All Questions
Tagged with standard-model field-theory
51
questions
2
votes
2
answers
140
views
When is the Lagrangian a Lorentz scalar?
The Lagrangian $\mathcal{L}$ can be defined as the Legendre transform (when it exists) of the Hamiltonian $\mathcal{H}$, a non-Lorentz scalar quantity (as $\mathcal{H} =T^{00}$). My questions are,
...
- 1,611
0
votes
0
answers
47
views
How to add a non-chiral lepton doublet to the Standard Model?
How would the Standard Model Lagrangian (before symmetry breaking) change if we were to add a non-chiral lepton doublet $\ell_{L,R}$ with weak hypercharge $y=-\frac{1}{2}$ to the $SU(2)\times U(1)$ ...
- 21
0
votes
0
answers
62
views
Would it be possible to build the standard model in terms of Joos-Weinberg spinors?
The Joos-Weinberg equation describes spinors of arbitrary spin. Could we replace all of the existing matter fields (scalar, fermionic, gauge, Rarita Schwinger, etc.) with JW spinors and still end up ...
- 19
1
vote
0
answers
66
views
In Peskin & Schroeder's QFT book page 704, the definition of electric charge is opposite?
In Peskin's book Chapter 4, the QED Lagrangian in Eq.(4.3) which contains the interaction term $$\mathcal{L}_{\mathrm{int}}=-q\bar{\psi}\gamma^\mu\psi A_{\mu}\tag{4.3}.$$ From this Lagrangian we can ...
- 19
0
votes
1
answer
217
views
Gauge Boson Self-Interactions with covariant derivative
Self-Interactions of the unphysical gauge bosons $W_1, W_2, W_3$ are written within the gauge term
$L_\mathrm{Gauge}=-\frac{1}{4} W_{\mu \nu} W^{\mu \nu}$
with $W_{\mu \nu}= \partial_\mu W_\nu - \...
- 15
0
votes
1
answer
116
views
Lagrangian for quarks and pions
I need to understand how starting from the free Lagrangian
$$
\mathscr{L} = \bar{q}(i \not\partial - \hat{m})q
$$
and based on the chiral angle associated with the pion field and the quark field ...
- 21
4
votes
1
answer
151
views
How to properly count the SM particles degrees of freedom?
I'm studying the thermal history of the universe, and I found a bit difficult to properly identify the correct number of d.o.f. for each SM particle. I'm referring to the usual factor
$$g_{*}(T)=\sum_{...
- 475
0
votes
1
answer
154
views
Dirac adjoint of $SU(2)$ lepton doublet
The leptonic $SU(2)$ left-handed doublet is
$$L_L = \begin{pmatrix}\nu_L\\ e_L\end{pmatrix}.$$
Both $\nu_L$ and $e_L$ are Dirac spinors so both are 4-spinors. The dirac adjoint on 4-spinors is the ...
1
vote
1
answer
83
views
Charged and neutral currents in electroweak theory
We describe electroweak theory by $SU(2)_L\times U(1)_Y$. This group has four generators which will be the W's, Z and $\gamma$ and we get 4 associated currents. We complexify the first 2 generators of ...
2
votes
2
answers
202
views
Confusion about baryon number violation in the standard model
I'm reading Gauge Theory by David Tong and not understanding the concept of baryon number violation. I understand that the massless Dirac field has two symmetries, an $e^{i\theta}$ $U(1)$ symmetry and ...
- 23
1
vote
1
answer
96
views
Is there any other field with charged sources other than electromagnetic field?
What are all the fields that we know so far that can be associated to charges of the kind "+" and "-" (not necessarily the electric +/- charges). I already know the EM field. Are ...
- 156
3
votes
1
answer
177
views
Custodial transformation in the SM Higgs
I am reading this paper (or this link), and I'm troubled by the custodial transformation. So, I will use the notations and equation labels appearing in this paper.
If we write the Higgs field into the ...
- 1,421
2
votes
0
answers
111
views
How is the $SU(2)_L$ conjugation applied?
I'm reading a paper where they introduce the lepton doublets $L$ and "their $SU(2)_L$ conjugations" $\tilde{L}$, which I'm guessing means
$$
\tilde{L} = i\sigma_2L^*.
$$
After $\textit{vev}$,...
- 525
0
votes
0
answers
130
views
Effective Field Theory with Higgs integrated out
I have been trying to get the low energy EFT Lagrangian from EW Lagrangian of standard model not with the effective action principle but with Equation of Motion
EW Lagrangian part concerning Higgs
$$\...
- 3,464
1
vote
1
answer
48
views
Peskin QFT eq.(20.80) derivation
In the derivation of electroweak current (P&S eq.(20.80)), we start with
$$\begin{equation}
\mathcal{L}=\bar{E}_L(i \not D) E_L+\bar{e}_R(i \not D) e_R+\bar{Q}_L(i \not D) Q_L+\bar{u}_R(i \not D) ...
- 1,421