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Completing the very good answer made by Andre Holzner, the electron and the positron in the initial state, have a non negligible probability to emit a photon with a significant energy. In particle physics jargon, this is called the ISR standing for Initial State Radiation. Therefore, you always have to be slightly above the threshold production to circumvent ...


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In principle, you don't need to tune to 'exactly' this energy but having less than $m_h + m_Z$ suppresses this diagram. Having more should typically give you a higher cross section because there is 'more phase space' the final state particles can be in, i.e. the 'excess' energy will just be used as kinetic energy of the final state particles ($Z$ and $h$ ...


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This equation suggests a path integral, of a Lagrangian that contains terms for both general relativity and the Standard Model in highly abbreviated form. Compressing it all into one line is a stunt, of course, rather than an actually useful equation. :) It glosses over many technical issues (for instance that we don't actually know how to do quantum ...


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To study Higgs mechanism, we can use a Lagrangian of the form: \begin{align} \mathcal{L}=(D_{\mu}\phi)^2-\frac{1}{4} F_{\mu\nu}F^{\mu\nu}-V(|\phi|) \end{align} Where: \begin{align} V(|\phi|)&=-2v^2|\phi|^2+|\phi|^4 \\ &=(|\phi|^2-v^2)^2-v^4 \\ D_\mu \phi&=\partial_{\mu}\phi+\mathrm{i}e A_{\mu} \phi \\ F_{\mu\nu}&=\partial_{\mu} ...


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I don't think it's proper to say that the spontaneous breaking of anything is attributed to the Higgs mechanism. It's a postulate of the theory that the potential takes a certain shape, and that shape leads to a symmetry, and that the symmetry is spontaneously broken. The Higgs mechanism is a consequence of that. The symmetry that is broken is the local ...


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For any particle, we can define a continuous quantum number - its momentum $k^\mu$ and a discrete internal quantum number - for instance, its spin or charge under some symmetry group (note spin is also the charge under Lorentz transformations). The continuous quantum number defines the mass of the particle via $k^2 = -m^2$. In any actual theory, $m^2$ is ...


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What equation do we use to measure the energy level of a string, to determine it's “particle correlation” We have already measured the particles. We have studied their properties and "measured" their quantum numbers as expressed in this table Measured within ( using the tools of) the standard theory of quantum mechanics and special relativity. ...


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From the previous comments, I'm quite sure $W_\mu$ transforms with a phase-factor. $$W_\mu \rightarrow e^{i\theta}W_\mu$$ therefore mixing the charged components of the $W$ field.


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Let me attempt to answer your question, since your question is about SO(10) GUT model, so I will assume that you have the knowledge of simpler version of GUT namely SU(5) GUT model and also little of group theory. You have 4 different questions >>> 01. Isn't this term ($\psi^{T} C \psi$) already invariant under SO(10)? 02. Doesn't this term ($\psi^{T} C ...



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