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How can we see that the group $N$ generated by $$ g = (e^{2\pi i/3} I, -I, e^{i\pi /3}) \in SU(3)\times SU(2)\times U(1) $$ acts trivially on all fields in the Standard Model? First of all, note that $g$ is in the center of $SU(3)\times SU(2)\times U(1)$. Therefore its representative in the adjoint representation is the identity. Since gauge bosons ...


The main point is that if one has a consistent gauge theory with matter with gauge group $$G:=SU(3)\times SU(2)\times U(1),$$ if one divides $G$ with a normal subgroup $N$, the matter representations of the matter fields could potentially become multi-valued. However, it is possible to choose $N=\mathbb{Z}_6$ in such a way that the standard model matter ...


Baez actually has another paper (with Huerta) that goes into more detail about this. In particular, Sec. 3.1 is where it's explained, along with some nice examples. The upshot is that the hypercharges of known particles work out just right so that the action of that generator is trivial. Specifically, we have Left-handed quark Y = even integer + 1/3 ...


Color charge in the sense of "being blue, red, green" is not a quantum mechanical observable because the $\mathrm{SU}(3)$ gauge transformations mix the colors. This means it is meaningless to say "We have a blue particle", because we can perform a gauge transformation and then we "have a red particle". Since physical descriptions related by gauge ...


My "answer" to this question is, for the moment at least, do more reseach and update this current note with more details as I discover them. I am reluctant to withdraw this question for the moment, I asked it ahead of myself and my knowledge level but I will return to it, even if only for my own personal notes. The answer to my question may lie in a ...


I can think some speculative or unorthodox answers, and sure others can do, so please allow me to mark this answer as Community Wiki: three generations make a nice number of degrees of freedom for a GUT model. Assuming that the neutrinos have companions of the other chirality, one generation has 36 degrees of freedom. With this, the MSSM happens to have ...


The relativistic mass of the photon is not zero, it is $\frac{h\nu}{c^2}$. The rest mass of the photon is zero, but according to spec. rel it goes always with $c$.


No, there are just spin-0, spin-1 and spin-1/2 particles, even the Higgs-Boson is 0.


The VEV is quantum mechanical, it can not be read off from the Lagrangian. To find the VEV from the potential requires one to quantise the theory, then calculate the effective action at strong coupling. What should happen is that at strong coupling the quarks form hadrons; which are quark condensates. To perform the calculations is very tough and not yet ...


In addition to TwoBs' comments, in the 90s, there had been many collisions at SLAC (USA) with polarized electron/positron beams of the SLC collider running at the $Z$ pole. Therefore, the right handed component of the electroweak interaction has been extensively tested. See the wikipage: http://en.wikipedia.org/wiki/SLAC_National_Accelerator_Laboratory


Is there something wrong with this process? (it will admittedly be suppressed by $|V_{su}|^2\approx \frac{1}{20}$, i.e. "doubly cabbibo suppressed") or maybe even replace the Z boson with gluons.


Is there anyone knowledgable enough in this area who would be able to comment on some of the possible theoretical/ hypothetical implications of the existence of spin 3 particles? Is there any thought that their existence could imply additional fundamental forces? If you look at the presentation linked in the link you gave , in page five, you will see ...


As ACuriousMind said, the fact that the particle is composite makes it less earth-shattering. The interesting thing here (I think...not a high-energy guy) is that it's the first example of this kind of spin-3 particle, in particular flavored. Other composite spin-3 particles have been known before, the first one I found was a Boron nucleus.


Yes, wikipedia has a table which lists the 19 free parameters that need to be tuned by experiments. These include, as you already said, the masses of the elementary particles including the Higgs Boson, and some other notable ones are: CKM Mixing angles and CP-violation phase. Gauge coupling of he three symmetries (U(1), SU(2), SU(3)). Higgs VEV

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