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The 2018 Particle Data Group gives a value of $880.2\pm 1.0$ s for free neutron lifetime, as an average of the seven best measurements. As can be seen, the measurements have non-overlapping confidence intervals. As discussed in (Wietfeldt 2014) the different experimental methods do not agree on the value. Wietfeldt gives the formula of the lifetime as $$\...


6

Simplest way? The $\Delta^{++}\sim uuu$ has to be a color singlet. It has spin 3/2, so it is flavor and spin symmetric. But fermion quarks need to be in a fully antisymmetrized state. Can you make an SU(4) singlet out of three antisymmetrized copies of an SU(4) representation, the way you can for SU(3)? (No.) (By now, you simply experimentally check R in $e^+...


3

This feels like a perfect storm of misconceptions, unleashed by unscrupulous popular science writing. Helicity is Lorentz-variant, so, as you envision, may be reversed by changing your frame. It is either positive or negative; never left-or right handed. Chirality is relativistically invariant, so a left-handed particle is left-handed in any frame, and ...


3

You might get better answers if you actually identified the particles involved and their decays. I'll just remind you of the dimensional analysis aspect of all of them, which you drill in an introductory HEP course: For weak decays involving one dominant scale, Γ with units of energy must go as the amplitude-squared, involving an exchange of a virtual W in ...


2

How could an up quark turn into a down quark through practical means? It cannot. Quantum mechanics is not deterministic, it depends on the probability of the decay, in this case, happening. Look at the decay It is a weak decay, and in addition it goes to a virtual W, and the probability of this happening is very small due to the weak vertex and the mass ...


2

The hierarchy problem has to be framed in the context of beyond standard model physics. You have to distinguish between 5 mass scales, namely $m$: the mass of the particle in concern, e.g. Higgs mass $m_H$. $\Lambda$: the UV cutoff scale of the regularization scheme (in dimensional regularization (DR), $\frac{1}{\epsilon}$ plays the role of $\Lambda$, ...


1

The rule for virtual particles is that they respect energy-momentum conservation at vertices but they do not need to be "on-shell", which amounts to saying that the combination $E^2 - p^2 c^2$ does not necessarily give the square of the rest mass of the corresponding real particle.


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Short answer: The second diagram is not the same as the first. In the second diagram there is another massive charged particle (top quark) present. A photon cannot spontaneously decay (you used the word decay which is technically not the same as pair production) into an charged lepton-antilepton pair because the leptons have a rest mass/rest frame while the ...


1

Lets make the comments into an answer: How does this relate to the image below? Are the black lines representative of gluons? The black line represent quarks, the wiggly ones gluons. So are gluons what mediate pion exchange, which is in turn what binds protons and neutrons with the strong nuclear force? The strong nuclear force is a spill over force from ...


1

Yes you are right that for electrons or muons, their Yukawa coupling is certainly NOT $O(1)$. You can have two interpretations of Mark Thomson's remark: The ratio of electron mass vs top quark mass is around $10^{-5}$. It is certainly NOT $O(1)$, but it is not as bad as $10^{-20}$ when comparing fermion mass with Planck mass. So Mark Thomson means that the ...


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Historicaly: From theoretical considerations, in 1934 Hideki Yukawa predicted the existence and the approximate mass of the "meson" as the carrier of the nuclear force that holds atomic nuclei together. If there were no nuclear force, all nuclei with two or more protons would fly apart due to electromagnetic repulsion. Yukawa called his carrier ...


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The point is that we define the new coupling parameter e as $$e:=g\sin\theta_W=g'\cos\theta_W$$ in order to avoid carrying around these longer expressions


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Phonons do not have all the ingredients required in the Standard Model (local symmetry, three fermion generations, scalar multiplet, SSB). Is this the reason why phonon are not in the boson list of SM? The table of particles axiomatically assumed for the standard model consists of point elementary particles, i.e.non composite. Phonons by the your ...


1

I'll talk just about leptons since I think this is enough to discuss this issue. We build our model with one ${\rm SU}_L(2)\times{\rm U}_Y(1)$ symmetry. In this model the leptons are represented by a left chiral fermion $\ell_L$ and a right chiral fermion $\ell_R$. The $\ell_L$ forms an ${\rm SU}_{L}(2)$ doublet with its corresponding neutrino $\nu^\ell$. We ...


1

Ugh... if you are cool with dismissing potential Majorana masses violating lepton number, then his playful hypothetical does make sense: In a mass term you connect left-chiral fermions with right-chiral ones. Since SU(2) is chiral, it wouldn't break chiral symmetry like QCD, generating masses, and it certainly would not couple the left-chiral fermions to ...


1

According to Georgi's definitions in Section 2.1, a set of generators for a group $G$ is a set of linear operators $\{X_{a}\}$ in a representation $D$ of $G$ on a vector space $V$, such that for any smooth family $g(\alpha_{1}, \dotsc, \alpha_{n}) \in G$ we have $$ D(g(\alpha_{1}, \dotsc, \alpha_{n})) = \exp\left(i\sum_{a}\alpha_{a}X_{a}\right) $$ This means ...


1

Nobody knows. Like photons and the Z boson, neutrinos could be their own anti-particle. It would be the only fermion[*] to be like that and would be called a Majorana fermion. However, neutrons are not their own anti-particles despite having no electric charge. Anti-neutrons are made of anti-quarks and annihilate with normal neutrons. Neutrinos could be ...


1

As an analogy, consider a toss of two coins. The outcome of each coin toss can be heads (H) or tails (T): HH HT TH TT Since we don't care about the order of the coins (just as we don't care which $W$ actually decayed to quarks/leptons), we can write think of this as: HH 2*HT TT


1

You have two $W$. For the final state $qql\nu$, one $W$ decays to $qq$, the other to $l\nu$. But the decay to $qq$ could come either from the first W or the second W, thus you have the following possibilities : First possibility -first $W$ decays to $qq$, thus the second $W$ decays to $l\nu$. -second $W$ decays to $l\nu$, thus the first $W$ decays to $qq$. ...


1

There is no such thing as the lifetime of a quark. We can talk about the lifetime of a neutron, because a neutron can exist as a free particle. Its half-life is about 15 minutes. But it would obviously be wrong to imagine that therefore a 12C nucleus will decay in a matter of minutes because its neutrons are going to decay. 12C is absolutely stable. Other ...


1

Yes, the values of the masses are real positive numbers. Recall how you find them out of the complex matrix Y. Note first that $Y Y^\dagger$ is hermitian, and has positive-eigenvalues, and so can be written as $$ Y Y^\dagger = U D ^2 U^\dagger $$ for some unitary U and diagonal real D with no zero entries, for simplicity. Take the positive square roots. ...


1

I think it is misleading to look at the total width, because the breakdown into partial widths is quite different. One thing to compare is the $3g$ width (basically the total hadronic width). According to PDG $$ \Gamma(\psi(2s),3g)=299 keV\cdot 10\% = 30 keV $$ $$ \Gamma(J/\psi(1s),3g)=93 keV\cdot 66\% = 60 keV $$ The same pattern is seen in Upsilon states ...


1

First let's consider this in the context of a very simple toy model, which however is not the Standard Model. In particular, we will just imagine one fermion and one scalar field with a Yukawa coupling \begin{equation} S = \int {\rm d}^4 x \left( - \frac{1}{2}(\partial \phi)^2 -V(\phi )+ i\bar{\psi} \gamma^\mu \partial_\mu \psi - m \bar\psi \psi - g \bar\psi ...


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What I have so far understood from my limited knowledge of quantum field theory and standard model is that the unification of strong force with electroweak force is still a conjecture that needs to be verified by experiments. So far there has not been conclusive evidence of unification of two domains. The conjecture is that that at high enough energies the ...


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