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8

The relevant Lie group isomorphism reads $$\tag{1a} U(2)~\cong~[U(1)\times SU(2)]/\mathbb{Z}_2. $$ In detail, the Lie group isomorphism (1a) is given by $$U(2)~\ni~ g\quad\mapsto\quad $$ $$ \left(\sqrt{\det g}, \frac{g}{\sqrt{\det g}}\right) ~\sim~ \left(-\sqrt{\det g}, -\frac{g}{\sqrt{\det g}}\right)$$ $$\tag{1b}~\in ~[U(1)\times SU(2)]/\mathbb{Z}_2.$$ ...


6

The "generations" of matter are mainly based on the electroweak symmetry group $\mathrm{SU}(2)_L\times\mathrm{U}(1)$. All fundamental quantum fields are either a "singlet" or a "doublet" under the $\mathrm{SU}(2)$ part of this symmetry. The left-handed fields usually form doublets, and the up- and the down- quark form the first, the strange- and the ...


4

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 ...


3

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.


3

I think they just take a large amount of material and look for protons decaying in it. There are a lot of protons, so in order for none of them to decay the half-life must be absurdly long.


2

First, note that the equation you use is only valid when all relativistic particles are in thermal equilibrium. The more general equation, which allows for particles with different temperatures, is $$ g(T) = \sum_B g_B\left(\frac{T_B}{T}\right)^4 + \frac{7}{8}\sum_F g_F\left(\frac{T_F}{T}\right)^4 $$ where $T$ is the photon temperature and $T_B$, $T_F$ are ...


2

The Higgs mechanism is a theoretical formulation answering how a gauge boson may acquire a mass. The Higgs mechanism predicts the existence of a particle, called the Higgs boson. Particles may decay, for example the neutron decays into a proton, electron and a neutrino. Similarly the Higgs boson can decay. Its decay into two photons was the discovery ...


2

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


1

In standard model, the mass of a particle can be explain by either Dirac or Weyl equation. The first thing is that neutrinos are can't be described by any of the above equations (Dirac equation or Weyl equation) in the standard model because no right handed neutrinos are observed. Dirac equation needs four spinors to explain the mass of any particle. But in ...


1

You use that Im$(ab)= $Re$(a)$Im$(b) + $ Re$(b)$Im$(a)$, for $$a = V_{ub}V^*_{ud}\qquad\qquad b=V^*_{cb}V_{cd}$$ to get \begin{align*} \text{Im}(V_{ub}V^*_{ud}V^*_{cb}V_{cd})&=\text{Re}(V_{ub}V^*_{ud})\text{Im}(V^*_{cb}V_{cd}) + \text{Re}(V^*_{cb}V_{cd})\text{Im}(V_{ub}V^*_{ud}) \\ &=\text{Re}(V_{ub}^*V_{ud})\text{Im}(V^*_{cb}V_{cd}) - ...


1

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


1

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 ...



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