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The Standard Model is consistent in perturbative expansions. It is inconsistent non-perturbatively but all these inconsistencies only show up "qualitatively" at energies well above the Planck energy – where we know the non-gravitational Standard Model to be inapplicable, anyway. The inconsistencies of the Standard Model involve the Landau poles – the ...


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Yes, massive particles such as W-bosons, Z-bosons, quarks, and leptons couple to the Higgs field via the cubic (Yukawa) interaction, so they may also exchange the virtual Higgs. Yes, because the virtual particle is massive, one gets the Yukawa potential that includes the exponential dumping with distance. This "Higgs force" is much less fundamental and ...


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The reason is that the $SU(2)$ invariant in $\mathbf{2}\otimes\mathbf{2}$ (or in their complex conjugate $\mathbf{2}^*\otimes \mathbf{2}^*$) is given by contracting the two $\mathbf{2}$ with the anti-symmetric $2\times 2$ matrix $\epsilon_{ab}$, as $i\tau_2$ is. In the case at hand the two $\mathbf{2}^*$ are $\bar{Q}$ and the $\Phi^*$. You could form another ...


4

The Standard Model Yukawa interactions must be $SU(3)\times SU(2) \times U(1)_Y$ gauge invariant. The down-type Yukawa interaction is $$ \mathcal{L} \supset -y_d \bar Q \phi d_R + \text{h.c.}. $$ This is indeed gauge invariant. The $\bar Q d_R$ form a colour singlet ($3^* \times 3$), the $\bar Q \phi$ form an $SU(2)$ singlet ($2^*\times2)$, and the whole ...


4

The difference between the Higgs boson and the bosons of the three/four fundamental (depending whether you include gravity as a quantized theory or not) actions is that the latter are associated with gauge symmetries, while the Higgs plays a role in spontaneous symmetry breaking. Photons, W- and Z-bosons, gluons and gravitons arise from the requirement that ...


4

I addressed this a little at your other question but this one is more like physics. Yes, they're decay product lists. Beware that if all the modes are only "seen" or "not seen," you are sort of looking at the hairy edge of what's experimentally accessible. The indented lines are subtypes of the same reaction. Using your example, a neutral particle can ...


3

Lets analyse the Majorana condition and the Majorana mass term. A massive Majorana neutrino $\chi_j$ (a Majorana spin $1/2$ fermion) having mass $m_j>0$ can be described in a local quantum field theory (eg. the standard model) by a four component spin $1/2$ field $\chi_j(x)$ which satisfies the Dirac equation and the Majorana condition which reads: $$ ...


3

Indeed, the Standard Model is consistent in perturbative expansions, which acutally means that we do not really know if the Standard Model is consistent or not. So it is possible that the original Standard Model with 15 Weyl fermions per family is not consistent. In other words, there may not exist any well defined quantum model, whose low energy effective ...


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The important point is the fact that such a mass term breaks the gauge symmetry (Edit: I am assming that you want to build the Majorana mass term using SM available fields -- no extension considered -- of which there is only $\nu_L$). Namely, the desired term is (one generation suffices): $$\frac{1}{2}\,M\, \nu_L^T \,\mathcal{C}^\dagger\,\nu_L\, +\, ...


2

Quark oscillations don't exist by the definition of a quark. A quark is defined as a mass eigenstate and thus it is not going to oscillate with time (energy eigenstates don't charge with time of course!). To see how this works consider the relevant quark interaction terms without any choice of basis, \begin{equation} - m _d \bar{d} d - m _u \bar{u} u - i ...


1

The easiest way to form $SU(2)$ singlets in the most general way is to use the techniques of Young Tableau. The method is discussed from a physicists perspective in many lecture notes online. One such example is given here. Using such method its easy to show that 2 lepton doublets make a singlet and a triplet under $SU(2)$, \begin{equation} 2 \otimes 2 = 3 ...


1

The standard model of particle physics is the unification of electroweak and strong interactions: The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. It was developed throughout the latter half of the 20th century, as a ...



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