All Questions
12
questions
1
vote
0
answers
42
views
Cubic coupling beyond Yukawa
Consider a massless Dirac or Majorana fermion $\psi$ and a massless scalar $\phi$. They interact through a Lagrangian $\mathcal{L}_I(\phi,\psi)$. I would like to understand what are the cubic ...
- 165
1
vote
1
answer
82
views
Is the mass term of a neutral fermion zero?
[Note: my question can be a duplicate of this one, but I don't understand the answer given there.]
At various places, e.g., in the first slide of this lecture, it is argued that for a neutral fermion $...
- 353
4
votes
0
answers
116
views
Is it possible to express any quadratic fermionic system in terms of a quadratic majorana system and viceversa?
Can one always write, for some suitable matrix $M$
$$
H= \sum^N_{jk}(A_{jk}c^\dagger_jc_k+B_{jk}c_jc_k+h.c.)=i\sum^{2N}_{jk} M_{jk} \gamma_j\gamma_k,
$$
for any $A,B$? And viceversa, can one always ...
- 1,544
0
votes
0
answers
57
views
Classifying elementary fermions
Familiar elementary (non-composite) relativistic fermions are of the Dirac, Weyl, and Majorana kinds. Are there other kinds allowed in principle by relativistic quantum physics? If not, why not?
Are ...
- 11
0
votes
0
answers
118
views
Majorana Mass term for $SU(2)_L$ doublets
Assume we add a colorless and hyperchargeless $SU(2)_L$ fermion doublet to the Standard Model.
$$L=\left(\begin{matrix}L_u\\L_d\end{matrix}\right)$$
Then, considering gauge invariance, the ...
- 765
5
votes
1
answer
114
views
Internal flavor symmetry of the $N$ left-handed complex Weyl spinors v.s. $N$ real Majorana spinors: ${\rm U}(N)$ vs. ${\rm O}(2N)$ or ${\rm O}(N)$
Consider 4d spacetime, it seems that for massless particles, we can easily change
the left-handed complex Weyl spinor basis (2 component in complex $\mathbb{C}$ for Euclidean spacetime Spin(4))
to
...
- 4,336
20
votes
3
answers
4k
views
Why do people say that neutrinos are either Dirac or Majorana fermions?
The question of whether a given particle "is" a Dirac or Majorana fermion is more subtle than is sometimes presented. For example, if we just consider the "old" Standard Model with massless neutrinos, ...
- 48.4k
0
votes
0
answers
89
views
Spin 1/2 Fermion With Both Majorana and Dirac Masses?
I will use Van der Waerden notation in the following:
It is easy to construct both Majorana and Dirac mass terms in the lagrangian of a Dirac spinor with left-handed component $\phi_{\alpha}$ and ...
- 3,514
3
votes
2
answers
1k
views
Pseudoscalar fermion mass
Is it possible to add to a lagrangian a pseudoscalar mass term for the fermion:
$$i M \bar{\psi} \gamma_5 \psi$$
The $i$ makes it hermitian. Would this cause any inconsistency in the field theory? If ...
- 31
5
votes
1
answer
413
views
Photons are self-conjugate but neutrinos may or may not: why is that?
Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified.
Although the neutrinos are ...
- 26.8k
5
votes
0
answers
209
views
Is $\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}$ true for two different spin 1/2 fermions?
In the context of seesaw mechanism or Dirac and Majorana mass terms, one often see the following identity
$$
\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}.
$$
Here, I am using 4 ...
- 495
32
votes
5
answers
3k
views
Why do or don't neutrinos have antiparticles?
This was inspired by this question. According to Wikipedia, a Majorana neutrino must be its own antiparticle, while a Dirac neutrino cannot be its own antiparticle. Why is this true?
- 11.4k