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First: Scientific theories are never proven, only not falsified. Repeat that until it sinks in. Now, for the actual content of the question: That we only have perturbative ways to compute the S-matrix/scattering amplitudes for the Standard Model is not a reason to doubt its validity. Almost no physical system, apart from toy models, can be solved exactly, ...

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Suppose you have a quark of color state $\lvert q\rangle$. Or equivalently, you could write the color state as a 3-component vector, but for now I'm abbreviating it with a smaller symbol. Anyway, if that quark interacts with a gluon whose color matrix is $T_g$, the outgoing quark has a color state of $T_g\lvert q\rangle$. A red-antired gluon would be ...

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Very weird things are happening indeed. Unless you take a step back and think... By choosing the upper component to carry the vacuum expectation value, you will find that the electric charge $Q=T^3+Y$ appears to no longer be conserved by the vacuum (try it out by making the appropriate transformation). Instead, the conserved charge is now $Q_\text{new} = ... 3 The 3 pions can be considered as 3 states of the same particle, the isospin being used to label the 3 states. Since pions are bosons, the total wave function must be symmetric (Pauli principle). The total wave function is the (tensorial) product of space-wave function, spin wave-function and isospin wave-function. Spin wave-function is symmetric since pions ... 1 Both protons and neutrons are made up of two types of quarks: up (u) and down (d). Protons are uud and neutrons udd. QCD, the strong force binds these quarks together into protons and neutrons (technically, the binding involves a "sea" of gluons and quark-antiquark pairs). There is an approximate symmetry of QCD called isospin. Both the u and d quarks are ... 1 If you calculate the ratio between the proton mass and its constituent quarks, you'll see that the quarks actually account for only 1.0% of the proton mass. A similar calculation for a neutron shows that quark masses account for 1.3% of the neutron mass. Thus for both of these particles, 99% of the mass is not simply the sum of masses of the subatomic ... 1 baryons are a superclass of protons and neutrons. More broadly, they would be considered to be any particles made up of three quarks. They will interact via both the strong and electroweak forces Leptons are spin 1/2 particles that interact via the electroweak force but not the strong force. photons are neither leptons nor baryons (which are both ... 1 I don't really like summaries like that cause there's too many short-cuts taken in the summary - but that's my personal take, you don't have to share that opinion. I like this one better, as it has pictures: http://abyss.uoregon.edu/~js/cosmo/lectures/lec22.html The first sentence you quoted - as pointed out, is incorrect, or, at least, said badly. "As ... 1 In standard model, the mass of a particle can be explain by either Dirac or Weyl equation. The first thing is that neutrinos are can't be described by any of the above equations (Dirac equation or Weyl equation) in the standard model because no right handed neutrinos are observed. Dirac equation needs four spinors to explain the mass of any particle. But in ... 1 The actual values of the Yukawa couplings are arbitrary, and put in by hand (depending on the mass) and the matrices chosen are labelled however you like. That said, you are always free to choose which component of your scalar field gets a vev, by a global rotation. The scalar fields as you have written them are related by such a rotation$$\phi' = ... 1 JakobH's comment as an answer: The electroweak gauge group$\mathrm{SU}(2)_L \times \mathrm{U}(1)_Y$is broken into the electromagnetic$\mathrm{U}(1)_\text{em}$by the Higgs field acquiring a non-zero vacuum expectation value, granting masses to the quark and$W^\pm,Z\$ bosons. Thus, at the scale where up- and down-type quarks have very different masses, we ...

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