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Results tagged with standard-model
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user 36793
A model of the basic particles and forces featuring six quarks, three charged leptons, three massless neutral leptons and four fundamental force carrying bosons. The twelve fermions are arranged into three generations, while the bosons serve to explain the electromagnetic interaction plus the strong and weak nuclear forces (and the Higgs mechanism). Do NOT use this tag for the standard model of cosmology, etc..
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Can we derive the formula $Q=I_3+\frac{1}{2}(B+S)$ instead of accepting it as an empirical r...
The electric charge of a quark or lepton, $Q$, is related to the third component of the weak Isospin $T_3$ and weak hypercharge $Y$ according to the formula $$Q=T_3+\frac{Y_W}{2}.\tag{1}$$ This, in a …
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Anomalous baryon current in the Standard Model (SM) and the stability of free protons within...
In the Standard Model, the baryon number is not exactly conserved due to anomaly but the decay rate is extraordinarily small at ordinary temperatures. Does this make free protons unstable in the Stand …
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Anomalous magnetic moment form factor of $e^-,\mu^-$ and $\tau^-$ in QED
The anomalous magnetic moment form factor $F(q^2)$ of an elementary fermion at $q^2=0$, calculated at one-loop, is $$F_2(0)=\frac{\alpha}{2\pi}.$$ At least at this order (order-$\alpha$), $F_2(0)$ doe …
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Physical meaning of the form factors $F_1(q^2)$ and $F_2(q^2)$ for $q^2\neq 0$
The charge form factor $F_1(q^2)$ and the anomalous magnetic moment form factor $F_2(q^2)$ have clear interpretations at the value $q^2=0$ i.e. $F_1(0)$ is equal to the charge of the electron and $F_2 …
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Physical significance of the reality of an ${\bf N}$ representation: how the nature of inter...
Background The fundamental representation of ${\rm SU(N)}$ is denoted by ${\bf N}$ and the conjugate of the fundamental is denoted by ${\bar{\bf N}}$. If the representation ${\bf N}$ is related to ${ …
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A particle without gauge interactions
Sterile neutrinos do not have any gauge interaction (electroweak or strong) but only gravitational.
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Help me understand Lepton universality
In the limit of low momentum transfer i.e., $q^2\ll M_W^2$ and vanishing electron and muon mass, the electronic and muonic decay modes have equal decay rates i.e. $$\Gamma(\tau\to e^-\bar{\nu}_e\nu_\t …
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Why is the smallness of Higgs mass not technically natural?
Technical naturalness
The smallness of a parameter $\theta$ in the Lagrangian of a quantum field theory is said to be technically natural, if in the limit of vanishing $\theta$, the theory has some …
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Bare mass versus the mass form spontaneous symmetry breaking
Consider renormalization in $\phi^4$ theory $$\mathscr{L}=(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{\lambda}{4}\phi^4$$ where $m$ and $\lambda$ are respectively the unobservable bare mass and bare c …
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Why is the relation $M_W=M_Z\cos\theta_W$ true only at tree-level?
In Glashow-Weinberg-Salam electroweak theory, the relation $$M_W=M_Z\cos\theta_W\tag{1}$$ is said to be remain true only at the tree-level; it receives corrections from the loop diagrams. See here. Bu …
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What was the prediction of the standard electroweak theory about the $W$ and $Z$ boson masses?
The standard electroweak theory has two coupling constants $g$ and $g^\prime$. In this theory, the $W$ mass and $Z$ mass are given by $$M_W=\frac{1}{2}gv,~M_Z=\frac{1}{2}(g^2+g^{\prime 2})^{1/2}v$$ wh …
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Why does the upper component of a $SU(2)$ doublet has $T^3=1/2$ and lower component $T^3=-1/...
For a $SU(2)$ doublet, why does the upper component have $T^3=1/2$ and lower component $T^3=-1/2$?
I know that this can be answered in the Standard Model by using $Q=T^3+Y/2$. But that is because we …
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Light neutrino number from the invisible decay width of $Z$ boson, and precluding heavy neut...
The $Z$ boson decays into pairs of quarks and leptons. While the decays to quarks pairs and charged lepton pairs can be observed, the decays to $\nu\bar\nu$ are cannot be. By subtracting the visible d …
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4
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A question about the notation of the Standard model
The ${\rm SU(2)_L}$ doublets, for example, the left-handed quark doublets $Q_{iL}\equiv(u_{iL}, d_{iL})^T$ are assigned quantum numbers $(\textbf{3},\textbf{2})_{+1/6}$, which means $Q_{iL}$ are tripl …
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Higgs is neutral but decays into photons-Why?
Higgs is neutral and therefore cannot have electromagnetic interactions. Then how can it decay into a pair of photons? Does it mean that particles need not be charged to have electromagnetic interacti …
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