All Questions
Tagged with standard-model lagrangian-formalism
75
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
1
answer
52
views
Different representations of the Yukawa interaction
during studying Yukawa sector of the SM, I got confused with different reps of the Yukawa interaction.
First, this is what I am familiar with(let me show only electron mass term):
$$y_e \bar{L}_e H ...
- 47
1
vote
1
answer
62
views
Where does the baryon number appear in the Lagrangian of the standard model?
In the standard model Lagrangian, the electric charges of the particles are the coefficients of the interaction terms (e.g. $(-2/3e)u'Au$ for the up quark shows it's charge is $(2/3)e $)
How can we ...
- 25
0
votes
1
answer
217
views
Gauge Boson Self-Interactions with covariant derivative
Self-Interactions of the unphysical gauge bosons $W_1, W_2, W_3$ are written within the gauge term
$L_\mathrm{Gauge}=-\frac{1}{4} W_{\mu \nu} W^{\mu \nu}$
with $W_{\mu \nu}= \partial_\mu W_\nu - \...
- 15
0
votes
1
answer
116
views
Lagrangian for quarks and pions
I need to understand how starting from the free Lagrangian
$$
\mathscr{L} = \bar{q}(i \not\partial - \hat{m})q
$$
and based on the chiral angle associated with the pion field and the quark field ...
- 21
1
vote
1
answer
60
views
Concluding that local $SU(2)$ symmetry implies that we have charged and uncharged fields
In Samoil Bilenky's (2nd. ed) "Introduction to the Physics of Massive and Mixed Neutrinos," he constructs the $SU(2)$ Yang-Mills model.
He starts by introducing the doublet (section 3.2, ...
2
votes
0
answers
38
views
Understanding $\mathscr{L}_Y^{\text{down} }=-\sqrt{2}\sum _{a,q}\overline{\psi }_{iL}Y^{\text{down} }_{iq}q'_RH+\text{h.c.} $
Currently reading Bilenky's "Introduction to the Physics of Massive and Mixed Neutrinos." (2nd ed.)
On page 56 (Section 3.4 on the Standard model) elaborates
"Let us assume that in the ...
1
vote
1
answer
162
views
Is there a phenomenological Lagrangian which can reproduce the long-range potential between quarks?
The long-range potential between quarks in a confining gauge theory increases linearly with the potential:
$$
V(r)=\sigma r \tag{1}
$$
where $\sigma$ is the string tension.
In QFT, one can calculate ...
- 742
0
votes
0
answers
130
views
Effective Field Theory with Higgs integrated out
I have been trying to get the low energy EFT Lagrangian from EW Lagrangian of standard model not with the effective action principle but with Equation of Motion
EW Lagrangian part concerning Higgs
$$\...
- 3,464
1
vote
0
answers
42
views
Detailed calculation to obtain Feynman rules of Standard Model
I am looking for a note deriving all interaction terms in detail of the Standard Model (after spontaneous symmetry breaking)?
In short, I need a note/reference showing in details how all the terms ...
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
0
votes
1
answer
144
views
Why does the Higgs Mechanism give different masses to different particles?
What makes a quark different from an electron in the "eyes" of the Higgs Field? Does it have to do with the specific values of hypercharge and isospin associated with these particles? What ...
- 7,319
1
vote
1
answer
67
views
What are the differences between electroweak interactions before and after unification?
I am very confused by this point, although its mathematical description is not hard. I still cannot see how these two theories are "unified", which term in lagrangian indicates this ...
- 995
3
votes
1
answer
66
views
Could the Higgs field be noted $H^{\mu}$, in the same spirit as $W^{\mu}$ and $Z^{\mu}$?
The $W$ and $Z$ particles are noted in Lagrangian in the form of $W^{\mu}$ and $Z^{\mu}$, in order to construct quantities such as $W_{\mu}W^{\mu}$ and $Z_{\mu}Z^{\mu}$.
Could the Higgs (that appears ...
