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3

If a particle changes flavor, it's a charged-current weak decay. Example: $n\to pe\bar\nu$. If there's a neutrino in the final state, it's a weak interaction. Decay example: $\pi^+\to\mu^+\nu$. See also neutrino scattering. If parity isn't conserved, it's a weak interaction. Examples: $K^0 \to 2\pi$ and $K^0 \to 3\pi$. Note that kaon decays and $K\... 4 See, the thing is that spin is actually a vector — it has also a direction. When considering such vector in quantum mechanics, 2 observables describe it completely: its norm ($S$) and projection on one of the axis (usually,$S_z$). For a spin-$\frac12$particle the norm is$S=\frac12$and$S_z = \pm \frac12$. Then, for a system of 3 spin-$\frac12$particles,... 4 "A bunch of cool complex analysis stuff popped up and solved my problem" is about as honest as it gets. But physicists do this from more or less their first differential equation: using$e^{i \omega t}$to track both solutions via the cool-ness of complex analysis. There's no a priori or manifestly physics-based reason to do it that way. In the "original" ... 0 The QCD Lagrangian that has a CP violating symmetry is $${\cal L}~=~-\frac{g^2}{4}F_{ab}F^{ab}~-~\frac{g^2\theta}{4} {F_{ab}}^* F^{ab}~+~\bar\psi(i\gamma^a D_a~-~me^{i\gamma_5\theta})\psi$$ where the angle$\theta$is the chiral phase and a field that mixes fields. It is even proposed to look for this angle or field in its mixing of electromagnetic$\vec E$... 1 0) Note that in general, there is no need for the lattice spacings in different direction to be the same, as long as they all go to zero in the continuum limit. We can, for example, take the lattice spacing in the$x$direction to be$a$, and the spacing in the$y$direction to be$2a$. This is frequently done to achieve better resolution without the ... 2 Confinement is a low energy phenomenon. By this I mean that as you increase the energy with which you probe the properties of quarks they appear more and more like free particles. This property is called asymptotic freedom. If we had some hypothetical accelerator capable of doing experiments at energies where stringy effects start to be significant it would ... 0 I think the above picture with captioning below answers the question best, at least for me. Basically the green quark emits a green-antiblue gluon, turning it blue. This gluon is absorbed by the blue gluon, and it changes from blue to green, restoring the color symmetry and keeping the Baryon overall colorless. And it happens so fast that no overall Baryon ... 0 No, not at all! The color of the quarks has no effect whatsoever. If you're studied intro physics, you know that a potential$V(x)$is identical in every way to a potential$V(x) + V_0$for some constant$V_0$. Now consider two hydrogen atoms, where I've set the potential at infinity to be$3 \text{ V}$for one of them and$4 \text{ V}$for the other. ... 0 Hadrons come in 2 families: baryons and mesons. Both of them consist from colourless combinations of quarks. Mesons contain pairs of quarks of colour-anticolour and hadrons contain 3 quarks of different colours making them white in analogy with regular colour perception. You are right that quark can change its colour by interaction with gluons, but the ... 0 So basically you start with some current in SCET. You do the matching on the full QCD and you observe that not all of the divergences cancel. As usual you have to introduce a counter-term in your effective theory. What is special in SCET is that at the one loop level your bare Willson coefficient will have terms of the order of$\frac{1}{\epsilon^2}$and$\...

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It is not true that scale invariance requires strong interactions. After all, free scalar field theory is scale invariant (and so is classical electromagnetism). In high energy interactions approximate scale invariance emerges because asymptotic freedom implies that free field theory is indeed a useful starting point. QCD is subtle because we cannot study ...

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@Michael Brown is right. The SM has 12 exactly conserved charges. All local invariances, a fortiori also imply global invariances, if you ignore (for the sake of argument) the spacetime variability of transformation parameters/angles. So SU(3) has 8, not 3 conserved charges, RG, BG, .... The group has 8 generators. Likewise, SU(2) has 3, not 2 conserved ...

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