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Supersymmetric theories are based on the introduction of an extra symmetry between fermions and bosons. Standard Model is very non-supersymmetric, so people have been considering "minimal" supersymmetric extensions of the standard model (MSSM). So, first of all, your question title is not entirely correct - we are talking about minimal versions of ...


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I presume you take $$ \Phi = (v_1+h_1) e^{i\xi_1/v_1},\\ \chi = (v_2+h_2) e^{i\xi_2/v_2}, $$ for dimensional consistency, with $\langle h_i\rangle=0=\langle \xi_i\rangle$. The potential is flat w.r.t. the $\xi_i$s. Ignore the Higgses $h_i$ at first. The remaining piece of the Lagrangian is $$ \frac{1}{2}e^2[ v_1^2(A_\mu-\frac{1}{ev_1}\partial_\mu\xi_1 )^2 +...


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I'm not sure how to undo the untold damage of popular science writing wispy metaphors, entrapping you to think along elusively absurd lines. From your careful wording I can see you are not involving the Higgs boson, soundly, but just the Higgs bosonic field, whose vacuum expectation value achieves three things through the symmetry realization it shapes. It &...


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It is broken to whichever subgroup of the original group that leaves the VEV unchanged.


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A decay doesn't have a cross section associated with it, only a decay width. Most likely they are referring to the production cross section for the process $\rm X+X\to H\to W^+W^-$ at some specific collider. Note that this depends on the identity of the initial particles and their momenta. It can also depend on other properties such as the polarization of ...


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The ground state (or vacuum state) minimizes the energy, not just the potential. A solution of the field equations with non-constant field $\phi$ (satisfying $|\phi(x)|=\phi_{0}$, so that the potential is minimized) will still have kinetic energy associated with it—making it automatically not the vacuum. That’s all there is to say about finding the vacuum ...


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The term "quantum entanglement exists" is a subset of the term "there exists a single quantum mechanical wavefunction describing the system". If you know the wavefunction, i.e. have a mathematical description of it, the theory of quantum mechanics has constraints on quantum numbers and their conservation, so quantum numbers are "...


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You're supposed to think of $\mu^2$ as a parameter, and there's no need to consider if it $>0$ or $<0$. You proceed by minimising the potential and then seeing that the nature of vacuum/vacua is different for $\mu^2>0$ and $\mu^2<0$. As @CosmasZachos mentioned in the comments, it is certainly a function of $T$. The exact function can be ...


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Let's say you have a certain gauge theory, i.e., a QFT with gluons plus, perhaps, some other matter fields. Take for example one of such matter fields $\phi$. In general $\phi$ will couple to the gluons, i.e., it will interact with them. In fact, it is possible that $\phi$ only interacts with some of the gluons. Let's give these objects some names. Take the ...


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You get a pure imaginary number because the decay from rest of a Higgs into two W bosons is not allowed kinematically, for the masses you used.


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