7

Flavor is entirely orthogonal to color - the gluon(s) neither "know" nor "care" about flavor, but the existence of different quarks still leads to phenomena descending from the strong force that you wouldn't get without them: What remains of the strong force on the scale between nucleons is often called the residual strong force and can ...


3

Looks like the classic "catch my sloppiness" exercise on Schwartz. (My students got extra credit for those). I edited your question to drop P&S in favor of S, clearly your intention. Let's only deal with $F_\pi\sim 93$MeV, to avoid confusion. In your (1), you took his τs to be Pauli σs, when he clearly takes them to be the real SU(2) ...


2

No, "lifetime of an up quark" is utterly meaningless (at least here, but I'd be hard pressed to find legitimate contexts for it...). The lifetime discussed is that of a neutral pion, decaying by the F diagram (sorry) In words, the pion "resolves" to virtual states of its valence quarks, u or d, which then couple to two real photons, to ...


1

Just to state the result for the beta-function associated to QCD \begin{equation} \beta = -\frac{g^2}{32 \pi^2} \left(\frac{11}{3}N_c - \frac{2}{3}N_f \right) \end{equation} in which $N_c$ is the amount of colours and $N_f$ is the amount of flavours. Essentially, both terms boil down to antiscreening and screening respectively. A single quark can be ...


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