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Results tagged with chirality
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user 66086
Chirality is defined through the ±1 eigenvalue under action of γ^5 on ψ, a Dirac field thus projected into its left- or right-handed component by the projection operators (1−γ^5)/2 or (1+γ^5)/2 on ψ. For massless particles (only!) chirality coincides with [helicity], a notion which is frame-dependent, and hence ambiguous for massive particles. Avoid using the [helicity] tag instead: the projectors *must* be implied.
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Spinor components in Dirac Equation are 'coupling'?
I'm not sure what physical intuition you are after about the coupled components of Dirac spinors, which describe a particle and an antiparticle of both spin directions each. The Dirac Equation with yo …
- 66.3k
1
vote
Yukawa Interaction with Chiral Fermions
I suspect you are trapped in bad notation, which, sadly, is quite common, even though you appreciate the crucial chirality-flipping $\gamma^0$ involved in the overbar. … My first guess for your two-chirality-flip effective interaction, so, then no chirality-flip interaction, is
$$igm\phi\overline{\psi_L}(/\!\!\partial ~/\Box) ~~\psi_L= igm \phi~~\overline{\psi}(/\!\! …
- 66.3k
0
votes
Shouldn't there be a Particle for Changing Left-handed to Right-handed Particles and Vice Ve...
I gather you appreciate the crucial difference between chirality & helicity for massive particles, and never use L and R for helicity, which is $\pm$. … chiral projectors slip past the $\gamma^0$ implicit in the overbar and flip to the other kind, enforcing the opposite chirality of the particle destroyed by the term. …
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1
vote
Accepted
How is the chirality for the weak interaction conserved for non-relativistic neutrinos?
I am unclear what you are asking, but here is the connection of slow fermions' helicity and chirality. … No, really slow neutrinos produced by weak interactions change chirality, as per above. In their frame, only about half will interact weakly. …
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3
votes
Accepted
Higgs Boson and Chirality
point, in that this Higgs particle, h, therefore couples identically to its v.e.v. to the fermions, also linking their chiralities: so, when those fermions emit higgses, virtual or not, flipping their chirality …
- 66.3k
3
votes
Accepted
The chirality of the standard model fermions
...right-handed neutrinos could be included in the Standard Model by extending the fermion content. But these would be completely neutral under the Group of Standard Model. Why is that a problem? Why …
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1
vote
Accepted
Interactions in nonlinear chiral theories
Yes, it is there to ensure that there is no mixing between the singlet, displayed separately, and the octet, so you do not double count.
The coefficient of $g_8^M$ contains no singlet.
The 3×3 matrix …
- 66.3k
1
vote
Accepted
Chiral Lagrangian Field
Is there a meaning to take this field as an exponential function of the generators?
From your basic Lie group theory you presumably appreciate the logic of the chiral model of the astounding Gürsey: …
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3
votes
Accepted
Does particle parity play any role in matter anti-matter annihilation?
The dominant force in the Standard Model is electromagnetism, by far, a vectorlike interaction which preserves parity, with interaction vertex
$$
eA_\mu (\overline {e_L } ~\gamma^\mu e_L + \overline …
- 66.3k
10
votes
Accepted
How does changing handedness cause mass?
Chirality is a Lorentz-invariant, mathematical, unintuitive notion: a Dirac fermion ψ, has a L- and a R-chiral piece. Chirality is defined through the operator γ5, which has eigenvalues ±1. … Books describe how chirality is connected to helicity and spin, but you might not need to know the details, if the math cloys you. …
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2
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Accepted
How is the property of chirality used?
The mass term transitions a propagating particle into one of the opposite chirality, whereas in the absence of this mass term, chirality is preserved. … But the mass term
connects the two chiralities, L→R, R→L, so chirality may switch as the fermion travels along. …
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1
vote
Accepted
Chirality in muon decay
I would personally use a R subscript for it, to indicate the actual chirality of the particle, and prevent the misreading you evince here, but then I'd confuse others... …
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3
votes
Explaining "Left" and "Right" to an Alien using Chirality and Helicity
Chirality is also odd under parity (L is sent to R). …
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2
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Accepted
Coefficient of effective chiral Lagrangian of $\pi\pi$ scattering
Importantly, observe what you might know, namely the method in the madness of the Lie algebra elements involved,
$$L=\frac{F^{2}}{4} \rm{Tr}(\partial_{\mu}U^{\dagger}\partial^{\mu}U)= \frac{F^{2}}{4} …
- 66.3k
3
votes
How do massless particles have the same chirality and helicity when they are different prope...
.
$$
But this manifestly commutes with chirality, $\gamma^5$, so the two operators share eigenvectors.
Left-chiral ones have negative helicity, and right-chiral ones positive helicity. … Note how a fermion reverses chirality, spin and helicity upon charge conjugation. …
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