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There are many ways to generate the topological term $$(\bar\theta + \theta_a)G\tilde G\,.$$ Let's consider the simplest example, known as the KSVZ mechanism. Let's introduce a new vector-like quark $q$ to the standard model Lagrangian. "Vector-like" means that the quark does not have chiral symmetry, and so it is an electroweak singlet. It is a ...

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Without more context, the usual meaning of active quark is quarks whose rest mass is lower than the energy scale of the environment. So for example, the active quarks of $T = 0$ QCD are $u,d,s$ because they all have rest mass lower than the QCD scale, $\Lambda_\text{QCD}\approx 200\text{ MeV}$. In response to your updated question, active quarks are on shell....

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I have figured out an analogy and I would like to draw people's attention to it. Any constructive comment is welcome. Consider an electron (or any other spin-$1/2$ particle) in a magnetic field $\vec{B}=B\hat{z}$ along the positive $z$-axis. Both the spin-up and spin-down states are eigenstates of the Hamiltonian but with eigenvalues $\pm\hslash/2$. ...

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Following T. Plehn (p.7) the UV-renormalisation introduces a dependence on the renormalisation scale $\mu$ and then the IR-regularisation introduces a further dependence on the factorisation scale $\mu_F$. However, one is free to choose $\mu$, such that one can set $\mu:=\mu_F$ R. Brock et al.(p.104), D.E. Soper(p.38), W.K. Tung(p.19). Hence, J.C. Collins' ...

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If you want a more descriptive and a simple mathematical treatment using the formulation of electrodynamics and quantum mechanics, then Leonard Susskind's series of lectures will give you a lot of insights!! Here is the Link : https://inspirehep.net/literature/1532

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Quarks that are lighter than the QCD scale, ($\sim 200\,{\rm MeV}$) will always be confined, but heavier ones can be unbound. The top quark weighs $170\,{\rm GeV}$, so it can be unbound. The QCD scale is the mass scale that pops out when you renormalize the strong interactions.

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This is because the force-versus-distance law for quarks is such that the farther away from one another you pull a pair of quarks, the harder they attract one another. It is as if they were attached to each other with a rubber band (a very stiff one!). If you pull them far enough apart, there's enough energy stored in the system to create a new pair of ...

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Only the weak interactions can change the net flavour. The process $d + \bar{d} \to g$ and $g \to s + \bar{s}$ does not change the net number of down quarks or the net number of strange quarks, where the net number is the number of quarks minus the number of antiquarks.

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