!}\left(\frac{\epsilon}{2\pi}\right)^2\left\{ \frac{1}{1+e^{\beta(\epsilon-\mu)}}-\theta(-\epsilon)\right\} =\frac{1}{3!}\left(\frac{\mu}{2\pi}\right)^3+\left(\frac{\mu}{2\pi}\right)\frac{T^2}{4!}\\ \int_{-\infty}^\infty \frac{d\epsilon}{2\pi}\frac1{3!}\...

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The standard model of particle physics, which has the quarks and leptons in group structures of $SU(3) \times SU(2) \times U(1)$ was developed BECAUSE most of the data of particle physics can be fitted with this model, and because it is successful in predicting new data. That is why you can write a number of possible quark states and quark antiquark states, ...

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This is a question that entails the ability to manage QCD at low energies and this is an active field of research yet as we are not able to do it, unless for lattice computations. It can be considered as part of the more general problem of the determination of the phase diagram of QCD (see my answer here). The idea of chiral symmetry breaking in strong ...

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